Participatory Notes Essay

Participatory Notes commonly know as P-Notes or PNs are instruments issued by registered foreign institutional investors (FII) to overseas investors, who wish to invest in the Indian stock markets without registering themselves with the market regulator, the Securities and Exchange Board of India – SEBI. SEBI permitted foreign institutional investors to register and participate in the Indian stock market in 1992. Investing through P-Notes is very simple and hence very popular amongst foreign institutional investors. Contents 1 Working 2 Need 3 Participatory Notes Crisis of 2007 4 Trends in PN 5 References Working Participatory notes are instruments used for making investments in the stock markets. However, they are not used within the country. They are used outside India for making investments in shares listed in that country. That is why they are also called offshore derivative instruments. In the Indian context, foreign institutional investors (FIIs) and their sub-accounts mostly use these instruments for facilitating the participation of their overseas clients, who are not interested in participating directly in the Indian stock market. For example, Indian-based brokerages buy India-based securities and then issue participatory notes to foreign investors. Any dividends or capital gains collected from the underlying securities go back to the investors. Need Anonymity: Any entity investing in participatory notes is not required to register with SEBI (Securities and Exchange Board of India), whereas all FIIs have to compulsorily get registered. It enables large hedge funds to carry out their operations without disclosing their identity. Ease of Trading: Trading through participatory notes is easy because participatory notes are like contract notes transferable by endorsement and delivery. Tax Saving: Some of the entities route their investment through participatory notes to take advantage of the tax laws of certain preferred countries. Money Laundering: PNs are becoming a favourite with a host of Indian money launderers who use them to first take funds out of country through hawala and then get it back using PNs.

Shouldice Hospital Limited. Case Study Analysis

EXHIBIT 1 Acceltion,s Service Guarantee Quaury oF Srnvlcn GueneNTEE TheAccelIionQualitvofServiceGuaranteedefines,AcceI1ion,sassurance*, Ifj:r:fl†. ‘,f†,iljtm3;:ru:mlFj *-Hiri,†Ã¢â‚¬ Ã¢â‚¬  dil;;affi,. irn † 1. Perfonnance Guarantee a†ri,,iuo. , or'te-. *r,sea ne. â€Å"i,, is the same as Accellion guarantees that the performance of the. Net-work uproading and downloading content, Accellion service' will be no t*t p†. â€Å"*t of that w1n hich';;. hr;†*d by a benchmik origin as a resurt of usine the site being accessejfrom r. ‘ ‘r†Ã¢â‚¬ Ã¢â‚¬Ëœibii , ffi,ltji'fi ::,Ti:T:t ‘u p†Ã¢â‚¬Ëœf†Ã¢â‚¬ËœÃ¢â‚¬ Ã¢â‚¬ ilffi, p†,ro. *u,'†Ã¢â‚¬  *iTly*il? ::T::#? Jr:[:il:,:xHi. il:ilabilitv, 3.Customer Service -â€Å",****,L,;;tr o;;;,%li o, o†. ;r,o. ,. excludingForce Maieureand schedured Maintenance for customers Guarantee should Accellion fail to meet the service levels set out in section s 1 and 2 with one (L) month's service fee ror Accenion will credit ttre monttirir†Ã¢â‚¬ tua-*n†r,,n† r†,i†[Gl3bove account .;;†d;;;;iili,i†t*. mer the customer,s ritten notice to Accellion of such failure gives w withi'ii;;6) aays rrom ttre J* ,†Ã¢â‚¬ r1 rrrr†re occurred. with this requirement,wil r†rr†it. rt†t†;il;;/r The Customer's rrii†* t†. â€Å"*fry right to receive such credit. Accellion will notify the c†ttom†Ã¢â‚¬Ëœ. ,o L:::I†frffixirabre or anv other iI* ir'i1 ;s r,or. , liauyrf;;;y*. J of scheduled Maintenance. I reas†Ã¢â‚¬ ;;;ni†;;ii p;fi;', ffir;tn† c,,i. -,†Ã¢â‚¬ . 1;J;;i;;ii,†Ã¢â‚¬ Ã¢â‚¬ ,saryf the service acrion to *†fffflflffi[rffi;';::lJ;:,Ji;:;†*,†. :il$J;t3i:J:fl*f;::il::#*il::::†* 4. Security and privacy policy ,o any inquiry in re,a,ion,o Accellion has comolete respect for the Customer's privac y and that of any custome,r data stored in Accellion service does not require Acce,ion servers. The Customers i† prtJa† i†y;a:lr'r†i;;te servers' All information provided details for the data being stored on the to a†. â€Å"uio†iy' tLr† c†. r. i',†r';;;r†i'i;, he Customer,, ;il:ilT I†v r,u,,† u†t†,, ,or† b†r,†rit. A,ccerion w,I not hat the Disclosure of Customer's itrtt'†Ã¢â‚¬Ëœti. † 5. iui]'i. A. â€Å"†[ion's ;t;il:;,,, &:i:T†Ã¢â‚¬ ,t:ffi:1nir. ;r',1;li:ffi;d##Hi; ilJ'A'ff1†³Ã¢â‚¬ËœX;1T'. |,H:†fiH^dr:1[:o'aut, to possession shalr i-tu†t *'† . ifntI . ,*p. ffity onlybe made where such disclosure is *a to the terms or use or â€Å",,]o,† Accellion will ensure-that th† ct'stom†Ã¢â‚¬ s informatiorr and data [areJ ke{1cur9 or imProPer use' which includes t'trqg;ii*r;uur† rt†p, io rr. ri,fil,tr1r,. mer,s adenrity d protected from unauthorized access i before granring access. EXHllBlr Dear Team, 2 orAcclrionEmail to All Accellion staff Announcing the Launch of the oos Guarantee [T X':i'ji:#:ffi11:;J:T? ,i? :]†#t'^Y^:l:1*8 vua,ry ot ervlce guarantee read it over very carefully. vo† iulLri†Ji;;;;;1/†;†*u16 Quarirvof service suarantee (Qos). prease Please ancr puts t ‘† ownership o in this company to deliver. C†r,o. â€Å"†. , ompanf c ustomers aon,r wen+ . â€Å"J9,flT? ‘L†l31d irt nuts *he -o*r,†rrnipi†n ever d o,. ,;t;;t-;1q6btcDDrve' ;†;;;;† ,;;h#; theirnetwo'rkrip;*;;irr†rilrhcfi–,*–. –. ,f1. ‘-t-â€Å",LevelAgreement(sLA);ttruy;†rt**i *::::;ilffl:r. H,ffi :Slfl a*Xi A;::#J:ffi â€Å"‘,,*:mf :'†**:*;$ii+,r,fr;y:'^,'†j,:nTffi 18,. #,†l*iF:iqd-. i†Ã¢â‚¬ ;'ffi â€Å"H? ::1H:J:†H:'†;T†;1f 3†³tr:; As a member of the Accellion –Lt, vl\_. 1. team, you are key to our client,s satisfaction. Thanks in advance for your suPport in making our clients and ourselves successful. |.. 4? j:|ir!. -. ‘!. ii. ‘,l:*||-:i;:1:†|:|i||::l.. ;:::1,;:::;:;j::i. ];::|:i:]i::::::jl:]]j:::::]:. :::]] L. what is the marketing impact of a well-designed guarantee? 2. Eaaluate Exhibit the_ seraice design of Acceilion,s guarantee shown in r-. How ffictiae wilr it ui rn communicating seraice exceuence to potentiar and current customers? would you recommend any changes to its design or imple_ mentation? 3†² will he guarantee be successfut in creating a curture for seraice exceilence within Aiceilion? whit erse may be needed for achieoing such a culture? . Do you 4' think customers mEht take adaantage of this guarantee and â€Å"stage† seraice f;ilures to inaokeTlrr'grorantee? If yes, how could Acceuion minimize potentiar iheating on its guarantee? The Accellion Service Guaran tee Sg1r Case 16 Shouldic e Ho spit al Limite d (Abri dge d) JeuEs Hpsrprr AND Rocnn HellowELL A Canadian hospital specializing in hernia operations is considering whether and how to expand the reach of its seraices, including expansion into other specialty areas.Various proposals haae been adaanced to increase the capacity of the hospital without demotiaating the staff or losing control oaer seraice quality, which, in addition to achieoing excellent medical outcomes, has created a aery deaoted base of patient â€Å"alumni. † Options include adding Saturday surgical operations, building an extension, and constructing a neTD hospital in another location, perhaps in the United States. TWo shadowy figures, enrobed and in slippers, walked slowly down the semi-darkened hall of the Shouldice Hospital. They didn't notice Alan O'Dell, the hospital's managing director, and his guest.Once they were out of earshot, O'Dell remarked good nature dLy, â€Å"By the way they act, you'd think our patients own this place. And while they're here, in a way they do. † Following a visit to the five operating rooms, O'Dell and his visitor once again encountered the same pair of patients still engrossed in discussi. g their hernia operations, which had been performed the previous morning. HrsroRY An attractive brochure that was recently printed, although neither dated nor distributed to prospective patients, described Dr. Earle Shouldice, the founder of the hospital: Dr. Shouldice's interest in early ambulation stemmed, ffi:.? :T,]1;5,T? j:T]:J†H-â€Å",H,::,T#|'^# the girl's subsequent refusal to stay quietly in bed. In spite of her activity, no harm was done, and the experience recalled to the doctor the postoperative actions of animals upon which he had performed sur gery. They had all moved about freely with no ill effects. By 1,940, Shouldice had given extensive thought to several factors that contributed to early ambulation following surgery. Among them were the use of a local anesthetic, the nature of the surgical procedure itself, the design of a facility to encourage movement without unnecessarily causing discomfort, and the postoperative egimen. With these things in mind, he began to develop a surgical technique for repairing herniasl that was superior to others; word of his early success generated demand. Dr. Shouldice's medical license permitted him to operate anywhere, even on a kitchen table. However, as more and more patients requested operations, Dr. Shouldice created new facilities by buying a rambling 130acre estate with a 17,}}0-square foot main house in the Toronto suburb of Thornhill. After some years of planning, a large wing was added to provide a total capacity of 89 beds. Dr. Shouldice died in 1965. At that time, ShouldiceHospital Limited was formed to operate both the hospital and clinical facilities under the surgical direction of Dr. Nicholas Obney. In 1999, Dr. Casim Degani, an internationally-rec o g nrzed autho rity, b ecame surge on-inchief. By 2004,7,600 operations were performed per year. THr SHouLDtcE METHoD Only external (vs. internal) abdominal hernias were repaired at Shouldice Hospital. Thus most first-time repairs, â€Å"primaries,† were straightforward operations requiring about 45 minutes. The remaini. g procedures involved patients suffering recurrences of hernias previously repaired elsewhere. Many of the recurrences and very difficult hernia repairs required 90 minutes or more. In the Shouldice method, the muscles of the abdominal wall were affanged in three distinct layers, and the opening was repaired-each layer in turn-by overlapping its margins as the edges of a coat might be overlapped when buttoned. The end result reinforced the muscular wall of the abdomen with six rows of sutures (stitches) under the skin cover, which was then closed with clamps that were later removed. (Other methods might not separate muscle layers, often involved feH,er :ilil';,†#:1â⠂¬ ³3i*:ffi':T,'†:nvorvedtheinsertionotCoPyright O 2004 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call 1-800515-7685, write Harvard Business School Publishing, Boston, MA021,63, or go to http://www. hbsp. harvard. edu. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadshee! or transmitted in any form or by any means–electronic, mechanical, photocopying, recording, or otherwise-without the permission of Harvard Business School. Professor James Heskett prepared the original version of this case, â€Å"Shouldice Hospital Limited,† HBS No. 583-068.This version was prepared jointly by Professor James Heskett and Roger Hallowell (MBA 1989, DBAI997). HBS cases are developed solely as the basis for class discussion. Cases are not intended to serve as endorsements, sources of primary data, or illusfrations of effective or ineffective management. 592 A typical first-tim e repair could be completed with the use of preoperative sedation (sleeping pill) and analgesic (pain killer) plus a local anesthetic, an injection of Novocain in the region of the incision. This allowed immediate post-operative patient ambulation and facilitated rapid recovery. THe PaTIENTS' ExpERIENcEMost potential Shouldice patients learned about the hos- pital from previous shouldice patients. Although thousands of doctors had referred patients, doctors were less likely to recommend shouldice because of the generally regarded simplicity of the surgery, often considered a â€Å"bread and butter† operation. Typically, many patients had their problem diagnosed by upersonal physician and then contacted Shouldice directly. Many *tru made this diagnosis themselves. The process experienced by shouldice patients depended on whether or not they lived close enough to the hospital to visit the facility to obtain a diagnosis.Approximately 10% of shouldice patients came from outside t he province of ontario, most of these from the United States. Anoth er 60†³/o of patients lived beyond the Toronto area. These out-of-own patients often were diagnosed by mail using the Medical Information Questionnaire shown in Exhibit L. Based on information in the questionnaire, a shouldice surgeon would determine the type of hernia the respondent had and whether there were signs that some risk might be associated with surgery (for example, an overweight or heart condition, or a patient who had suffered a heart attack or a stroke n the past six months to a year, or whether a general or local anesthetic was required). At this point, a patient was given a operating date and sent a brochure describing the hospital and the shouldice method. If necess ary, a sheet outlining a weight-loss program prior to surgery was also sent. A small proportion was refused treatment, either because they were overweight, represented an undue medical risk, or because it was determined that they di d not have a hernia. Arriving at the clinic between 1:00 p. M. and 3:00 p. M. the duy before the operation, a patient joined other atients in the waiting room. He or she was soon examined in one of six examination rooms staffed by surgeons who had completed their operating schedules for the day. This examination required no more than 20 minutes, unless the patient needed reassurance. (patients typic ally exhibited a moderate level of anxiety until their operation was completed. ) At this point it occasionally was discovered that a patient had not corrected his or her weight problem; others might be found not to have a hernia at all. In either case, the patient was sent home. After checking administrative details, about an hour fter arrivin 8 at the hospital, a patient was directed to the room number shown on his or her wrist band. Throughout the process, patients were asked to keep their luggage (usually light) with them. All patient rooms at the hospital were semiprivate, containi^ g two beds. patients with similar jobs, backgrounds, or interests were assigned to the same room to the extent possible. upon reaching their rooms, patients busied themselves unpack ing, getting acquainted with roommates, shaving themselves in the area of the opera- tion, and changing into pajamas. At 4:30 P. M. , a nurse's orientation provided the roup of incoming patients with information about what to expect, including the need for exercise after the opera- tion and the daily routine. Accordi. g to Alan OiDell, â€Å"Half are so nervous they don't remember much. ,, Dinner was then served, followed by further recreation, and tea and cookies at 9:00 p. M. Nurses emphasized the importance of attendance at that time because it provided an opportunity for preoperative patients to talk with those whose operations had been completed earlier that same duy. Patients to be operated on early were awakened at 5:30 A. M. tcl be given preop sedation. An attempt was ade to schedule operations for roommates at approximately the same time. patients were taken to the preoperating room where the circulating nurse administered Demerol, an analgesic, 45 minutes before surgery. A few minutes prior to the first operation at 7:20 A. M. , the surgeon assigned to each patient administered Novocain, a local anesthetic, in the operati. g room. This was in contrast to the typical hospital procedure in which patients were sedated in their rooms prior to being taken to the operating rooms. upon the completion of their operation, during which a few patients were â€Å"cha tty', and fuily aware of hat was going on, patients were invited to get off the operating table and walk to the post-operating room with the help of their surgeons. According to the director of nursing: Ninety-nine percent accept the surgeon,s invitation. while we use wheelchairs to return them to their rooms/ the walk from the operating table is for psychological as well as physiologicai [blood pressure, respiratory] reasons. patients prove to themselves that they can do it, and they start their all-important exercise immediately. Throughout the day after their operation, patients were encouraged to exercise by nurses and housekeepers alike. By 9:00 P. M. n the duy of their operations, all patients were ready and able to walk down to the dining room for tea and cookies, even if it meant climbing stairs, to help indoctrinate the new â€Å"crass† admitted that duy. on the fourth morning, patients were ready for dis- charge. During their stay, patients were encouraged to take advantage of the opportunity to explore the premises and make new friends. Some members of the staff felt that the patients and their attitudes were the most important shouldice Hospital Limited (Abridged) 593 (HIBIT ;†EF 1 Medical lnformation O,uestionnai re 5 ‘n,ti,rBER (or Rural Route or P. O. Box) Province/StateTown/City SHOULDICE HOSPITAL 7750 Bayview Avenue Box 379, Thornhill, Ontario L3T 4A3 Canada Ph one (418) 889-1 125 Telephone # (Thornhill – One Mile North Metro Toronto) tq-Frhrr. 1^i il3$-1- rr=CBlv'lATlON: Please give name of lnsurance Company and Numbers. MEDICAL .nS,-IANCE: (Please bring hospital certificates) INFORMATION nLR3r:,r- ‘. a – r. l IJCE: (Please bring insurance certificates) OTHEH SURGICAL INSURANCE Patients who live at a distance often prefer their examination, admission and operation to be arranged all on a single visit – to save making two lengthy journeys. The whole kEl&anr:r Name of Business Are you the owner? f Retired Yes – purpose of this questionnaire is to make such arrangements possible, although, of course, it cannot replace the examination in any way. Its completion and return will not put you Former Occupation No under any obligation. Do you smoke? Please be sure to fill in both sides. tr-! n? -? : asr,ssrcn date? (Please give as much advance notice as possible) ry*esi:,-s =-(–, Sa:-‘:a;' cr Sunday. ffiEr h ,s *crJ FOR OFFICE USE ONLY Type of Hernia This information will be treated as confidential. ;I†EXIEEIEEIRIE: ffi iMEfrgles ory' cqJd n=trr [email  protected] :rE] cr*en rr d yotrr operatirn a tir lrctrr ru=ight EXHIBIT 1 (ConttnueolPLEASEBEACCURATE! :Misleadrngfuures.. *fiâ‚ ¬rl. cFeoxâ‚ ¬Ã¢â€š ¬]r3†² admissionday,couldmeanposFonementolyqJropeGlhontrlll†,yc'-,,[e,Etri Waist (muscles THIS IS YOUR CHART – PLEASE MARK IT! APPROXIMATE SIZE. † Walnut (or less) Hen's Egg or Lemon GraPefruit (or more) INFORMATION ESSENTIAL EXTRA and put that apply to your hernias Use only the sections v. lu H a / in each relaxed)†Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬ Ã¢â‚¬Ëœins' is your health now E treatment: Pressure Excess bodY fluids Chest Pain (â€Å"angina†) lrregular Heartbeat Ulcers Anticoagulants (to delaY blood-clotting or to â€Å"thin the blood†) F t ‘ Name of anY Prescnbe: pills, tab lets or caPsutres 1otake regularlY – A nY condition Please tick regular for which You are having Diabetes Asthma & Bronchitis Y ,JI GOOD ; Blood ,JI Chest (not exPancld' il il t] t] I il I il still be finished in time for a 12:30 P. M. lunch in the staff dining room. Upon finishing lunch, surgeons not scheduled to operate in the afternoon examined incoming patients. A surgeon's day ended by 4:00 P. M. In addition, a surgeon could expect to be on call one weekday night in ten and one weekend in ten. Alan O'Dell commented that the position appealed to doctors who â€Å"want to watch their children grow up. A doctor on call is rarely called to the element of the Shouldice Program.Accordi^g to Dr. Byrnes Shouldice, son of the founder, a surgeon on the staff, and a 50% owner of the hospital: Patients sometimes ask to stay an extr a day. Why? Well, think about it. They are basically well to begin with. But they arrive with a problem and a certain amount of nervousness, tension, an d anxiety about their surgery. Their first morning here they're oPerated on and experience a Sense of relief from Something that's been botheri. g them for a long time. hospital and has regular hours. † Accordi. g to Dr. They are immediately able to get around, and they've got a three -duy holiday ahead of them with a Per- Obney:When I interview ProsPective surgeons, I look for experience and a good education. I try to gain some insight into their domestic situation and personal interests and habits. I also try to find out why a surgeon wants to switch positions. And I try to determine if he's willing to perform the repair exactly as ,::it i ? ffi : †'il† JilI% IL:x *,x'*#: have the run of the 3 patients, make friends easily, and hospital. In summer, the most common after-effect from the surgery is sunburn. he's told. This is no place for prima donnas. Tue NuRsEs' ExPERtENcE Dr. Shouldice added: 34 full-time-equivalent nurses staffed Shouldice each 24 hour period.H owever, during non-oPerating hours, only six full-time-equivalent nurses were on the premises at any given time. While the Canadian acutecare hospital average ratio of nurses to patients was 1,:4, at Shouldice the ratio was 1:15. Shouldice nurses spent an unusually large proPortion of their time in counseli. g activities. As one suPervisor commented, â€Å"We don't use bedpans. † According to a manager, â€Å"shouldice has a waiting list of nurses wanting to be hired, while other hospitals in Toronto are short-staffed and perpetually junior resident in surgery performs. Hernia repair Tiaditionally recruiting. † hernia is often the first operation thatThe hospital employed 10 full-time surgeons and other major operations. This is quite wrong, ES is borne out by the resulting high recurrence rate. It is a tricky anatomical area and occasionally very complicated, especially to the novice or those doing very fer*hernia repairs each year. But at Shouldice Hospital a surgeon learns the Shouldice technique over a periol of several months. He learns when he can go fast anc when he must go slow. He develops a pace and a L?. xli;J!. T,:i'†Ã¢â‚¬ *11:1†²-x1'*:1i#;il'It;. TJ: geons. We teach each other and try to encourage a 8 each duy. a scrubbing scheduled operation at 7:30 A. M. hortly before the first If the first operation was routine, it usually was completed by 8:15 A. M. At its conclusion, the surgical team helped the patient walk from the room and summoned the next patient. After scrubbrng, the surgeon could be ready to operate again at 8:30 A. M. Surgeons were advised to take a coffee break after their second or third operation. Even So, a surgeon could complete three routine operations and a fourth involving a recurrence and Shouldice Hospital Limited (Abridged) tr– achieve absolute perfection. Excellence is the eneml' of good. part-time assistant surgeons. TWo anesthetists were also on site.The anesthetists floated among cases e xcept when general anesthesia was in use. Each operating team required a surgeon, an assistant Surgeofl, d scrub nurse, and a circulating nurse. The operatirg load varied from 30 to 36 operations per duy. As a result, each surgeon typically performed three or four oPerations A typical surgeon's duy started with a L' regarded as a relatively simple operation compared to group effort. And he learns not to take risks Tne DocroRs' ExPERIENcE 595 ‘ a Chief Surgeon Degani assigned surgeons to an oPerating room on a daily basis by noon of the preceding da1†² This allowed surgeons to examine the specific patienE hat they were to operate on. Surgeons and assistants H-ere rotated every few days. Cases were assigned to give do. tors a non-routine operation (often involving a recurrencâ‚ ¬ several times a week. More complex Procedures ^'erâ‚ ¬ assigned to more senior and experienced members of th† staff. Dr. Obney commented: If something goes wrong, we want to make sure t ha: we have an experienced surgeon in charge. Experience is most important. The typical general surgeon mai perform 25 to 50 hernia operations per yeaL Ours Perform 750 or more. The L0 full-time surgeons were paid a straight salan' typically fi,aa,000. In addition, bonuses to doctors 'ere distributed monthly. These depended on Profit, indir-icual productivity, and performance. The total bonus Pc-‘i paid to the surgeons in a recent year was aPProximate-‘r $400,000. Total surgeon compensation (including benefir was approximately 15% more than the average income for kitchen staff several times a d,ay, and the hospitar staff to o'D efi, â€Å"weuse arl fresh ingredients and prepare the food from scratch in the kitchen. ,, The director of housekeeping pointed out: a surgeon in Ontario. Training in the shouldice technique was important eat together. Accordi^g to ecause the procedure could not be varied. It was accomplished through direct supervision by one or more of the seni or surgeons. The rotation of teams and frequent consultations allowed for an ongoing opportunity to appraise performance and take corrective action. where possibre, I former shouldice patients suffering recurrences were assigned to the doctor who performed the first operation â€Å"to allow the doctor to rearn from his mistake. ,, Dr. obney commented on being a shouldice surgeon: ilH:*XX##'#Hlti:iJf mx;^:†x$::: ing notes [for confidence], e.. oriaging eachither, and walking around, getting exercis.. briourse, e,re in the rooms straightenirg ,p throughout the day. This gives the housekeepers ; chancl to josh with the patients and to encourage them to exercise. A doctor must decide after several years whether he to do this for the rest of his liie because, just a Iultt in other speciarties-for exampre, radiology_h. s loses touch with other medical disciplines. If h; stays for five years, he doesn't leave. Even among younger doctors , few elect to leave. ?,. i. |. 1.. lrt|ii;. ; |ii|:. :. ||::)|:|ii||. |i::|||||:. :|::||:::|:::|:::::::::::::::::::::::::::::::::: The shouldice Hospital contained two facilities in one uilding-the hospital and the clinic. On its first-level, the hospital contained the kitchen and dining rooms. The sec_ ond level contained a large, open tounge area,the admis_ sions offices, patient rooms, and a spacious grass-covered Florida room. The third revel had aaaitiond fatient rooms and recreational areas. patients could be seln visiting in each others'rooms, walking up and down hallways, loung_ irg in the sunroom, and making use of light recreational facilities ranging from a pool table to an exercycle. Alan o'Dell pointed out some of the features of the hospital: The rooms contain no telephone or television ets. If a patient needs to make a call or wants to watch terevi_ sion, he or she has to take a walk. The steps are designed specialry with a smalr rise to alow patients recently operated on to negotiate the stairs without undue dis comfort. E-â€Å"†Iy rqluru foot of the hospital is carpeted to reduce the hospital feeling and the possi_ bility of a fall. Carpetir,g urro gives tf,e phce a smell other than that of disinfJctant. ‘ This- facility was designed by an architect with input from Dr. Byrnes shouldice and Mrs. w. H. uiquhart (the daughter of the founder). The facility was discussed for years and many changes in the lans were made before the first concrete was poured. A number of unique policies were also instituted. For example, parents accompanying children here for an operation stay free.. you may wonder why we can do it, but we learned that *. rrre more in nursing costs than we spend for the parent's room and board. have- only three on my housekeeping staff for the entire facility. one of the reasons for ; f†* housekeep_ that we don't need to change rinens during a ::? ,tr patient's four- duy stay. Arso, the medical staff doesln,t The clinic housed five operating rooms, a labor ator y, and the patient-recovery room. In totar, the stimated cost to furnish an operating room was $30,000. This was con_ siderably less than for other hospitals requiring a bank of equipment with which to administer anesthetics for each room. At shourdice, two mobile units were used by the anesthetists when needed. In addition, the complex had one â€Å"crash cart† per floor for use rf a patient should suffer a heart attack or stroke. ilin|,4|'i|4? l|:j:i|'i|:|j|!. :||i:|. |::::::|||:::;:i. :|:::):':|::::::|::::|::::):::::::::':1: Alan O'Dell described his job: we try to meet people's needs and make this as good a place to work as possible. There is a strong concern or employees here. Nobody is fired. [This was later reinfor. â€Å"-d by Dr. shouldice, who described a situa_ tion involvirg two employees who confessed to theft in the hospital. They agreed to seek psychiatric help and were allowed to remain on the itu. l As a resurt, turnover is low. our administrative and suppor t staff are non_ union,. b†, we try to maintain a pay scale higher than the union scale for comparabl. Jou, in the area. we have a profit-sharing prin that i, ,. prrate from the docto*: year the administrative and support -LTt staff divided up $60,000. If work needs to be done, peopre pitch in to herp each other.A unique aspect oi o,,r, administration is that I insist that each secretary is trained to do another's work and in an emergency is able to switch to another function immediatlly. we don,t have an organization chart. A chart tends io make people think they're boxed in jobs . a r try to stay one night a week, having dinner and ristening to the patientJto find out how things are really goinf uro. rnd here. Patients and staff were served food prepared in the same kitchen, and staff members picked up iood from a cafeteria line placed in the very .. r,t. , of the kitchen. This pro'ided an opportunity for everyone to chat with he Operating Costs The 2004 budgets for the hosp ital and clinic were close to $8. 5 millions and $3. 5 million, respectively. 6 Shouldice Hospital Limited (Abridged) Sgz EXH lB lT FIoor Supenisor 2 Organization Chart Lab (4) Operating Laundry Room Housekeeping Office Accounting Medical Grounds (3) (2) Supervisor I Head Head Nurse urse (2) Record (2) Dietary (r7) I5 (2) (3) i al[eets three limes a year or as needed. bUeets as needed (usually twice a month). lnformallv reports to Executive Committee. Physical Surgeons Assistant Plant (12) Surgeons (7) Anesthetist (t) pared to an average charge of $5,240 for operations per_ ormed elsewhere. if. l. rlii. ,i. l. ,,:::. ::i:ll|::::l. ::. :::l:.. ::::|:. :|:::|::. :::::|:'. ::|::):|::::::::::: Hernia operations were among the most common per_ formed on mares. In 2000 an estimated r. ,000,000 such operations were performed in the united states alone. Round-trip fares for traver to Toronto from various major cities on the North American continent ranged from roughly $20A to $600. when our backlog of scheduled operations gets too large, we The hospitar arso provided annual checkups to alumni, free of charg.. Muny occurred at the time of the According to Dr. Shouldice: wonder patient reunion. The most recent eunion, featuring dinner and a floor show, was held at afirst-class hotel in down_ town Toronto and was attende d by 1,000 former patients, many from outside Canada. ho* many peopre decide instead to p†rfor* the operation. Every have their rocal doctor time we've expandea o11 capacity, th† backrog has declined briefly, onry to climb or,. u again. Right now at 2,400,]1 ir rarger than it has ever been and is grow_ irg by 100 every six months. The hospitar relied entirely on word-of-mouth adver_ tising, the importance of which was suggested by the results of a poil carried out by i. :i|,i. ]||,)|:i. ||. ;|,. ii:. ||:||:. |,. )||:|:||. :||,.. |:|||::::||:::'. ::::::::::::: when asked about major questions confronting the man_ agement of the hospital, Dr. s hourdice cited I aesire to seek ways of increasing the hospitals capacity while at the same time maintaining . oriror over the quatity of service delivered, the future role of government in the operations of the hospital, and the use of the shouldice name by potential competitors. As Dr. shouldice put it: Im a doctor first and an entrepreneur second. For students of Depaul lrxiriuit 3 shows a portion results). Although little systematic data about university as part of a project of these atients had been collected, Alan o'Dell remarked that ,,if we had to rery on wearthy patients onry, our practice would be much smaller. ,, Patients were attracted to the hos pitar, in part,by its reasonable rates. Charges for a typical operation were four days of hospital sta y at $? 20 p. iau anda $650 surgical fee for a prim ary inguinar (the most common example, we courd refuse permission to other doctors ah. – hospitar. The y may copy our technique and Tisappry it or misinform *,. i. pati ents about the use of it. rni, resurts in failure, and we are f, who want to visit hernia). An additional fee of $300 was assessed f generar anesthesia was required (in about 20% of cases). These charges com_ ExHlBlr Direction: you. 5. B concerned that the technique will be blamed. But Shourdice Hospitar Annuar Patient Reunion Data For each question, please place a check mark as it applies to 4 /7 22 Nationalitv Directions: please place a check mark in nation you represent and please write in your province, state or country where it applies. Canada America Europe J6 -]] province sate a†*r, ee 2 /o ua'rl ,o/ // 63% 5 /6 /960 7 5†² %dt 39. 54% 5/. /6% fl. 63% 4/. 56% 30. 23% /6. 26% occupation Ilave you been overnight in a hospital other than u*@' houldice befone your operation? !* j! _ No lZ What brought Shouidice Hospital to your attention? Friend 8†² ,1 Doctor Rerative . . , 6r. 1//o _0. %% EzW,/. rticre ,9 , Did you have a si',gle 26; or double /6 other 4 ,iiJ†#Zw hernia operation? 56,/4% fi. s6% 9. Is this your first Annual Reunion? yes No fi .10 . , If no, how many reunions have you iiM ,,a†fz',fl ^tt 10. Do you feel that Shouldice Hospital to, ,* * – per,son? â€Å"r†Ã¢â‚¬ 0 Most definitely Definitety 6 JZ Very iittle Not 66,05% /a%% 7 Z_. reaubrc _fl 42. 6J% 6-/0 ruo,rn,re – 5 z17J% !:;::::; :'r'; #, at all Shouldice Hospital Limited (Abridged) 599 EXHIBIT 3 (Continued) fhat impressed you the most about your stay at Shouldice? check one answer for each of the following. for operation and hospital P1ease s Not Somewhat 27. 9d1 Imporiant /4 Somewhat Imporbant 32. 56% // Somewhat Important 25. 5/l /5 Somewhat Important 34. 5E% Not 7 /6. 26% Important 32. 56% Not ImPortant 6 /S,6dl 3 6,96% Not 27,9/k Somewhat 5 /0 Important 25 Important n. fi% 23,2fl1 56. /5% † sbouldice Hospital hardly seemed like a hospital at all. † Somewhat Very 5 /3 Importani 25 Importani Important //. 63% 30. 23% 55. /4% gi ve the MAIN REASON why you reiurned for this annual In a few words, reunion. Very Important 2 4. 65% SomewhaiVery 39. 53% Friendships witb Patients Not Important / 2. 3? l Not Important 3 6'96% Not ImporLant we're doctors, and it is our obligation to help other Alan O'Dell added his own concerns: surgeons learn. On the other hand , it's quite clear that others arc tfying to emulate us. Look at this ad. [The advertisement is shown in Exhibit 4. ) This makes me believe that we should add to our capacity, either here or elsewhere. Here, we could go to Saturday operations and increase our caPacity by 2O%. Throughout the year, no oPerations are sched- How should we be marketing our services? Right now we don't advertise directly to patients.We're uled for Saturdays or Sundays, although patients whose operations are scheduled late in the week remain in the hospital over the weekend. Or, with an investment of perhaps $4 million in new sPace/ we even afraid to send out this new brochure we' ve pu: together, unless a potential patient specificallrrequests it, for fear it will generate too much demand. Our records show that just under 1% of our EXHIBIT 4 Advertisement by a Shouldice Competitor could expand our number of beds by 50%, and schedule the operating rooms more heavily. On the other hand, given Sovernment regulation, do we want to invest more in Toronto?Or should we establish another hospital with similar design, perhaps in the United States? There is also the possibility that we could diversify into other specialties offering similar opportunities such as eye surgerf, yancose veins, or diagnostic services (e. 9. , colonoscopies). For now we're also beginnirg the process of groomirg someone to succeed Dr. Degani when he retires. He's in his early 60s, but at some point we'll have to address this issue. And for good reason, he's resisted changing certain successful procedures that I think we could improve on. We had quite a time changing the schedule for the admi nistration ofDemerol to patients to increase their comfort level during the operation. Dr. Degani has oPPosed a Satutday operating program on the premise that he won'tbe here and won't be able to maintain proper control. 500 Shouldice Hospital Limited (Abridged) Canadian Hernra Ctinic Hernias (Ruptures) Required Under local anesthesia as by Canadian method. No Overnight Hospital Stay, Co nsult atio n s Witho ut Char ge 23061St. Rd. 7 BOCA R{ION, FLA. 33433 482-7755 patients are medical doctors, a significantly high percentage. How should we capttahze on that? I'm also concerned about this talk of Saturday operations.We are already getting good utrltzation of this facility. And if we expand further, it will be very difficult to maintain the same kind of working relationships and attitudes. Already there are rumors floatirg around among the staff about it. And the staff is not pleased. The matter of Saturday operations had been a topic of conversation among the doctors as well. Four o f the older doctors were opposed to it. While most of the younger doctors were indifferent or supportive , at least two who had been at the hospital for some time were particularly concerned about the possibility that the issue would drive wedge between the two groups. As one put it, â€Å"I'd hate to see the practice split over the issue. † EruDNOTES Most hernias, knows as external abdominal hernias, are protrusions of some part of the abdominal contents through a hole or slit in the muscular layers of the abdominal wall which is supposed to contain them. Well over 90% of these hernias occur in the groin area. Of thes e,by far the most common are inguinal hernias, many of which are caused by u slight weakness in the muscle layers brought about by the passage of the testicles in male babies through the groin area shortly before birth.Aging also contributes to the development of inguinal hernias. Because of the cause of the affliction, 85oh of all hernias occur in males. 2. Ba sed on tracking of patients over more than 30 years, the gross recurrence rate for all operations performed at Shouldice was 0. 8%. Recurrence rates reported in 1†³. the literature f or these types of hernia varied greatly. However, one text stated, â€Å"In the United States the gross rate of recurrence for groin hernias approaches 70†³/†. † monet ary references in the case are to Canadian dollars. $1 US equaled $1. 33 Canadian on February 23, 3. A11 2004. n Exhibit 2 was prepared by the casewriter, based on conversations with hospital personnel. 4. The chart 5. This figure included a provincially mandated return 6. on investment. The latter figure included the bonus pool for doctors. SIUDY OuEsrtoNs L. What is the market for this seraice? Hout successful is 2. Shouldice Hospital? Define the seraice model for Shouldice. How does each of its elements contribute to the hospital's success? 3. As Dr. Shouldice, what actions, if any, would you take to expand the h ospital's capacity and how utould you implement such changes? Shouldice Hospital Limited (Abridged) 601

Military Support Eases the Reality of War for Military Families

The military offers a lifetime of opportunities to young Americans and there families.  Ã‚   Many young people see joining the military as a great escape to a better life, an education that is vital yet paid for, and security for their families.   The military offer great incentives and benefits, but there is also the risk of being sent to war.The immediate effects of war on family members of military personal are psychological including separation anxiety and the fear of losing a loved one.   Many people see the military as a tough system which sends people to work or war and does not offer any repercussions.   This is not the case.   Reviewing the effects of separation anxiety and the fear of losing a loved along with the programs the military has set up to help families through this transition will enable others to see this is not a one sided phenomenon.Separation anxiety occurs when families are separated effecting the spouse and children as well as the military persona l, causing heartache for all parties involved.   Spouses and children are often at the butt of separation anxiety especially during times of war.   Children often have many questions regarding war and the concept of terrorism. The military has great services available to help families cope during this difficult time including local support groups and psychological support.The military has also incorporated virtual help for deployed military personal.   The thinking behinds this being that a soldier knows â€Å"that if his comrades see him talking with one of the shrinks on base, they would lose trust in him, label him a head case. A medical file soon would contain records of the visit. If he ever wanted a promotion, he'd have to explain the weakness of his mind†(Berton, 2004).   So with virtual therapy nothing is displayed on the soldier’s record and the soldier receives the emotional support and help he needs to cope with this difficult time.Fear of losing a l oved one can lead to many types of psychological distress.   This fear may cause anxiety or depression in family members. Beth Sneller gave some insight about military families â€Å"In some ways, they almost feel guilty. When many military parents hear about the death of a local soldier they think at first how glad they are it isn't their child. But then, they say, that relief gives way to a deep feeling of sadness. ‘Every time you hear of a death, you can't help but feel emotional for those poor parents’ said Rod (A father whose son is an army captain)† (Sneller, 2004, p. 13).There fear of losing a loved one has many military families seeking support from local facilities or internet groups.   The internet groups support those who have lost a loved one â€Å"so almost weekly, they say, they're sending condolences to friends across the nation who have lost loved ones overseas. ‘Every single time a picture gets flashed across in the evening news, it's deeply personal,’ said Nancy Manzie of Naperville, whose son, Brent Lewis, is in the inactive Marine reserves. Even if they don't know the soldier (personally), they still feel a connection to his or her family† (Sneller, 2004, p. 13).When considering the military’s effect on society during our current war and wars of the past there has been a negative outlook among the public.   There are rumors of injured soldiers not receiving proper medical care when they return home to the states.   The tough and rigorous lifestyle causes people to shy away from seeking psychological help because of the way the will be viewed by their friends and peers. â€Å"Army Reserve Sgt. Mike Durant, 33, who fought in Al Doha, Iraq, about 20 miles south of Baghdad fromFebruary 2005 to January 2006, said the view toward therapy among the ranks was â€Å"comparable to what it was in the 1940s.† During his tour, Durant, who now lives in Sacramento, saw a friend blown up by an improvised explosive device. At the time, his wife at home was in the process of divorcing him. Durant admitted he had thought of killing himself. â€Å"I wanted the waiting to be over,† he said. â€Å"We'd do IED sweeps along the same roads, some days all day. You were just waiting for it to happen to you.You were waiting to get blown up.† His officers ordered him to visit a field Combat Stress Center for a mandatory 72-hour evaluation. Even before he returned to his battalion, he knew his commanders had lost faith in him. Anyone who was shipped to the shrinks, or sought treatment, was a liability. â€Å"In their eyes, I was no longer reliable,† Durant said. â€Å"I couldn't be trusted. I was unstable to them.† Even though he had been a member of the unit for 10 years and had served as an infantry team leader who was responsible for three men, Durant said that, while he was not officially demoted on paper, his duties dropped from one of leadership to tha t of a rifleman. â€Å"Before I was sent there, I was fairly respected and highly regarded,† he said. After his time at the Combat Stress Center, Durant said, â€Å"Peers and friends didn't want anything to do with me; it was like I had some sort of disease†(Burton, 2004).The military still has strict over the top views about many things.   It is important to keep in mind that the United States Military has been one of the strongest military forces in the world for hundreds of years.   We as a nation are kept safe, happy, and considerably wealthy, compared to other countries, because of the strength of our military.   The military is aware of the damage that can be done by separating a couple or a family and they take every step possible to ease the pain. There is compassion within the military, just not when it comes to warfare.Sneller, B. (2004, October 13). For Military Families, Every Death Hits Close to Home. Daily Herald (Arlington Heights, IL), p. 13. Retr ieved March 19, 2007, from Questia database: https://www.questia.com/read/1G1-123950032/for-military-families-every-death-hits-close-to-home

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Law - Essay Example Bright when he moved in to the house. Mr. Bright brought the property through Devon Aspects, an estate agent, upon the advice of his solicitors KPG Solicitors who in turn hired Reliable Surveys to do the structural survey of the property. Reliable Surveys assigned the actual task of surveying to Miss Norris, a newly-licensed surveyor. The issue in this case is whether or not Mr. Bright is compensable for his loss in the event he sells his Devon property at its present market value. If he is, the subsequent underlying issue is from whom he shall recover and what kind of action shall he bring before the court. At this stage however, recovery is a purely hypothetical matter since Mr. Bright has not yet sold his property and hence, has not yet actually incurred a loss. After a careful perusal and analysis of the problem, taking into account the participation of each and every person and entity involved, the Reliable Surveys stands as the most viable party from whom a civil action for recovery of compensation under the case Hedley Byrne v. Heller will be most successful in the event of the actuality of such loss. In the case at bar, Miss Norris, the neophyte surveyor of Reliable Surveys is the raison d’etre of Mr. Bright’s present predicament. Her haphazard and lackadaisical examination of the Devon property caused her to miss the crack on the back wall of the aforesaid house and the evident defect in the elevation from the back angle as well as the dilapidating gutter. Neither did the management of Reliable Surveys subject Miss Norris’ findings to a review and the basis of her findings which described the property as â€Å"good and sound† in her report signed on behalf of the former. There is a characteristic negligence on the part of both Miss Norris and her employer in the performance of their obligation. It is only reasonable to consider filing

School Bus and Dumb Pigs Essay Example for Free

School Bus and Dumb Pigs Essay Narrator: Megan’s father asked her to feed the pigs on her way to school. He said†¦Ã¢â‚¬ ¦. Father: Megan please feed the pigs but don’t open the gate. Pigs are smarter than you think. Don’t open the gate. Megan: right I will not open the gate. Not me no sir no no no no. Narrator: so Megan went to the pig pen. She looked the pigs. The pigs looked at Megan. Megan: these are the dumbest looking pigs I have ever seen. They stand here like lumps on a bump. They wouldn’t do anything if I did open the gate. Narrator: so Megan opened the gate just a little bit. The pigs stood there and looked at Megan. They didn’t do anything. Megan said Megan: these are the dumbest looking pigs I have ever seen. They stand here like lumps on a bump. They wouldn’t do anything even go out the door if the house was on fire. Narrator: so Megan opened the gate a little bit more. The pigs stood there and looked at Megan. They didn’t do anything. Then Megan yelled†¦ Megan: HEY YOU DUMB PIGS! Narrator: the pigs jumped up and ran over Megan, WAP- WAP- WAP-WAP-WAP and out the gate. When Megan got up she couldn’t see the pigs anywhere. She said Megan: UH OH, I am in bad trouble. Maybe pigs are not so dumb after all. Narrator: then she went to tell her father the bad news. When she got to the house Megan heard a noise coming from the kitchen. Then it went, Pig: OINK OINK OINK Megan: that doesn’t sound like my mother. That doesn’t sound like my father. that sounds like pigs. Narrator: she looked in the window. There was her father sitting at the breakfast table. A pig was drinking his coffee. A pig was eating his news paper and a pig peeing on his shoe. Father: Megan you opened the gate. Get these pigs out of here. Narrator: Megan opened the front door a little bit. The pigs stood and looked at Megan. Finally Megan opened the front door all the way and yelled†¦Ã¢â‚¬ ¦. Megan: HEY YOU DUMB PIGS. Narrator: the pigs jumped up and ran right over Megan, WAP- WAP-WAP-WAP And out the door. Megan ran outside chassed all the pigs into the pig pen and shut the gate. Then she looked at the pigs a said†¦Ã¢â‚¬ ¦ Megan: your are still dumb, like lumps on a bump. Narrator: then she ran off to school. Just as she was about to open the front door of the school she heard a sound. Pigs: OINK OINK OINK. Narrator: she said †¦Ã¢â‚¬ ¦. Megan: that doesn’t sound like my teacher. That doesn’t sound like the principal. That sounds like pigs Narrator: Megan looked in the principle’s window. There was a pig drinking principal’s coffee. A pig was eating the principal’s newspaper. And a pig was peeing on the principal’s shoe. The principal yelled†¦. Principal: Megan, get these pigs out of here! Narrator: Megan opened the front door of the school a little bit. The pigs didn’t do anything. She opened the door all the way and yelled†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Megan: HEY YOU DUMB PIGS. Narrator: the pigs jumped up and ran right over Megan, WAP-WAP-WAP-WAP and out the door. Megan went into the school she sat down at the desk and said†¦Ã¢â‚¬ ¦.. Megan: that’s that I finally got rid of all the pigs. Narrator: then she heard a noise. Pig: OINK OINK OINK Narrator: Megan opened her desk and there a new baby pig. The teacher said†¦ Teacher: Megan get that dumb pig out of here. Megan: Dumb? Who ever said pigs were dumb? Pigs are smart. I am going to keep it for a pet. Narrator: at the end of the day the school bus finally came Megan walked up to the door then heard something say, Pig: OINK OINK OINK Narrator: Megan said Megan: that doesn’t sound like the bus driver that sounds like the pigs. Narrator: she climbed up the stairs and looked in the bus. There was a pig driving the bus, pigs eating the seats and pigs lying in the aisle. A pig shut the door and drove the bus down the road. It drove the bus all the way to Megan’s farm, through the barnyard and right into the pig pen. Megan got out of the bus walked across the barnyard and marched into the kitchen. She said†¦. Megan: the pigs are all back in the pig pen. They came back by themselves. Pigs are smarter than you think. Narrator: and Megan never let out any more animals out again. At least not any more pigs

Types of Colonies Essay Example for Free

Types of Colonies Essay English colonies were one of three types of colonies. The first being a joint-stock colony. In this type of colony the king of England would grant a charter to a joint-stock company that would ensure settlers the same rights as Englishmen. Joint-stock colonies were only meant to last a few years. After which, stockholders hoped to earn a profit. Many people were attracted with the promise of gold. The second type was a royal colony. This type of colony was directly controlled by the king. The king appointed a governor and a council which served as an advisory body to the governor. The council had an the upper house of the colonial legislature and the highest court in the colony. The lower house was a bicameral legislature and was elected by property holders who met voting qualifications. Laws passed by the legislature had to be approved by the king. Finally, was the proprietary colony. A Proprietary Colony is a colony in which the king gave land to people called proprietors. Most of these colonies are run under a charter agreement. Private land owners picked governors to rule the colonies. Governors then chose a council and colonist elected representatives to an assembly. This type of colony resembled feudalism. The plantation colonies included Maryland, South Carolina, North Carolina, Virginia and Georgia. They were financed by the English crown and made proprietary colonies except for Virginia which was financed through the Virginia Company and was a joint-stock colony. The colonies were founded for different reasons. Virginia was founded in search of gold. North and South Carolina was founded to grow foodstuffs and to export non-English products. Maryland was founded for religious freedom. Georgia was founded to be a buffer against Spanish expansion from Florida and to be a haven for people in debt and prisoners of England. The plantation colonies exported agricultural products such as the cash crops indigo, tobacco, and rice. These colonies were dependent on the labor of indentured servants at first but by the seventeenth century black slaves became the source of labor. The enormous plantations were owned by few and they had an aristocratic attitude. They did have a form of democratic self-government however the rich plantation owners controlled the government because they were the only people who could afford to pay for all their own expenses. The plantation colonies did allow for some religious toleration. There wasnt much opportunity for social and political mobility. Education was much sparser in the plantation colonies than the others colonies. New England colonies included New Hampshire, Massachusetts, Connecticut, and Rhode Island. These colonies were financed by joint-stock companies although Rhode Island had started out as a squatter colony. All of the New England colonies were founded mainly for religious freedom. Because of limited farm land, new englanders had to find a different source of income. New Englands colonies offered fish, furs, and ships to England. A mercantile network made them a part of the triangle trade. Trade became the cornerstone of colony’s economy. New England had a provincial government. In this government freeman (adult males who belonged to the puritan congregations) were the only people allowed to vote in provincial elections. This was about two-fifths of the adult male population. However all male property holders were allowed to discuss and vote on town government issues. New England was the less ethnically mixed than the southern colonies because of its stony soil. However, the clean water and cool temperatures lessened the spread of germs and added ten years to the life span of settlers migrating from the old world. This contributed to family stability and in turn gave new englanders a strong, tranquil social structure. Opportunity for social and political mobility was available to most men willing to work for it. Education was extremely important in New England, towns with more than fifty families were required to provide elementary education. A majority of adults knew how to read and write and only eight years after founding Massachusetts, Puritans established Harvard College. The middle colonies included New York, Pennsylvania , New Jersey, and Delaware . New York, New Jersey, and Delaware were all originally founded by the Dutch to make a quick profit in the fur trade and were financed by the Dutch West India Company until 1644 when England took over. Pennsylvania however, was founded by William Penn, a Quaker. His reason for founding Pennsylvania was to be a haven for religious liberties and other Quakers . He secured a charter from the king in lieu of the debt still owed to his father. The middle colonies werent as aristocratic as New England nd the plantation colonies because land holdings were intermediate in size, with the exception of New York. The middle colonies were more ethnically diverse than the other colonies and the most religiously tolerant. Very few class distinctions existed because of the large middle class. The middle colonies government was a combination of the New England and south government. They had modified both the county govern ment and the town-meeting government into one. People had much democratic control and men could vote if they owned property. Social and political mobility was greater in the middle colonies because desirable land was more easily acquired. Their soil was very fertile and they became known as the bread colonies for exports of grain. However, the middle colonies did not limit themselves to just farming as an income and also traded. Their three main rivers ,the Susquehanna , the Delaware , and the Hudson, all allowed them access to the fur trade. They also had some industry , such as ship building thanks to their excellent harbors and rivers. Colonial leaders agreed that education was important but did not provide it like New England. The decision to educate children was left to the families until 1683, when a Pennsylvania law was passed, requiring that all children be taught to read and write and be trained in a useful trade. In conclusion, all three colonies had many similarities and differences. All of the colonies were almost entirely English and had British freedoms. All were under a mercantile economy until the revolution. To some degree all had religious toleration and a self-government. All of them also gave new settlers the opportunity to make money and climb the social ladder, although it was harder in some colonies than others. All of the colonies eventually were made into royal colonies with the exception of Pennsylvania, Connecticut, and Rhode Island. Almost every colony utilized a two-house legislative body. Although very alike the colonies also had many differences. Plantation colonies were very spread out and depended on slavery for income. They were the most aristocratic, had a scattered population and only some religious toleration. Social and political mobility was much harder in the plantation colonies and government was controlled by wealthy land owners. The New England colonist were mostly puritan and werent as religiously tolerant as the other colonies. They also had more industry instead of farming because of less available farm land. They were mainly known for their ship building and fishing. New England stressed education and held town meetings often to vote on local issues. The middle colonies were the most ethnically diverse, religiously tolerant, and democratic of the colonies except for aristocratic New York. They were a mix of the plantation colonies and New England in almost everything. There was little class distinctions and a large middle class. Money could be made not only in farming but in industry too.

Identification of Unknown Carbohydrates | Lab Report

Identification of Unknown Carbohydrates | Lab Report INTRODUCTION One of the main types of nutrients is the carbohydrates. Carbohydrates are the most vital foundation of energy for your body. Our digestive system has a capacity to change carbohydrates into glucose or most commonly known as blood sugar. Our body gets energy used by our cells, tissues and organs from this sugar. Carbohydrates also stores additional sugar in our liver and muscles. Carbohydrates may be simple or complex depending on its chemical structure. Simple carbohydrates are also known as simple sugars. They are commonly established in refined sugar such as white sugar. Complex carbohydrates of starches includes grain products like bread, crackers, pasta and rice. MATERIALS AND METHODS A. Identification of Unknown Carbohydrate Samples Approximately 1.00 ml of the known carbohydrate samples and the two unknown samples were transferred on separate labelled test tubes. About 1.00 ml of Molisch reagent then 1.00 ml of concentrated H2SO4 was added to each sample. The test was observed for any change and was recorded. With the use of new batch of samples each time, the remaining tests were conducted: (a) Iodine test 1.00 ml of iodine reagent was added to each sample. (b) Benedicts test 1.00 ml of Benedict reagent was added to each sample then heated using water bath. (c) Barfoeds test 1.00 ml of Barfoeds reagent was added to each sample then heated using water bath. (d) Seliwanoffs test 1.00 ml of Seliwanoff reagent was added to each sample then heated using water bath. (e) 2,4-DNP test 1.00 ml of 2,4-DNP was added to each sample then heated using water bath. The identity of the unknown samples was determined by comparing it to the known carbohydrate samples. B. Hydrolysis of Starch Exactly 50.0 ml of 5% starch solution was transferred in a 100-ml beaker. Precisely 5.00 ml of concentrated sulfuric acid or hydrochloric acid was added. The sample was covered with aluminium foil and was heated using water bath. Two 1.00 ml volume of the sample were transferred in a test tube. Exactly 1.00 ml of iodine reagent was added to one tube and 1.00 ml of Benedicts reagent was added to the other. The reaction was observed. The sample was heated continuously. Two 1.00 ml volume of the sample was transferred between every 5 minute interval and tested with iodine and Benedicts reagent as above until formation of blue-black complex in iodine stops and formation of brick red colour in Benedicts reagent ensues. RESULTS AND DISCUSSIONÂ   In Molisch test, the result turned out to be positive or slow reaction. It is because of the formation of the reaction with alpha-naphthol in the occurrence of sulfuric acid. In this test, all type of carbohydrates will give a positive result. Benedicts solution is a deep-blue alkaline solution used in testing the existence of the aldehyde functional group, -CHO. Benedict;s reagent consists of blue copper (II) ions which are condensed to copper (I).These ions will then be precipitated as red copper (I) oxide which is not soluble in water. In Benedicts test, monosaccharides and disaccharides except for sucrose give a positive result. It is when the result is a brick red precipitate. In Barfoeds test, the copper ion in solution oxidizes reducing monosaccharides. This is for the formation of a carboxylic acid and red precipitate of copper (I) oxide in 3 minutes. In Seliwanoffs test, the reagent dehydrates ketohexoses to form 5-hydroxymethylfurfural which will further react with resorcinol, that is present in the reagent, to produce a red product in 2 minutes. In Iodine test, all polysaccharides such as glycogen and starch give positive result. The sample turns to blue-black color.

Phillippe Jaques :: History

Phillippe Jaques When people hear the name Louis Riel, some fill up with anger, others fill up with a thankful sense of happiness, like me and my grandfather for example. Louis was Metis, this was the product of a Voyageur and Indian women having a child. The Metis were famed for their hunting and tracking abilities and were often employed individuals or groups as guides or interpreters. Their farming tradition had its roots in the Red River settlement of Manitoba. Following the massive exodus into Sasketchewan, the Metis again established farms and homesteads. The difficulties encountered by the Metis in gaining clear entitlement to their land and the intervention of land speculators when scrip was issued caused most Metis to lose possession of their farms. "York" boats played a major role in the fur trade industry as they replaced freight canoes on the main water systems of Canada in the late 19th century. They had a larger carrying capacity and required fewer men to operate them. This enabled furs to be transported faster and more economically than by canoe. It took eighteen men to run the York boats: a helmsman to give the orders for rowing, a man to steer and sixteen men to pull the oars. Sails were often used to catch favourable winds. The inland sailors who manned these boats were predominently the Metis men who worked for the fur companies. The The Voyageurs wanted to remain friends with these they married the Indian women. He was a man who stuck up for the rights of his people, such as my grandfather. In this essay I will tell you how Louis Riel contributed to the Confederation within the years 1869-1885, and how it affected my life. I was born on a very cold night on November 16, 1867. I grew up in a very poor family, we barley had enough food for my four other brothers and sisters, and my grandmother. We had to take my grandmother in our home because my grandfather, at the time had to fight with the other metis people to try to get us some reasonable rights. My grandfather, Phillippe Jaques, looked up to, and respected Louis Reil greatly, that's why Phillippe went through this journey with Louis. The reason that Phillippe respected Louis so much was because Louis Reil stood up for everything that he belived in. In 1821 the Hudson Bay company had created a union with the first nations people.

Conflict in William Shakespeares Romeo and Juliet Essay -- William Sh

Conflict in William Shakespeare's Romeo and Juliet Romeo and Juliet is a tragic play about the love relationship between the young Romeo and Juliet, who belong to 2 ancient family names that hold a grudge against each other, the Montagues and the Capulets. There are also many other conflicts which ultimately stop Romeo and Juliet form being together. The story was written by the famous play writer, William Shakespeare, and originated the poem, 'the Tragicalle Historye' of Romeo and Juliet written in 1452. Throughout the play conflict is a very important issue and was the main reason the relationship ended in tragedy. In Romeo and Juliet, conflict is the focal point of the play as most of the story is based around this. The conflict in the play is introduced through nature, social and personal levels of feud. The first major conflict that is essential to the play, and is the backbone of the whole story is the feud between the families, the Montague?s and the Capulet?s is very important as it is introduced in the prologue, ?From ancient grudge break to new mutiny? showing that the conflict has existed for many generations and once again the feud has arisen to boiling point. The next line, ?where civil blood makes civil hands unclean?, gives us the impression that the conflict between the Montagues also involves many other people, which helps to show the extent of the conflict. This is reinforced by the fact that even the servants of the families are quarrelling during the beginning of the play, just before the big fight that involves the whole of Verona. Shakespeare shows this by making the servant use insults that were used at ... ...o and Juliet as a tragic production. This is because without conflict the story would not carry the message of how people should put their quarrels to bed before they have disastrous effects and make you realise that people should live together in peace and harmony. Conflict is the backbone of the play with one major feud branching off into many other smaller feuds between various characters. Romeo and Juliet would be meaningless with out feuds as it helps to keep the play moving by adding an extra dimension, this can be seen in any story as without feuds no story would be successful. This is specifically shown in Romeo and Juliet wit the play being built around the feud between the two families grudges over each other, causing the relationship between Romeo and Juliet to be kept secret and further tearing them apart.

Interview To Dow Jones :: essays research papers

Interview to Dow Jones Q. What is the biggest challenge facing Dow Jones in the next few years? A. To continue investing in new products and services that will strengthen our franchises, increase our competitiveness and produce new revenue flows in the future, while at the same time being careful in setting priorities, prudent in controlling costs, and committed to producing strong annual profits. Q. Who are the major competitors of Dow Jones? A. In the broadest sense, any quality products or services that compete for the time and attention of busy businesspeople compete with Dow Jones. More specifically, we have some franchises such as The Wall Street Journal that are dominant in their fields. In other cases, we face particular competitors; Dow Jones Telerate, for example, competes with Reuters in offering real-time financial information around the world. We believe, however, that Dow Jones is a unique company in a number of important respects. Our businesses are balanced roughly 50-50 between print and electronic information. More than 40% of our operating profit is now earned outside the U.S. We are a focused company. We are not a media conglomerate, nor an entertainment company. We stick to our business of business, providing information essential to an ever expanding and increasingly interconnected worldwide business community. Q. What is the strategy behind your television operations? A. Dow Jones aims to provide business news in any form customers want it. When we looked at our operations a few years ago, television was the missing means of delivery for our business news. We began by pioneering with Asia's first business channel, Asia Business News, in late 1993 and followed with Europe's first business channel, European Business News, in early 1995. Both have achieved significant distribution success and viewer acceptance. Both also take advantage of Dow Jones' existing news flows and news talent in those regions. When we launch WBIS+ in New York later this year, we will begin daily business programming in the U.S., thus adding the third component of a global business network. The ITT sports programming will help to draw even larger audiences. Q. What is the profile of a typical Wall Street Journal reader? A. The typical reader of the Journal spends 49 minutes every business day with the newspaper. He or she might be a senior executive of a large corporation or the entrepreneur-owner of a smaller company. The reader is more likely to live in California than New York, has a median age of 46 and a median household income of $117,900. Interestingly, most of the customers registering for the Journal's Internet service are not current Journal readers.

Genetics of Organisms lab report

Measuring only a few millimeters in length, fruit flies take up a fraction of the room of other organisms such as fish or rats that have also been used in such research. The flies are small enough to be compact, yet large enough to be seen in great detail under a dissecting microscope. Due to their size, cost of food and space to house them is extremely low, making them easily accessible to schools and laboratories every. Veer. The entire life cycle Of the fruit fly is a mere 30 days, 7-12 days of which are spent maturing. 2-15 hours after eggs are laid, larvae emerge for 4 days to grow and feed on toting fruit (which their eggs were laid on) before undergoing a 4 day metamorphosis after which they are adults. The rest of their adult lives are spent eating and mating (Fruit Fly). Females are able to mate as soon as 12-18 hours after the 4 day metamorphosis. Differentiating male and female flies is quite simple; males (left) have sex combs which look like small black dots on their fro nt legs and have fewer dark lines across their abdomen.Females (right) are typically larger and have dark stripes across the abdomen and have an ovipositor extending from the lower abdomen (Lab Seven). Today, fruit flies are being used in stem cell research of gremlin cells. These highly vital gremlin cells become gametes and carry on the evolution of a species. Researchers at the university of Utah have been studying how germ stem cells protect themselves from becoming somatic cells using fruit flies.It all began in 1 922 at Massachusetts Institute of Technology where Ruth Lehmann discovered a gene she named â€Å"Oscar†. Oscar is responsible for adding a vital protein to the plasma of the germ stem cell that when inactive inhibits the production Of germ cells. When it is turned on, germ cells are produced and kept as stem cells through â€Å"extreme transcriptional repression†. During this process, DNA is inhibited from being transcribed to RNA which in turn means no gene expression.This research is delving into the specifics of stem cells which are suspected to hold treatments for many diseases (Scheduler). While our lab wasn't investigating the mechanics of stem cell development, we studied the inheritance of traits though generations of flies. Our objective was to see the different patterns of inheritance that genes can take. To have exults as close to expected as possible we kept temperature, food and light constant throughout all tests as controls and let the mating and passing of traits be the variable.Keeping all other factors constant we hypothesized that if cross A showed monophonic inheritance it would have a 1:2:1 ratio, dibber crosses would have a 9:3:3:1 ratio and sex linked inheritance would show a ratio of inheritance. Materials Fruit Flies (Drosophila Melanomas) Cross A: Sepia female x Wild male Cross 8: Vestigial female x Sepia male Cross C: White female Wild male Colored tape Petri dishes Fruit fly blue media Flyway Plastic vi als (with foam stoppers) Microscopes Paint Brushes Funnels â€Å"Morgue† Ice packs Procedure 1.Obtain a vial of Fl generation flies (either cross A,B, or C and make sure to label the vials as such). The first objective is to remove the flies from the vial without having them fly away. To prevent this, wedge a wand that has been dipped in fly nap between the foam stopper and the vial so that it reaches into the vial to anesthetize the flies. To help immobilizers them, placing the vials in a cool location or on an ice pack can help to calm them as they are Elian on environmental factors. 2.After the flies have been anesthetized, remove them from the vials and place them in Petri dishes with labels matching the vials they came from to avoid confusion. To remove the immobilizers flies from the vial, it is important to be gentle and avoid crushing any flies. The majority of the flies should fall from the vial when it is inverted, but to remove any that are left, a paintbrush can b e very useful to move them without causing them any harm. 3. Once the flies are in Petri dishes, place them on ice packs to prevent the flies from waking up during counting.Place the ice pack and Petri dish under a dissecting microscope. With the help of the microscope, record the sex and phenotype of all flies. To maneuver the flies within the Petri dish, use a paint brush to avoid harm. The characteristics of sexing flies is described in the introduction on page 2. 4. Once the flies have been sorted by sex and phenotype, prepare the vials for the PA generation. Mix equal parts dry food and water and let it set in the vial. Make sure to label the vial with the phenotypes of each parent of the cross. . Once the vials are prepared, begin placing in pairs of male and male flies into the correctly labeled vials. Use paint brushes for moving flies if necessary. Cap these vials and place them in a warm area. These flies will mate and produce the IF generation 6. After the IF vials have b een sitting for approximately 10-12 days, remove the adult flies. By this time the flies will have mated and the female will have laid her eggs. Removing the adults will prevent Fl flies from mating with IF offspring.To do this, carefully use Nap (technique as described in step 1), being aware that fly larvae are more sensitive and may be fatally harmed by â€Å"over-napping†. Remove the flies by inverting the vial and placing the adult Fl flies in the â€Å"morgue† (a jar containing alcohol or baby oil). Then close the vial and allow it to sit for another 12-15 days. 7. After 12-15 days have passed, record the sex and phenotype of all adult flies. As described in steps 1-3 Flyway will be used to anesthetize the flies before they are removed from the vials to be put into Petri dishes for counting.Once all of the flies have been counted and recorded, place them into the â€Å"morgue† and dispose Of all vials. Rest Its Fl Results: Cross A -? Wild Male x Sepia Fema le E – Wild eyes e – Sepia eyes Cross B – Sepia eye normal wing male x Wild eye vestigial wing female beef x Beef Fee Beef Sepia eyes e F – Normal wings f – Vestigial Wings Cross C -? Wild male x White female Exe x EXE Exe Exe e – White eyes IF results: Cross A – Wild male x Wild female Chi-square Analysis Phenotype # Observed # Expected (o-e) (0-e)2 (0-e)2/e Wild eyes 256 260 -4 16 . 615 91 87 4 . 1 83 Chi-square Value . 25 Null Hypothesis: If a monophonic cross is performed between two fruit flies that are both heterozygous for eye color, the expected offspring counts would be in a 3 wild: 1 sepia ratio and would have a chi square value less than 5. 99.

Flow Induced Vibration

FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH IVAN GRANT Bachelor of Science in Mechanical Engineering Nagpur University Nagpur, India June, 2006 submitted in partial ful? llment of requirements for the degree MASTERS OF SCIENCE IN MECHANICAL ENGINEERING at the CLEVELAND STATE UNIVERSITY May, 2010 This thesis has been approved for the department of MECHANICAL ENGINEERING and the College of Graduate Studies by: Thesis Chairperson, Majid Rashidi, Ph. D. Department & Date Asuquo B. Ebiana, Ph. D. Department & Date Rama S. Gorla, Ph. D. Department & Date ACKNOWLEDGMENTS I would like to thank my advisor Dr. Majid Rashidi and Dr.Paul Bellini, who provided essential support and assistance throughout my graduate career, and also for their guidance which immensely contributed towards the completion of this thesis. This thesis would not have been realized without their support. I would also like to thank Dr. Asuquo. B. Ebiana and Dr. Rama. S. Gorla for being in my thesis committe e. Thanks are also due to my parents,my brother and friends who have encouraged, supported and inspired me. FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH IVAN GRANT ABSTRACT Flow induced vibrations of pipes with internal ? uid ? ow is studied in this work.Finite Element Analysis methodology is used to determine the critical ? uid velocity that induces the threshold of pipe instability. The partial di? erential equation of motion governing the lateral vibrations of the pipe is employed to develop the sti? ness and inertia matrices corresponding to two of the terms of the equations of motion. The Equation of motion further includes a mixed-derivative term that was treated as a source for a dissipative function. The corresponding matrix with this dissipative function was developed and recognized as the potentially destabilizing factor for the lateral vibrations of the ? id carrying pipe. Two types of boundary conditions, namely simply-supported and cantilevered were consi dered for the pipe. The appropriate mass, sti? ness, and dissipative matrices were developed at an elemental level for the ? uid carrying pipe. These matrices were then assembled to form the overall mass, sti? ness, and dissipative matrices of the entire system. Employing the ? nite element model developed in this work two series of parametric studies were conducted. First, a pipe with a constant wall thickness of 1 mm was analyzed. Then, the parametric studies were extended to a pipe with variable wall thickness.In this case, the wall thickness of the pipe was modeled to taper down from 2. 54 mm to 0. 01 mm. This study shows that the critical velocity of a pipe carrying ? uid can be increased by a factor of six as the result of tapering the wall thickness. iv TABLE OF CONTENTS ABSTRACT LIST OF FIGURES LIST OF TABLES I INTRODUCTION 1. 1 1. 2 1. 3 1. 4 II Overview of Internal Flow Induced Vibrations in Pipes . . . . . . Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Composition of Thesis . . . . . . . . . . . . . . . . . . . . . . . iv vii ix 1 1 2 2 3 FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 2. 1 Mathematical Modelling . . . . . . . . . . . . . . . . . . . . . . . 2. 1. 1 2. 2 Equations of Motion . . . . . . . . . . . . . . . . . . . 4 4 4 12 12 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . 2. 2. 1 2. 2. 2 2. 2. 3 Shape Functions . . . . . . . . . . . . . . . . . . . . . Formulating the Sti? ness Matrix for a Pipe Carrying Fluid 14 Forming the Matrix for the Force that conforms the Fluid to the Pipe . . . . . . . . . . . . . . . . . . . . . 21 2. 2. 4 2. 2. 5Dissipation Matrix Formulation for a Pipe carrying Fluid 26 Inertia Matrix Formulation for a Pipe carrying Fluid . 28 III FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 31 v 3. 1 Forming Global Sti? ness Matrix from Elemental Sti? ness Matrices . . . . . . . . . . . . . . . . . . . . 31 3. 2 Applying Boundary Conditions to Global Sti? ness Matrix for simply supported pipe with ? uid ? ow . . . . 33 3. 3 Applying Boundary Conditions to Global Sti? ness Matrix for a cantilever pipe with ? uid ? ow . . . . . . . 34 3. 4 MATLAB Programs for Assembling Global Matrices for Simply Supported and Cantilever pipe carrying ? uid . . . . . . . . . . 35 35 36 3. 5 3. 6 MATLAB program for a simply supported pipe carrying ? uid . . MATLAB program for a cantilever pipe carrying ? uid . . . . . . IV FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 4. 1 V Parametric Study . . . . . . . . . . . . . . . . . . . . . . . . . . 37 37 FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 5. 1 Tapered Pipe Carrying Fluid . . . . . . . . . . . . . . . . . . . . 42 42 47 50 50 51 54 MATLAB program for Simply Supported Pipe Carrying Fluid . . MATLAB Program for Cantilever Pipe Carrying Fluid . . . . . . MATLAB Program for Tapered Pipe Carrying Flu id . . . . . . 54 61 68 VI RESULTS AND DISCUSSIONS 6. 1 6. 2 Contribution of the Thesis . . . . . . . . . . . . . . . . . . . . . Future Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY Appendices 0. 1 0. 2 0. 3 vi LIST OF FIGURES 2. 1 2. 2 Pinned-Pinned Pipe Carrying Fluid * . . . . . . . . . . . . . . Pipe Carrying Fluid, Forces and Moments acting on Elements (a) Fluid (b) Pipe ** . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 7 9 10 11 13 14 15 16 17 21 33 34 36 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 9 Force due to Bending . . . . . . . . . . . . . . . . . . . . . . . . .Force that Conforms Fluid to the Curvature of Pipe . . . . . Coriolis Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inertia Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pipe Carrying Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . Beam Element Model . . . . . . . . . . . . . . . . . . . . . . . . . Relationship between Stress and Stra in, Hooks Law . . . . . . 2. 10 Plain sections remain plane . . . . . . . . . . . . . . . . . . . . . 2. 11 Moment of Inertia for an Element in the Beam . . . . . . . . . 2. 12 Pipe Carrying Fluid Model . . . . . . . . . . . . . . . . . . . . . 3. 1 3. 2 3. 4. 1 Representation of Simply Supported Pipe Carrying Fluid . . Representation of Cantilever Pipe Carrying Fluid . . . . . . . Pinned-Free Pipe Carrying Fluid* . . . . . . . . . . . . . . . . . Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . 4. 2 Shape Function Plot for a Cantilever Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 3 Reduction of Fundamental Frequency for a Cantilever Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . 5. 1 Representation of Tapered Pipe Carrying Fluid . . . . . . . 39 40 41 42 vii 5. 2 6. 1 Introducing a Taper in the Pipe Carrying Fluid . . . . . . . . Representation of Pipe Carrying Fluid and Tapered Pipe Carrying Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 47 viii LIST OF TABLES 4. 1 Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . 38 4. 2 Reduction of Fundamental Frequency for a Pinned-Free Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . 40 5. 1 Reduction of Fundamental Frequency for a Tapered pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . . . 46 6. 1 Reduction of Fundamental Frequency for a Tapered Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . . . . . . . . 48 6. 2 Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity . . . . . . . . . . . . . . . . 49 ix CHAPTER I INTRODUCTION 1. 1 Overview of Internal Flow Induced Vibrations in Pipes The ? ow of a ? uid through a pipe can impose pressures on the walls of the pipe c ausing it to de? ect under certain ? ow conditions. This de? ection of the pipe may lead to structural instability of the pipe.The fundamental natural frequency of a pipe generally decreases with increasing velocity of ? uid ? ow. There are certain cases where decrease in this natural frequency can be very important, such as very high velocity ? ows through ? exible thin-walled pipes such as those used in feed lines to rocket motors and water turbines. The pipe becomes susceptible to resonance or fatigue failure if its natural frequency falls below certain limits. With large ? uid velocities the pipe may become unstable. The most familiar form of this instability is the whipping of an unrestricted garden hose.The study of dynamic response of a ? uid conveying pipe in conjunction with the transient vibration of ruptured pipes reveals that if a pipe ruptures through its cross section, then a ? exible length of unsupported pipe is left spewing out ? uid and is free to whip about and im pact other structures. In power plant plumbing pipe whip is a possible mode of failure. A 1 2 study of the in? uence of the resulting high velocity ? uid on the static and dynamic characteristics of the pipes is therefore necessary. 1. 2 Literature Review Initial investigations on the bending vibrations of a simply supported pipe containing ? id were carried out by Ashley and Haviland[2]. Subsequently,Housner[3] derived the equations of motion of a ? uid conveying pipe more completely and developed an equation relating the fundamental bending frequency of a simply supported pipe to the velocity of the internal ? ow of the ? uid. He also stated that at certain critical velocity, a statically unstable condition could exist. Long[4] presented an alternate solution to Housner’s[3] equation of motion for the simply supported end conditions and also treated the ? xed-free end conditions. He compared the analysis with experimental results to con? rm the mathematical model.His experi mental results were rather inconclusive since the maximum ? uid velocity available for the test was low and change in bending frequency was very small. Other e? orts to treat this subject were made by Benjamin, Niordson[6] and Ta Li. Other solutions to the equations of motion show that type of instability depends on the end conditions of the pipe carrying ? uid. If the ? ow velocity exceeds the critical velocity pipes supported at both ends bow out and buckle[1]. Straight Cantilever pipes fall into ? ow induced vibrations and vibrate at a large amplitude when ? ow velocity exceeds critical velocity[8-11]. . 3 Objective The objective of this thesis is to implement numerical solutions method, more specifically the Finite Element Analysis (FEA) to obtain solutions for di? erent pipe con? gurations and ? uid ? ow characteristics. The governing dynamic equation describing the induced structural vibrations due to internal ? uid ? ow has been formed and dis- 3 cussed. The governing equatio n of motion is a partial di? erential equation that is fourth order in spatial variable and second order in time. Parametric studies have been performed to examine the in? uence of mass distribution along the length of the pipe carrying ? id. 1. 4 Composition of Thesis This thesis is organized according to the following sequences. The equations of motions are derived in chapter(II)for pinned-pinned and ? xed-pinned pipe carrying ? uid. A ? nite element model is created to solve the equation of motion. Elemental matrices are formed for pinned-pinned and ? xed-pinned pipe carrying ? uid. Chapter(III)consists of MATLAB programs that are used to assemble global matrices for the above cases. Boundary conditions are applied and based on the user de? ned parameters fundamental natural frequency for free vibration is calculated for various pipe con? urations. Parametric studies are carried out in the following chapter and results are obtained and discussed. CHAPTER II FLOW INDUCED VIBRATION S IN PIPES, A FINITE ELEMENT APPROACH In this chapter,a mathematical model is formed by developing equations of a straight ? uid conveying pipe and these equations are later solved for the natural frequency and onset of instability of a cantilever and pinned-pinned pipe. 2. 1 2. 1. 1 Mathematical Modelling Equations of Motion Consider a pipe of length L, modulus of elasticity E, and its transverse area moment I. A ? uid ? ows through the pipe at pressure p and density ? t a constant velocity v through the internal pipe cross-section of area A. As the ? uid ? ows through the de? ecting pipe it is accelerated, because of the changing curvature of the pipe and the lateral vibration of the pipeline. The vertical component of ? uid pressure applied to the ? uid element and the pressure force F per unit length applied on the ? uid element by the tube walls oppose these accelerations. Referring to ? gures (2. 1) and 4 5 Figure 2. 1: Pinned-Pinned Pipe Carrying Fluid * (2. 2),balancing the forces in the Y direction on the ? uid element for small deformations, gives F ? A ? ? ? 2Y = ? A( + v )2 Y ? x2 ? t ? x (2. 1) The pressure gradient in the ? uid along the length of the pipe is opposed by the shear stress of the ? uid friction against the tube walls. The sum of the forces parallel Figure 2. 2: Pipe Carrying Fluid, Forces and Moments acting on Elements (a) Fluid (b) Pipe ** to the pipe axis for a constant ? ow velocity gives 0 0 * Flow Induced Vibrations,Robert D. Blevins,Krieger. 1977,P 289 ** Flow Induced Vibrations,Robert D. Blevins,Krieger. 1977,P 289 6 A ?p + ? S = 0 ? x (2. 2) Where S is the inner perimeter of the pipe, and ? s the shear stress on the internal surface of the pipe. The equations of motions of the pipe element are derived as follows. ?T ? 2Y + ? S ? Q 2 = 0 ? x ? x (2. 3) Where Q is the transverse shear force in the pipe and T is the longitudinal tension in the pipe. The forces on the element of the pipe normal to the pipe axis accelerate the pi pe element in the Y direction. For small deformations, ? 2Y ? 2Y ? Q +T 2 ? F =m 2 ? x ? x ? t (2. 4) Where m is the mass per unit length of the empty pipe. The bending moment M in the pipe, the transverse shear force Q and the pipe deformation are related by ? 3Y ?M = EI 3 ? x ? x Q=? (2. 5) Combining all the above equations and eliminating Q and F yields: EI ? 4Y ? 2Y ? ? ? Y + (? A ? T ) 2 + ? A( + v )2 Y + m 2 = 0 4 ? x ? x ? t ? x ? t (2. 6) The shear stress may be eliminated from equation 2. 2 and 2. 3 to give ? (? A ? T ) =0 ? x (2. 7) At the pipe end where x=L, the tension in the pipe is zero and the ? uid pressure is equal to ambient pressure. Thus p=T=0 at x=L, ? A ? T = 0 (2. 8) 7 The equation of motion for a free vibration of a ? uid conveying pipe is found out by substituting ? A ? T = 0 from equation 2. 8 in equation 2. 6 and is given by the equation 2. EI ? 2Y ? 2Y ? 4Y ? 2Y +M 2 =0 + ? Av 2 2 + 2? Av ? x4 ? x ? x? t ? t (2. 9) where the mass per unit length of the pi pe and the ? uid in the pipe is given by M = m + ? A. The next section describes the forces acting on the pipe carrying ? uid for each of the components of eq(2. 9) Y F1 X Z EI ? 4Y ? x4 Figure 2. 3: Force due to Bending Representation of the First Term in the Equation of Motion for a Pipe Carrying Fluid 8 The term EI ? Y is a force component acting on the pipe as a result of bending of ? x4 the pipe. Fig(2. 3) shows a schematic view of this force F1. 4 9 Y F2 X Z ?Av 2 ? 2Y ? x2 Figure 2. : Force that Conforms Fluid to the Curvature of Pipe Representation of the Second Term in the Equation of Motion for a Pipe Carrying Fluid The term ? Av 2 ? Y is a force component acting on the pipe as a result of ? ow ? x2 around a curved pipe. In other words the momentum of the ? uid is changed leading to a force component F2 shown schematically in Fig(2. 4) as a result of the curvature in the pipe. 2 10 Y F3 X Z 2? Av ? 2Y ? x? t Figure 2. 5: Coriolis Force Representation of the Third Term in t he Equation of Motion for a Pipe Carrying Fluid ? Y The term 2? Av ? x? t is the force required to rotate the ? id element as each point 2 in the span rotates with angular velocity. This force is a result of Coriolis E? ect. Fig(2. 5) shows a schematic view of this force F3. 11 Y F4 X Z M ? 2Y ? t2 Figure 2. 6: Inertia Force Representation of the Fourth Term in the Equation of Motion for a Pipe Carrying Fluid The term M ? Y is a force component acting on the pipe as a result of Inertia ? t2 of the pipe and the ? uid ? owing through it. Fig(2. 6) shows a schematic view of this force F4. 2 12 2. 2 Finite Element Model Consider a pipeline span that has a transverse de? ection Y(x,t) from its equillibrium position.The length of the pipe is L,modulus of elasticity of the pipe is E,and the area moment of inertia is I. The density of the ? uid ? owing through the pipe is ? at pressure p and constant velocity v,through the internal pipe cross section having area A. Flow of the ? uid through the de? ecting pipe is accelerated due to the changing curvature of the pipe and the lateral vibration of the pipeline. From the previous section we have the equation of motion for free vibration of a ? uid convering pipe: EI ? 2Y ? 2Y ? 2Y ? 4Y + ? Av 2 2 + 2? Av +M 2 =0 ? x4 ? x ? x? t ? t (2. 10) 2. 2. 1 Shape Functions The essence of the ? ite element method,is to approximate the unknown by an expression given as n w= i=1 Ni ai where Ni are the interpolating shape functions prescribed in terms of linear independent functions and ai are a set of unknown parameters. We shall now derive the shape functions for a pipe element. 13 Y R R x L2 L L1 X Figure 2. 7: Pipe Carrying Fluid Consider an pipe of length L and let at point R be at distance x from the left end. L2=x/L and L1=1-x/L. Forming Shape Functions N 1 = L12 (3 ? 2L1) N 2 = L12 L2L N 3 = L22 (3 ? 2L2) N 4 = ? L1L22 L Substituting the values of L1 and L2 we get (2. 11) (2. 12) (2. 13) (2. 14) N 1 = (1 ? /l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 15) (2. 16) (2. 17) (2. 18) 14 2. 2. 2 Formulating the Sti? ness Matrix for a Pipe Carrying Fluid ?1 ?2 W1 W2 Figure 2. 8: Beam Element Model For a two dimensional beam element, the displacement matrix in terms of shape functions can be expressed as ? ? w1 ? ? ? ? ? ?1 ? ? ? [W (x)] = N 1 N 2 N 3 N 4 ? ? ? ? ? w2? ? ? ?2 (2. 19) where N1, N2, N3 and N4 are the displacement shape functions for the two dimensional beam element as stated in equations (2. 15) to (2. 18). The displacements and rotations at end 1 is given by w1, ? and at end 2 is given by w2 , ? 2. Consider the point R inside the beam element of length L as shown in ? gure(2. 7) Let the internal strain energy at point R is given by UR . The internal strain energy at point R can be expressed as: 1 UR = ? 2 where ? is the stress and is the strain at the point R. (2. 20) 15 ? E 1 ? Figure 2. 9: Relationship between Stress and Strain, Hooks Law Also; ? =E Rel ation between stress and strain for elastic material, Hooks Law Substituting the value of ? from equation(2. 21) into equation(2. 20) yields 1 UR = E 2 (2. 21) 2 (2. 22) 16 A1 z B1 w A z B u x Figure 2. 0: Plain sections remain plane Assuming plane sections remain same, = du dx (2. 23) (2. 24) (2. 25) u=z dw dx d2 w =z 2 dx To obtain the internal energy for the whole beam we integrate the internal strain energy at point R over the volume. The internal strain energy for the entire beam is given as: UR dv = U vol (2. 26) Substituting the value of from equation(2. 25) into (2. 26) yields U= vol 1 2 E dv 2 (2. 27) Volume can be expressed as a product of area and length. dv = dA. dx (2. 28) 17 based on the above equation we now integrate equation (2. 27) over the area and over the length. L U= 0 A 1 2 E dAdx 2 (2. 29) Substituting the value of rom equation(2. 25) into equation (2. 28) yields L U= 0 A 1 d2 w E(z 2 )2 dAdx 2 dx (2. 30) Moment of Inertia I for the beam element is given as = dA z Figure 2. 11: Moment of Inertia for an Element in the Beam I= z 2 dA (2. 31) Substituting the value of I from equation(2. 31) into equation(2. 30) yields L U = EI 0 1 d2 w 2 ( ) dx 2 dx2 (2. 32) The above equation for total internal strain energy can be rewritten as L U = EI 0 1 d2 w d2 w ( )( )dx 2 dx2 dx2 (2. 33) 18 The potential energy of the beam is nothing but the total internal strain energy. Therefore, L ? = EI 0 1 d2 w d2 w ( )( )dx 2 dx2 dx2 (2. 34)If A and B are two matrices then applying matrix property of the transpose, yields (AB)T = B T AT (2. 35) We can express the Potential Energy expressed in equation(2. 34) in terms of displacement matrix W(x)equation(2. 19) as, 1 ? = EI 2 From equation (2. 19) we have ? ? w1 ? ? ? ? ? ?1 ? ? ? [W ] = N 1 N 2 N 3 N 4 ? ? ? ? ? w2? ? ? ?2 ? ? N1 ? ? ? ? ? N 2? ? ? [W ]T = ? ? w1 ? 1 w2 ? 2 ? ? ? N 3? ? ? N4 L (W )T (W )dx 0 (2. 36) (2. 37) (2. 38) Substituting the values of W and W T from equation(2. 37) and equation(2. 3 8) in equation(2. 36) yields ? N1 ? ? ? N 2 ? w1 ? 1 w2 ? 2 ? ? ? N 3 ? N4 ? ? ? ? ? ? N1 ? ? ? ? ? w1 ? ? ? ? ?1 ? ? ? ? ? dx (2. 39) ? ? ? w2? ? ? ?2 1 ? = EI 2 L 0 N2 N3 N4 19 where N1, N2, N3 and N4 are the displacement shape functions for the two dimensional beam element as stated in equations (2. 15) to (2. 18). The displacements and rotations at end 1 is given by w1, ? 1 and at end 2 is given by w2 , ? 2. 1 ? = EI 2 L 0 (N 1 ) ? ? ? N 2 N 1 ? w1 ? 1 w2 ? 2 ? ? ? N 3 N 1 ? N4 N1 ? 2 N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 )2 N4 N3 N1 N4 N2 N4 N3 N4 (N 4 )2 ? w1 ? ? ? ? ? 1 ? ? ? ? ? dx ? ? ?w2? ? ? 2 (2. 40) where ? 2 (N 1 ) ? ? L ? N 2 N 1 ? [K] = ? 0 ? N 3 N 1 ? ? N4 N1 N1 N2 (N 2 )2 N3 N2 N4 N2N1 N3 N2 N3 (N 3 ) 2 N1 N4 ? N4 N3 ? ? N2 N4 ? ? ? dx ? N3 N4 ? ? 2 (N 4 ) (2. 41) N 1 = (1 ? x/l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 42) (2. 43) (2. 44) (2. 45) The element sti? ness matrix for the beam is obtained by substit uting the values of shape functions from equations (2. 42) to (2. 45) into equation(2. 41) and integrating every element in the matrix in equation(2. 40) over the length L. 20 The Element sti? ness matrix for a beam element; ? ? 12 6l ? 12 6l ? ? ? ? 2 2? 4l ? 6l 2l ? EI ? 6l ? [K e ] = 3 ? ? l 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 6l 2l ? 6l 4l (2. 46) 1 2. 2. 3 Forming the Matrix for the Force that conforms the Fluid to the Pipe A X ? r ? _______________________ x R Y Figure 2. 12: Pipe Carrying Fluid Model B Consider a pipe carrying ? uid and let R be a point at a distance x from a reference plane AB as shown in ? gure(2. 12). Due to the ? ow of the ? uid through the pipe a force is introduced into the pipe causing the pipe to curve. This force conforms the ? uid to the pipe at all times. Let W be the transverse de? ection of the pipe and ? be angle made by the pipe due to the ? uid ? ow with the neutral axis. ? and ? represent the unit vectors along the X i j ? nd Y axis and r and ? rep resent the two unit vectors at point R along the r and ? ? ? axis. At point R,the vectors r and ? can be expressed as ? r = cos + sin ? i j (2. 47) ? ? = ? sin + cos i j Expression for slope at point R is given by; tan? = dW dx (2. 48) (2. 49) 22 Since the pipe undergoes a small de? ection, hence ? is very small. Therefore; tan? = ? ie ? = dW dx (2. 51) (2. 50) The displacement of a point R at a distance x from the reference plane can be expressed as; ? R = W ? + r? j r We di? erentiate the above equation to get velocity of the ? uid at point R ? ? ? j ? r ? R = W ? + r? + rr ? r = vf ? here vf is the velocity of the ? uid ? ow. Also at time t; r ? d? r= ? dt ie r ? d? d? = r= ? d? dt ? Substituting the value of r in equation(2. 53) yields ? ? ? ? j ? r R = W ? + r? + r (2. 57) (2. 56) (2. 55) (2. 53) (2. 54) (2. 52) ? Substituting the value of r and ? from equations(2. 47) and (2. 48) into equation(2. 56) ? yields; ? ? ? ?j ? R = W ? + r[cos + sin + r? [? sin + cos i j] i j] Sin ce ? is small The velocity at point R is expressed as; ? ? ? i ? j R = Rx? + Ry ? (2. 59) (2. 58) 23 ? ? i ? j ? ? R = (r ? r )? + (W + r? + r? )? ? ? The Y component of velocity R cause the pipe carrying ? id to curve. Therefore, (2. 60) 1 ? ? ? ? T = ? f ARy Ry (2. 61) 2 ? ? where T is the kinetic energy at the point R and Ry is the Y component of velocity,? f is the density of the ? uid,A is the area of cross-section of the pipe. ? ? Substituting the value of Ry from equation(2. 60) yields; 1 ? ? ? ? ? ? ? ? ? T = ? f A[W 2 + r2 ? 2 + r2 ? 2 + 2W r? + 2W ? r + 2rr ] 2 (2. 62) Substituting the value of r from equation(2. 54) and selecting the ? rst,second and the ? fourth terms yields; 1 2 ? ? T = ? f A[W 2 + vf ? 2 + 2W vf ? ] 2 (2. 63) Now substituting the value of ? from equation(2. 51) into equation(2. 3) yields; dW 2 dW dW 1 2 dW 2 ) + vf ( ) + 2vf ( )( )] T = ? f A[( 2 dt dx dt dx From the above equation we have these two terms; 1 2 dW 2 ? f Avf ( ) 2 dx 2? f Avf ( dW dW )( ) dt dx (2. 65) (2. 66) (2. 64) The force acting on the pipe due to the ? uid ? ow can be calculated by integrating the expressions in equations (2. 65) and (2. 66) over the length L. 1 2 dW 2 ? f Avf ( ) 2 dx (2. 67) L The expression in equation(2. 67) represents the force that causes the ? uid to conform to the curvature of the pipe. 2? f Avf ( L dW dW )( ) dt dx (2. 68) 24 The expression in equation(2. 68) represents the coriolis force which causes the ? id in the pipe to whip. The equation(2. 67) can be expressed in terms of displacement shape functions derived for the pipe ? =T ? V ? = L 1 2 dW 2 ? f Avf ( ) 2 dx (2. 69) Rearranging the equation; 2 ? = ? f Avf L 1 dW dW ( )( ) 2 dx dx (2. 70) For a pipe element, the displacement matrix in terms of shape functions can be expressed as ? ? w1 ? ? ? ? ? ?1 ? ? ? [W (x)] = N 1 N 2 N 3 N 4 ? ? ? ? ? w2? ? ? ?2 (2. 71) where N1, N2, N3 and N4 are the displacement shape functions pipe element as stated in equations (2. 15) to (2. 18). The displacements and rotations at end 1 is given by w1, ? 1 and at end 2 is given by w2 , ? . Refer to ? gure(2. 8). Substituting the shape functions determined in equations (2. 15) to (2. 18) ? ? N1 ? ? ? ? ? N 2 ? ? ? ? N1 w1 ? 1 w2 ? 2 ? ? ? N3 ? ? ? ? N4 ? ? w1 ? ? ? ? ? ?1 ? ? ? N 4 ? ? dx (2. 72) ? ? ? w2? ? ? ?2 L 2 ? = ? f Avf 0 N2 N3 25 L 2 ? = ? f Avf 0 (N 1 ) ? ? ? N 2 N 1 ? w1 ? 1 w2 ? 2 ? ? ? N 3 N 1 ? N4 N1 ? 2 N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 )2 N4 N3 N1 N4 N2 N4 N3 N4 (N 4 )2 ? w1 ? ? ? ? ? 1 ? ? ? ? ? dx ? ? ?w2? ? ? 2 (2. 73) where (N 1 ) ? ? L ? N 2 N 1 ? ? 0 ? N 3 N 1 ? ? N4 N1 ? 2 N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 ) 2 N1 N4 ? 2 [K2 ] = ? f Avf N4 N3 ? N2 N4 ? ? ? dx ? N3 N4 ? ? 2 (N 4 ) (2. 74) The matrix K2 represents the force that conforms the ? uid to the pipe. Substituting the values of shape functions equations(2. 15) to (2. 18) and integrating it over the length gives us the elemental matrix for the ? 36 3 ? 36 ? ? 4 ? 3 ? Av 2 ? 3 ? [K2 ]e = ? 30l 36 ? 3 36 ? ? 3 ? 1 ? 3 above force. ? 3 ? ? ? 1? ? ? ? ? 3? ? 4 (2. 75) 26 2. 2. 4 Dissipation Matrix Formulation for a Pipe carrying Fluid The dissipation matrix represents the force that causes the ? uid in the pipe to whip creating instability in the system. To formulate this matrix we recall equation (2. 4) and (2. 68) The dissipation function is given by; D= L 2? f Avf ( dW dW )( ) dt dx (2. 76) Where L is the length of the pipe element, ? f is the density of the ? uid, A area of cross-section of the pipe, and vf velocity of the ? uid ? ow. Recalling the displacement shape functions mentioned in equations(2. 15) to (2. 18); N 1 = (1 ? x/l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 77) (2. 78) (2. 79) (2. 80) The Dissipation Matrix can be expressed in terms of its displacement shape functions as shown in equations(2. 77) to (2. 80). ? ? N1 ? ? ? ? ? N 2 ? L ? ? D = 2? Avf ? N1 N2 N3 N4 w1 ? 1 w2 ? 2 ? ? ? 0 N3 ? ? ? ? N4 (N 1 ) ? ? ? N 2 N 1 ? w1 ? 1 w2 ? 2 ? ? ? N 3 N 1 ? N4 N1 ? 2 ? ? w1 ? ? ? ? ? ?1 ? ? ? ? ? dx ? ? ? w2? ? ? ?2 (2. 81) N1 N2 (N 2 )2 N3 N2 N4 N2 N1 N3 N2 N3 (N 3 )2 N4 N3 N1 N4 N2 N4 N3 N4 (N 4 )2 L 2? f Avf 0 ? w1 ? ? ? ? ? 1 ? ? ? ? ? dx ? ? ?w2? ? ? 2 (2. 82) 27 Substituting the values of shape functions from equations(2. 77) to (2. 80) and integrating over the length L yields; ? ? ? 30 6 30 ? 6 ? ? ? ? 0 6 ? 1? ?Av ? 6 ? ? [D]e = ? ? 30 30 ? 6 30 6 ? ? ? ? ? 6 1 ? 6 0 [D]e represents the elemental dissipation matrix. (2. 83) 28 2. 2. 5Inertia Matrix Formulation for a Pipe carrying Fluid Consider an element in the pipe having an area dA, length x, volume dv and mass dm. The density of the pipe is ? and let W represent the transverse displacement of the pipe. The displacement model for the Assuming the displacement model of the element to be W (x, t) = [N ]we (t) (2. 84) where W is the vector of displacements,[N] is the matrix of shape functions and we is the vecto r of nodal displacements which is assumed to be a function of time. Let the nodal displacement be expressed as; W = weiwt Nodal Velocity can be found by di? erentiating the equation() with time. W = (iw)weiwt (2. 86) (2. 85) Kinetic Energy of a particle can be expressed as a product of mass and the square of velocity 1 T = mv 2 2 (2. 87) Kinetic energy of the element can be found out by integrating equation(2. 87) over the volume. Also,mass can be expressed as the product of density and volume ie dm = ? dv T = v 1 ? 2 ? W dv 2 (2. 88) The volume of the element can be expressed as the product of area and the length. dv = dA. dx (2. 89) Substituting the value of volume dv from equation(2. 89) into equation(2. 88) and integrating over the area and the length yields; T = ? w2 2 ? ?W 2 dA. dx A L (2. 90) 29 ?dA = ?A A (2. 91) Substituting the value of A ?dA in equation(2. 90) yields; Aw2 2 T = ? W 2 dx L (2. 92) Equation(2. 92) can be written as; Aw2 2 T = ? ? W W dx L (2. 93) The Lagr ange equations are given by d dt where L=T ? V (2. 95) ? L ? w ? ? ? L ? w = (0) (2. 94) is called the Lagrangian function, T is the kinetic energy, V is the potential energy, ? W is the nodal displacement and W is the nodal velocity. The kinetic energy of the element †e† can be expressed as Te = Aw2 2 ? ? W T W dx L (2. 96) ? and where ? is the density and W is the vector of velocities of element e. The expression for T using the eq(2. 9)to (2. 21) can be written as; ? ? N1 ? ? ? ? ? N 2? ? ? w1 ? 1 w2 ? 2 ? ? N 1 N 2 N 3 N 4 ? ? ? N 3? ? ? N4 ? ? w1 ? ? ? ? ? ?1 ? ? ? ? ? dx ? ? ? w2? ? ? ?2 Aw2 T = 2 e (2. 97) L 30 Rewriting the above expression we get; ? (N 1)2 ? ? ? N 2N 1 Aw2 ? Te = w1 ? 1 w2 ? 2 ? ? 2 L ? N 3N 1 ? N 4N 1 ? N 1N 2 N 1N 3 N 1N 4 w1 ? ? 2 (N 2) N 2N 3 N 2N 4? ? ? 1 ? ? ? ? ? dx ? N 3N 2 (N 3)2 N 3N 4? ?w2? ? 2 N 4N 2 N 4N 3 (N 4) ? 2 (2. 98) Recalling the shape functions derived in equations(2. 15) to (2. 18) N 1 = (1 ? x/l)2 (1 + 2x/l) N 2 = (1 ? x/l)2 x/l N 3 = (x/l)2 (3 ? 2x/l) N 4 = ? (1 ? x/l)(x/l)2 (2. 9) (2. 100) (2. 101) (2. 102) Substituting the shape functions from eqs(2. 99) to (2. 102) into eqs(2. 98) yields the elemental mass matrix for a pipe. ? ? 156 22l 54 ? 13l ? ? ? ? 2 2? ? 22l 4l 13l ? 3l ? Ml ? [M ]e = ? ? ? 420 ? 54 13l 156 ? 22l? ? ? ? 2 2 ? 13l ? 3l ? 22l 4l (2. 103) CHAPTER III FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 3. 1 Forming Global Sti? ness Matrix from Elemental Sti? ness Matrices Inorder to form a Global Matrix,we start with a 6Ãâ€"6 null matrix,with its six degrees of freedom being translation and rotation of each of the nodes. So our Global Sti? ness matrix looks like this: ? 0 ? ?0 ? ? ? ?0 =? ? ? 0 ? ? ? 0 ? ? 0 ? 0? ? 0? ? ? ? 0? ? ? 0? ? ? 0? ? ? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KGlobal (3. 1) 31 32 The two 4Ãâ€"4 element sti? ness matrices are: ? ? 12 6l ? 12 6l ? ? ? ? 4l2 ? 6l 2l2 ? EI ? 6l ? ? e [k1 ] = 3 ? ? l 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 6l 2l ? 6l 4l ? 12 6l ? 12 6l ? (3. 2) ? ? ? ? 2 2? 4l ? 6l 2l ? EI ? 6l ? e [k2 ] = 3 ? ? l 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 6l 2l ? 6l 4l (3. 3) We shall now build the global sti? ness matrix by inserting element 1 ? rst into the global sti? ness matrix. 6l ? 12 6l 0 0? ? 12 ? ? ? 6l 4l2 ? 6l 2l2 0 0? ? ? ? ? ? ? 12 ? 6l 12 ? l 0 0? EI ? ? = 3 ? ? l ? 6l 2 2 2l ? 6l 4l 0 0? ? ? ? ? ? 0 0 0 0 0 0? ? ? ? ? 0 0 0 0 0 0 ? ? KGlobal (3. 4) Inserting element 2 into the global sti? ness matrix ? ? 6l ? 12 6l 0 0 ? ? 12 ? ? ? 6l 4l2 ? 6l 2l2 0 0 ? ? ? ? ? ? ? EI 12 ? 6l (12 + 12) (? 6l + 6l) ? 12 6l ? ? KGlobal = 3 ? ? l ? 6l 2 2 2 2? ? 2l (? 6l + 6l) (4l + 4l ) ? 6l 2l ? ? ? ? ? 0 0 ? 12 ? 6l 12 ? 6l? ? ? ? ? 2 2 0 0 6l 2l ? 6l 4l (3. 5) 33 3. 2 Applying Boundary Conditions to Global Sti? ness Matrix for simply supported pipe with ? uid ? ow When the boundary conditions are applied to a simply supported pipe carrying ? uid, the 6Ãâ€"6 Global Sti? ess Matrix formulated in eq(3. 5) is mo di? ed to a 4Ãâ€"4 Global Sti? ness Matrix. It is as follows; Y 1 2 X L Figure 3. 1: Representation of Simply Supported Pipe Carrying Fluid ? ? 4l2 ?6l 2l2 0 KGlobalS ? ? ? ? EI 6l (12 + 12) (? 6l + 6l) 6l ? ? ? = 3 ? ? l ? 2l2 (? 6l + 6l) (4l2 + 4l2 ) 2l2 ? ? ? ? ? 2 2 0 6l 2l 4l (3. 6) Since the pipe is supported at the two ends the pipe does not de? ect causing its two translational degrees of freedom to go to zero. Hence we end up with the Sti? ness Matrix shown in eq(3. 6) 34 3. 3 Applying Boundary Conditions to Global Sti? ness Matrix for a cantilever pipe with ? id ? ow Y E, I 1 2 X L Figure 3. 2: Representation of Cantilever Pipe Carrying Fluid When the boundary conditions are applied to a Cantilever pipe carrying ? uid, the 6Ãâ€"6 Global Sti? ness Matrix formulated in eq(3. 5) is modi? ed to a 4Ãâ€"4 Global Sti? ness Matrix. It is as follows; ? (12 + 12) (? 6l + 6l) ? 12 6l ? KGlobalS ? ? ? ? ?(? 6l + 6l) (4l2 + 4l2 ) ? 6l 2l2 ? EI ? ? = 3 ? ? ? l ? ?12 ? 6l 12 ? 6l? ? ? ? 6l 2l2 ? 6l 4l2 (3. 7) Since the pipe is supported at one end the pipe does not de? ect or rotate at that end causing translational and rotational degrees of freedom at that end to go to zero.Hence we end up with the Sti? ness Matrix shown in eq(3. 8) 35 3. 4 MATLAB Programs for Assembling Global Matrices for Simply Supported and Cantilever pipe carrying ? uid In this section,we implement the method discussed in section(3. 1) to (3. 3) to form global matrices from the developed elemental matrices of a straight ? uid conveying pipe and these assembled matrices are later solved for the natural frequency and onset of instability of a cantlilever and simply supported pipe carrying ? uid utilizing MATLAB Programs. Consider a pipe of length L, modulus of elasticity E has ? uid ? wing with a velocity v through its inner cross-section having an outside diameter od,and thickness t1. The expression for critical velocity and natural frequency of the simply supported pipe carrying ? uid is given by; wn = ((3. 14)2 /L2 ) vc = (3. 14/L) (E ? I/M ) (3. 8) (3. 9) (E ? I/? A) 3. 5 MATLAB program for a simply supported pipe carrying ? uid The number of elements,density,length,modulus of elasticity of the pipe,density and velocity of ? uid ? owing through the pipe and the thickness of the pipe can be de? ned by the user. Refer to Appendix 1 for the complete MATLAB Program. 36 3. 6MATLAB program for a cantilever pipe carrying ? uid Figure 3. 3: Pinned-Free Pipe Carrying Fluid* The number of elements,density,length,modulus of elasticity of the pipe,density and velocity of ? uid ? owing through the pipe and the thickness of the pipe can be de? ned by the user. The expression for critical velocity and natural frequency of the cantilever pipe carrying ? uid is given by; wn = ((1. 875)2 /L2 ) (E ? I/M ) Where, wn = ((an2 )/L2 ) (EI/M )an = 1. 875, 4. 694, 7. 855 vc = (1. 875/L) (E ? I/? A) (3. 11) (3. 10) Refer to Appendix 2 for the complete MATLAB Program. 0 * Flow Induced Vibrat ions,Robert D.Blevins,Krieger. 1977,P 297 CHAPTER IV FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH 4. 1 Parametric Study Parametric study has been carried out in this chapter. The study is carried out on a single span steel pipe with a 0. 01 m (0. 4 in. ) diameter and a . 0001 m (0. 004 in. ) thick wall. The other parameters are: Density of the pipe ? p (Kg/m3 ) 8000 Density of the ? uid ? f (Kg/m3 ) 1000 Length of the pipe L (m) 2 Number of elements n 10 Modulus Elasticity E (Gpa) 207 of MATLAB program for the simply supported pipe with ? uid ? ow is utilized for these set of parameters with varying ? uid velocity.Results from this study are shown in the form of graphs and tables. The fundamental frequency of vibration and the critical velocity of ? uid for a simply supported pipe 37 38 carrying ? uid are: ? n 21. 8582 rad/sec vc 16. 0553 m/sec Table 4. 1: Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity Velocity of Fluid(v) Ve locity Ratio(v/vc) 0 2 4 6 8 10 12 14 16. 0553 0 0. 1246 0. 2491 0. 3737 0. 4983 0. 6228 0. 7474 0. 8720 1 Frequency(w) 21. 8806 21. 5619 20. 5830 18. 8644 16. 2206 12. 1602 3. 7349 0. 3935 0 Frequency Ratio(w/wn) 1 0. 9864 0. 9417 0. 8630 0. 7421 0. 5563 0. 709 0. 0180 0 39 Figure 4. 1: Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity The fundamental frequency of vibration and the critical velocity of ? uid for a Cantilever pipe carrying ? uid are: ? n 7. 7940 rad/sec vc 9. 5872 m/sec 40 Figure 4. 2: Shape Function Plot for a Cantilever Pipe with increasing Flow Velocity Table 4. 2: Reduction of Fundamental Frequency for a Pinned-Free Pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 2 4 6 8 9 9. 5872 0 0. 2086 0. 4172 0. 6258 0. 8344 0. 9388 1 Frequency(w) 7. 7940 7. 5968 6. 9807 5. 8549 3. 825 1. 9897 0 Frequency Ratio(w/wn) 1 0. 9747 0. 8957 0. 7512 0. 4981 0. 2553 0 41 Figure 4. 3: Reduction of Fundamental Fr equency for a Cantilever Pipe with increasing Flow Velocity CHAPTER V FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH E, I v L Figure 5. 1: Representation of Tapered Pipe Carrying Fluid 5. 1 Tapered Pipe Carrying Fluid Consider a pipe of length L, modulus of elasticity E. A ? uid ? ows through the pipe at a velocity v and density ? through the internal pipe cross-section. As the ? uid ? ows through the de? ecting pipe it is accelerated, because of the changing curvature 42 43 f the pipe and the lateral vibration of the pipeline. The vertical component of ? uid pressure applied to the ? uid element and the pressure force F per unit length applied on the ? uid element by the tube walls oppose these accelerations. The input parameters are given by the user. Density of the pipe ? p (Kg/m3 ) 8000 Density of the ? uid ? f (Kg/m3 ) 1000 Length of the pipe L (m) 2 Number of elements n 10 Modulus Elasticity E (Gpa) 207 of For these user de? ned values we introduce a taper in the pipe so that the material property and the length of the pipe with the taper or without the taper remain the same.This is done by keeping the inner diameter of the pipe constant and varying the outer diameter. Refer to ? gure (5. 2) The pipe tapers from one end having a thickness x to the other end having a thickness Pipe Carrying Fluid 9. 8mm OD= 10 mm L=2000 mm x mm t =0. 01 mm ID= 9. 8 mm Tapered Pipe Carrying Fluid Figure 5. 2: Introducing a Taper in the Pipe Carrying Fluid of t = 0. 01mm such that the volume of material is equal to the volume of material 44 for a pipe with no taper. The thickness x of the tapered pipe is now calculated: From ? gure(5. 2) we have †¢ Outer Diameter of the pipe with no taper(OD) 10 mm †¢ Inner Diameter of the pipe(ID) 9. mm †¢ Outer Diameter of thick end of the Tapered pipe (OD1 ) †¢ Length of the pipe(L) 2000 mm †¢ Thickness of thin end of the taper(t) 0. 01 mm †¢ Thickness of thick end of the taper x mm Volume of th e pipe without the taper: V1 = Volume of the pipe with the taper: ? ? L ? 2 V2 = [ (OD1 ) + (ID + 2t)2 ] ? [ (ID2 )] 4 4 3 4 (5. 2) ? (OD2 ? ID2 )L 4 (5. 1) Since the volume of material distributed over the length of the two pipes is equal We have, V1 = V2 (5. 3) Substituting the value for V1 and V2 from equations(5. 1) and (5. 2) into equation(5. 3) yields ? ? ? L ? 2 (OD2 ? ID2 )L = [ (OD1 ) + (ID + 2t)2 ] ? (ID2 )] 4 4 4 3 4 The outer diameter for the thick end of the tapered pipe can be expressed as (5. 4) OD1 = ID + 2x (5. 5) 45 Substituting values of outer diameter(OD),inner diameter(ID),length(L) and thickness(t) into equation (5. 6) yields ? 2 ? ? 2000 ? (10 ? 9. 82 )2000 = [ (9. 8 + 2x)2 + (9. 8 + 0. 02)2 ] ? [ (9. 82 )] 4 4 4 3 4 Solving equation (5. 6) yields (5. 6) x = 2. 24mm (5. 7) Substituting the value of thickness x into equation(5. 5) we get the outer diameter OD1 as OD1 = 14. 268mm (5. 8) Thus, the taper in the pipe varies from a outer diameters of 14. 268 mm to 9 . 82 mm. 46The following MATLAB program is utilized to calculate the fundamental natural frequency of vibration for a tapered pipe carrying ? uid. Refer to Appendix 3 for the complete MATLAB program. Results obtained from the program are given in table (5. 1) Table 5. 1: Reduction of Fundamental Frequency for a Tapered pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 20 40 60 80 100 103. 3487 0 0. 1935 0. 3870 0. 5806 0. 7741 0. 9676 1 Frequency(w) 40. 8228 40. 083 37. 7783 33. 5980 26. 5798 10. 7122 0 Frequency Ratio(w/wn) . 8100 0. 7784 0. 7337 0. 6525 0. 5162 0. 2080 0The fundamental frequency of vibration and the critical velocity of ? uid for a tapered pipe carrying ? uid obtained from the MATLAB program are: ? n 51. 4917 rad/sec vc 103. 3487 m/sec CHAPTER VI RESULTS AND DISCUSSIONS In the present work, we have utilized numerical method techniques to form the basic elemental matrices for the pinned-pinned and pinned-free pipe carrying ? uid. Matlab programs have been developed and utilized to form global matrices from these elemental matrices and fundamental frequency for free vibration has been calculated for various pipe con? gurations and varying ? uid ? ow velocities.Consider a pipe carrying ? uid having the following user de? ned parameters. E, I v L v Figure 6. 1: Representation of Pipe Carrying Fluid and Tapered Pipe Carrying Fluid 47 48 Density of the pipe ? p (Kg/m3 ) 8000 Density of the ? uid ? f (Kg/m3 ) 1000 Length of the pipe L (m) 2 Number of elements n 10 Modulus Elasticity E (Gpa) 207 of Refer to Appendix 1 and Appendix 3 for the complete MATLAB program Parametric study carried out on a pinned-pinned and tapered pipe for the same material of the pipe and subjected to the same conditions reveal that the tapered pipe is more stable than a pinned-pinned pipe.Comparing the following set of tables justi? es the above statement. The fundamental frequency of vibration and the critical velocity of ? uid for a tapered and a pinned-pinned pipe carrying ? uid are: ? nt 51. 4917 rad/sec ? np 21. 8582 rad/sec vct 103. 3487 m/sec vcp 16. 0553 m/sec Table 6. 1: Reduction of Fundamental Frequency for a Tapered Pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 20 40 60 80 100 103. 3487 0 0. 1935 0. 3870 0. 5806 0. 7741 0. 9676 1 Frequency(w) 40. 8228 40. 083 37. 7783 33. 5980 26. 5798 10. 7122 0 Frequency Ratio(w/wn) 0. 8100 0. 7784 0. 7337 0. 6525 0. 5162 0. 2080 0 9 Table 6. 2: Reduction of Fundamental Frequency for a Pinned-Pinned Pipe with increasing Flow Velocity Velocity of Fluid(v) Velocity Ratio(v/vc) 0 2 4 6 8 10 12 14 16. 0553 0 0. 1246 0. 2491 0. 3737 0. 4983 0. 6228 0. 7474 0. 8720 1 Frequency(w) 21. 8806 21. 5619 20. 5830 18. 8644 16. 2206 12. 1602 3. 7349 0. 3935 0 Frequency Ratio(w/wn) 1 0. 9864 0. 9417 0. 8630 0. 7421 0. 5563 0. 1709 0. 0180 0 The fundamental frequency for vibration and critical velocity for the onset of instability in tapered pipe is approxim ately three times larger than the pinned-pinned pipe,thus making it more stable. 50 6. 1 Contribution of the Thesis Developed Finite Element Model for vibration analysis of a Pipe Carrying Fluid. †¢ Implemented the above developed model to two di? erent pipe con? gurations: Simply Supported and Cantilever Pipe Carrying Fluid. †¢ Developed MATLAB Programs to solve the Finite Element Models. †¢ Determined the e? ect of ? uid velocities and density on the vibrations of a thin walled Simply Supported and Cantilever pipe carrying ? uid. †¢ The critical velocity and natural frequency of vibrations were determined for the above con? gurations. †¢ Study was carried out on a variable wall thickness pipe and the results obtained show that the critical ? id velocity can be increased when the wall thickness is tapered. 6. 2 Future Scope †¢ Turbulence in Two-Phase Fluids In single-phase ? ow,? uctuations are a direct consequence of turbulence developed in ? uid, whe reas the situation is clearly more complex in two-phase ? ow since the ? uctuation of the mixture itself is added to the inherent turbulence of each phase. †¢ Extend the study to a time dependent ? uid velocity ? owing through the pipe. BIBLIOGRAPHY [1] Doods. H. L and H. Runyan †E? ects of High-Velocity Fluid Flow in the Bending Vibrations and Static Divergence of a Simply Supported Pipe†.National Aeronautics and Space Administration Report NASA TN D-2870 June(1965). [2] Ashley,H and G. Haviland †Bending Vibrations of a Pipe Line Containing Flowing Fluid†. J. Appl. Mech. 17,229-232(1950). [3] Housner,G. W †Bending Vibrations of a Pipe Line Containing Flowing Fluid†. J. Appl. Mech. 19,205-208(1952). [4] Long. R. H †Experimental and Theoretical Study of Transverse Vibration of a tube Containing Flowing Fluid†. J. Appl. Mech. 22,65-68(1955). [5] Liu. H. S and C. D. Mote †Dynamic Response of Pipes Transporting Fluids†. J. Eng. for Industry 96,591-596(1974). 6] Niordson,F. I. N †Vibrations of a Cylinderical Tube Containing Flowing Fluid†. Trans. Roy. Inst. Technol. Stockholm 73(1953). [7] Handelman,G. H †A Note on the transverse Vibration of a tube Containing Flowing Fluid†. Quarterly of Applied Mathematics 13,326-329(1955). [8] Nemat-Nassar,S. S. N. Prasad and G. Herrmann †Destabilizing E? ect on VelocityDependent Forces in Nonconservative Systems†. AIAA J. 4,1276-1280(1966). 51 52 [9] Naguleswaran,S and C. J. H. Williams †Lateral Vibrations of a Pipe Conveying a Fluid†. J. Mech. Eng. Sci. 10,228-238(1968). [10] Herrmann. G and R. W.Bungay †On the Stability of Elastic Systems Subjected to Nonconservative Forces†. J. Appl. Mech. 31,435-440(1964). [11] Gregory. R. W and M. P. Paidoussis †Unstable Oscillations of Tubular Cantilevers Conveying Fluid-I Theory†. Proc. Roy. Soc. (London). Ser. A 293,512-527(1966). [12] S. S. Rao †The Finite Element Method in Engineering†. Pergamon Press Inc. 245294(1982). [13] Michael. R. Hatch †Vibration Simulation Using Matlab and Ansys†. Chapman and Hall/CRC 349-361,392(2001). [14] Robert D. Blevins †Flow Induced Vibrations†. Krieger 289,297(1977). Appendices 53 54 0. 1 MATLAB program for Simply Supported Pipe Carrying FluidMATLAB program for Simply Supported Pipe Carrying Fluid. % The f o l l o w i n g MATLAB Program c a l c u l a t e s t h e Fundamental % N a t u r a l f r e q u e n c y o f v i b r a t i o n , f r e q u e n c y r a t i o (w/wn) % and v e l o c i t y r a t i o ( v / vc ) , f o r a % simply supported pipe carrying f l u i d . % I n o r d e r t o perform t h e above t a s k t h e program a s s e m b l e s % E l e m e n t a l S t i f f n e s s , D i s s i p a t i o n , and I n e r t i a m a t r i c e s % t o form G l o b a l M a t r i c e s which are used t o c a l c u l a t e % Fundamental N a t u r a l % Frequency w . lc ; n um elements =input ( ’ Input number o f e l e m e n t s f o r beam : ’ ) ; % num elements = The u s e r e n t e r s t h e number o f e l e m e n t s % i n which t h e p i p e % has t o be d i v i d e d . n=1: num elements +1;% Number o f nodes ( n ) i s e q u a l t o number o f %e l e m e n t s p l u s one n o d e l =1: num elements ; node2 =2: num elements +1; max nodel=max( n o d e l ) ; max node2=max( node2 ) ; max node used=max( [ max nodel max node2 ] ) ; mnu=max node used ; k=zeros (2? mnu ) ;% C r e a t i n g a G l o b a l S t i f f n e s s Matrix o f z e r o s 55 m =zeros (2? nu ) ;% C r e a t i n g G l o b a l Mass Matrix o f z e r o s x=zeros (2? mnu ) ;% C r e a t i n g G l o b a l Matrix o f z e r o s % f o r t h e f o r c e t h a t conforms f l u i d % to the curvature of the % pipe d=zeros (2? mnu ) ;% C r e a t i n g G l o b a l D i s s i p a t i o n Matrix o f z e r o s %( C o r i o l i s Component ) t=num elements ? 2 ; L=2; % T o t a l l e n g t h o f t h e p i p e i n meters l=L/ num elements ; % Length o f an e l e m e n t t1 =. 0001; od = . 0 1 ; i d=od? 2? t 1 % t h i c k n e s s o f t h e p i p e i n meter % outer diameter of the pipe % inner diameter of the pipeI=pi ? ( od? 4? i d ? 4)/64 % moment o f i n e r t i a o f t h e p i p e E=207? 10? 9; roh =8000; rohw =1000; % Modulus o f e l a s t i c i t y o f t h e p i p e % Density of the pipe % d e n s i t y o f water ( FLuid ) M =roh ? pi ? ( od? 2? i d ? 2)/4 + rohw? pi ? . 2 5 ? i d ? 2 ; % mass per u n i t l e n g t h o f % the pipe + f l u i d rohA=rohw? pi ? ( . 2 5 ? i d ? 2 ) ; l=L/ num elements ; v=0 % v e l o c i t y o f t h e f l u i d f l o w i n g t h r o u g h t h e p i p e %v =16. 0553 z=rohA/M i=sqrt ( ? 1); wn= ( ( 3 . 1 4 ) ? 2 /L? 2)? sqrt (E? I /M) % N a t u r a l Frequency vc =(3. 14/L)? sqrt (E?I /rohA ) % C r i t i c a l V e l o c i t y 56 % Assembling G l o b a l S t i f f n e s s , D i s s i p a t i o n and I n e r t i a M a t r i c e s for j =1: nu m elements d o f 1 =2? n o d e l ( j ) ? 1; d o f 2 =2? n o d e l ( j ) ; d o f 3 =2? node2 ( j ) ? 1; d o f 4 =2? node2 ( j ) ; % S t i f f n e s s Matrix Assembly k ( dof1 , d o f 1 )=k ( dof1 , d o f 1 )+ (12? E? I / l ? 3 ) ; k ( dof2 , d o f 1 )=k ( dof2 , d o f 1 )+ (6? E? I / l ? 2 ) ; k ( dof3 , d o f 1 )=k ( dof3 , d o f 1 )+ (? 12? E? I / l ? 3 ) ; k ( dof4 , d o f 1 )=k ( dof4 , d o f 1 )+ (6? E? I / l ? 2 ) ; k ( dof1 , d o f 2 )=k ( dof1 , d o f 2 )+ (6? E?I / l ? 2 ) ; k ( dof2 , d o f 2 )=k ( dof2 , d o f 2 )+ (4? E? I / l ) ; k ( dof3 , d o f 2 )=k ( dof3 , d o f 2 )+ (? 6? E? I / l ? 2 ) ; k ( dof4 , d o f 2 )=k ( dof4 , d o f 2 )+ (2? E? I / l ) ; k ( dof1 , d o f 3 )=k ( dof1 , d o f 3 )+ (? 12? E? I / l ? 3 ) ; k ( dof2 , d o f 3 )=k ( dof2 , d o f 3 )+ (? 6? E? I / l ? 2 ) ; k ( dof3 , d o f 3 )=k ( dof3 , d o f 3 )+ (12? E? I / l ? 3 ) ; k ( dof4 , d o f 3 )=k ( dof4 , d o f 3 )+ (? 6? E? I / l ? 2 ) ; k ( dof1 , d o f 4 )=k ( dof1 , d o f 4 )+ (6? E? I / l ? 2 ) ; k ( dof2 , d o f 4 )=k ( dof2 , d o f 4 )+ (2? E? I / l ) ; k ( dof3 , d o f 4 )=k ( dof3 , d o f 4 )+ (? ? E? I / l ? 2 ) ; k ( dof4 , d o f 4 )=k ( dof4 , d o f 4 )+ (4? E? I / l ) ; % 57 % Matrix a s s e m b l y f o r t h e second term i e % f o r t h e f o r c e t h a t conforms % f l u i d to the curvature of the pipe x ( dof1 , d o f 1 )=x ( dof1 , d o f 1 )+ ( ( 3 6 ? rohA? v ? 2)/30? l ) ; x ( dof2 , d o f 1 )=x ( dof2 , d o f 1 )+ ( ( 3 ? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 1 )=x ( dof3 , d o f 1 )+ (( ? 36? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 1 )=x ( dof4 , d o f 1 )+ ( ( 3 ? rohA? v ? 2)/30? l ) ; x ( dof1 , d o f 2 )=x ( dof1 , d o f 2 )+ ( ( 3 ? ohA? v ? 2)/30? l ) ; x ( dof2 , d o f 2 )=x ( dof2 , d o f 2 )+ ( ( 4 ? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 2 )=x ( dof3 , d o f 2 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 2 )=x ( dof4 , d o f 2 )+ (( ? 1? rohA? v ? 2)/30? l ) ; x ( dof1 , d o f 3 )=x ( dof1 , d o f 3 )+ (( ? 36? rohA? v ? 2)/30? l ) ; x ( dof2 , d o f 3 )=x ( dof2 , d o f 3 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 3 )=x ( dof3 , d o f 3 )+ ( ( 3 6 ? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 3 )=x ( dof4 , d o f 3 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof1 , d o f 4 )=x ( dof1 , d o f 4 )+ ( ( 3 ? rohA? v ? 2)/30? ) ; x ( dof2 , d o f 4 )=x ( dof2 , d o f 4 )+ (( ? 1? rohA? v ? 2)/30? l ) ; x ( dof3 , d o f 4 )=x ( dof3 , d o f 4 )+ (( ? 3? rohA? v ? 2)/30? l ) ; x ( dof4 , d o f 4 )=x ( dof4 , d o f 4 )+ ( ( 4 ? rohA? v ? 2)/30? l ) ; % % D i s s i p a t i o n Matrix Assembly d ( dof1 , d o f 1 )=d ( dof1 , d o f 1 )+ (2? ( ? 30? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 1 )=d ( dof2 , d o f 1 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; d ( dof3 , d o f 1 )=d ( dof3 , d o f 1 )+ ( 2 ? ( 3 0 ? rohA? v ) / 6 0 ) ; 58 d ( dof4 , d o f 1 )=d ( dof4 , d o f 1 )+ (2? ( ? 6? rohA? ) / 6 0 ) ; d ( dof1 , d o f 2 )=d ( dof1 , d o f 2 )+ (2? ( ? 6? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 2 )=d ( dof2 , d o f 2 )+ ( 2 ? ( 0 ? ro hA? v ) / 6 0 ) ; d ( dof3 , d o f 2 )=d ( dof3 , d o f 2 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; d ( dof4 , d o f 2 )=d ( dof4 , d o f 2 )+ (2? ( ? 1? rohA? v ) / 6 0 ) ; d ( dof1 , d o f 3 )=d ( dof1 , d o f 3 )+ (2? ( ? 30? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 3 )=d ( dof2 , d o f 3 )+ (2? ( ? 6? rohA? v ) / 6 0 ) ; d ( dof3 , d o f 3 )=d ( dof3 , d o f 3 )+ ( 2 ? ( 3 0 ? rohA? v ) / 6 0 ) ; d ( dof4 , d o f 3 )=d ( dof4 , d o f 3 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; ( dof1 , d o f 4 )=d ( dof1 , d o f 4 )+ ( 2 ? ( 6 ? rohA? v ) / 6 0 ) ; d ( dof2 , d o f 4 )=d ( dof2 , d o f 4 )+ ( 2 ? ( 1 ? rohA? v ) / 6 0 ) ; d ( dof3 , d o f 4 )=d ( dof3 , d o f 4 )+ (2? ( ? 6? rohA? v ) / 6 0 ) ; d ( dof4 , d o f 4 )=d ( dof4 , d o f 4 )+ ( 2 ? ( 0 ? rohA? v ) / 6 0 ) ; % % I n e r t i a Matrix Assembly m( dof1 , d o f 1 )=m( dof1 , d o f 1 )+ (156? M? l / 4 2 0 ) ; m( dof2 , d o f 1 )=m( dof2 , d o f 1 )+ (22? l ? 2? M/ 4 2 0 ) ; m( dof3 , d o f 1 )=m( dof3 , d o f 1 )+ (54? l ? M/ 4 2 0 ) ; m( d of4 , d o f 1 )=m( dof4 , d o f 1 )+ (? 3? l ? 2? M/ 4 2 0 ) ; m( dof1 , d o f 2 )=m( dof1 , d o f 2 )+ (22? l ? 2? M/ 4 2 0 ) ; m( dof2 , d o f 2 )=m( dof2 , d o f 2 )+ (4? M? l ? 3 / 4 2 0 ) ; m( dof3 , d o f 2 )=m( dof3 , d o f 2 )+ (13? l ? 2? M/ 4 2 0 ) ; m( dof4 , d o f 2 )=m( dof4 , d o f 2 )+ (? 3? M? l ? 3 / 4 2 0 ) ; 59 m( dof1 , d o f 3 )=m( dof1 , d o f 3 )+ (54? M? l / 4 2 0 ) ; m( dof2 , d o f 3 )=m( dof2 , d o f 3 )+ (13? l ? 2? M/ 4 2 0 ) ; m( dof3 , d o f 3 )=m( dof3 , d o f 3 )+ (156? l ? M/ 4 2 0 ) ; m( dof4 , d o f 3 )=m( dof4 , d o f 3 )+ (? 22? l ? 2? M/ 4 2 0 ) ; m( dof1 , d o f 4 )=m( dof1 , d o f 4 )+ (? 13? l ? 2?M/ 4 2 0 ) ; m( dof2 , d o f 4 )=m( dof2 , d o f 4 )+ (? 3? M? l ? 3 / 4 2 0 ) ; m( dof3 , d o f 4 )=m( dof3 , d o f 4 )+ (? 22? l ? 2? M/ 4 2 0 ) ; m( dof4 , d o f 4 )=m( dof4 , d o f 4 )+ (4? M? l ? 3 / 4 2 0 ) ; end k ( 1 : 1 , : ) = [ ] ;% A p p l y i n g Boundary c o n d i t i o n s k(: ,1:1)=[]; k ( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; k ( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; k x(1:1 ,:)=[]; x(: ,1:1)=[]; x ( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; x ( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; x; % G l o b a l Matrix f o r t h e % Force t h a t conforms f l u i d t o p i p e x1=? d(1:1 ,:)=[]; d(: ,1:1)=[]; d ( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; % G l o b a l S t i f f n e s s Matrix 60 d ( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; d d1=(? d ) Kg lobal=k+10? x1 ; m( 1 : 1 , : ) = [ ] ; m( : , 1 : 1 ) = [ ] ; m( ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) , : ) = [ ] ; m( : , ( 2 ? mnu? 2 ) : ( 2 ? mnu? 2 ) ) = [ ] ; m; eye ( t ) ; zeros ( t ) ; H=[? inv (m) ? ( d1 ) ? inv (m)? Kglobal ; eye ( t ) zeros ( t ) ] ; Evalue=eig (H) % E i g e n v a l u e s v r a t i o=v/ vc % V e l o c i t y Ratio % G l o b a l Mass Matrix % G l o b a l D i s s i p a t i o nMatrix i v 2=imag ( Evalue ) ; i v 2 1=min( abs ( i v 2 ) ) ; w1 = ( i v 2 1 ) wn w r a t i o=w1/wn vc % Frequency Ratio % Fundamental N a t u r a l f r e q u e n c y 61 0. 2 MATLAB Program for Cantilever Pipe Carrying Fluid MATLAB Program for Cantilever Pipe Carrying Fluid. % The f o l l o w i n g MATLAB Program c a l c u l a t e s t h e Fundamental % N a t u r a l f r e q u e n c y o f v i b r a t i o n , f r e q u e n c y r a t i o (w/wn) % and v e l o c i t y r a t i o ( v / vc ) , f o r a c a n t i l e v e r p i p e % carrying f l u i d . I n o r d e r t o perform t h e above t a s k t h e program a s s e m b l e s % E l e m e n t a l S t i f f n e s s , D i s s i p a t i o n , and I n e r t i a m a t r i c e s % t o form G l o b a l M a t r i c e s which are used % t o c a l c u l a t e Fundamental N a t u r a l % Frequency w . clc ; num elements =input ( ’ Input number o f e l e m e n t s f o r Pipe : ’ ) ; % num elements = The u s e r e n t e r s t h e number o f e l e m e n t s % i n which t h e p i p e has t o be d i v i d e d . =1: num elements +1;% Number o f nodes ( n ) i s % e q u a l t o num ber o f e l e m e n t s p l u s one n o d e l =1: num elements ; % Parameters used i n t h e l o o p s node2 =2: num elements +1; max nodel=max( n o d e l ) ; max node2=max( node2 ) ; max node used=max( [ max nodel max node2 ] ) ; mnu=max node used ; k=zeros (2? mnu ) ;% C r e a t i n g a G l o b a l S t i f f n e s s Matrix o f z e r o s 62 m =zeros (2? mnu ) ;% C r e a t i n g G l o b a l Mass Matrix o f z e r o s