Capital Punishment is Murder Essay example -- Argumentative Persuasive

The death penalty is Murder   The death penalty is state-authorized, planned murder.  It is ethically, morally, socially off-base.   Murder is the deliberate killing of one individual by another.  Capital discipline ends the life of one individual and utilizations another, the killer, to do it.  In the province of Indiana, the superintendent of the state jail goes about as the executioner.  The killing happens before the hour of dawn on a fixed day.  On that day, the superintendent, killer, flips a switch sending roughly 2,800 volts of electrical flow into the body of the sentenced detainee, in this manner finishing the detainee's life.  Upon consummation of the execution, one individual's life is purposefully finished by the demonstration of another.  The distinction, in any case, is that this homicide is excused by the state.  The state's Supreme Court, Appeals Courts, Superior Courts, and examiners all assume a significant job in overlooking the utilization of the death penalty.   Numerous precautionary measures are taken to guarantee that all fair treatment rights are given to the wrongdoer; nonetheless, I wonder how often we have executed blameless people.  In June 1992, in the territory of Virginia, a man was executed for the ruthless assault and murder of his sister-in-law.  Throughout his multi year remain waiting for capital punishment, he asserted he was not blameworthy of this crime.  We may never really know reality, yet his life was ended.  If his honesty could be demonstrated today, his discipline couldn't be reversed.  Without an uncertainty, we have executed guiltless individuals in this country.  truth be told, Hugo Bedau and Michael Radelet announced that 350 wrongly indicted people have been sent to death row. ... ...e the jail's meeting space for his daddy.  How would you tell this valuable, blameless youngster that his daddy is going to be slaughtered in an electric chair?  Who do you let him know is answerable for his daddy's death?  How would you comfort a mother as she sits sobbing the minutes prior to her solitary child is to be executed?  How, I wonder, do these individuals feel about equity being served?  In my inclusion with prisoners waiting for capital punishment, I consider the to be of their families as they experience the intrigue's procedure, trusting and imploring that their cherished one's sentence will be overturned.  The demise experienced by this arrangement of casualties is a moderate, since a long time ago, drawn out death.   Murder and the death penalty are synonymous.  Both comprise of the purposeful slaughtering of a human being.  Both are ethically, morally, and socially off-base.  

Mayan Civilization Advantages and Effect on America

Amayrani Mateo May 30,2012 KIPP-2016-NEUSocial Study Mayan Research Paper Did you realize that Mayan human progress left back wonderful tourist spots they made with their trend setting innovation? The Mayan spread all through Mexico, Belize, El Salvador, Honduras and Guatemala. They Mayans had truly trend setting innovation to take a gander at the sky and have the option to make schedules. They had the option to watch the sky and make deductions. The Mayan human progress was not the same as some other civilization.Mayan developments ought to be educated in schools on account of their effect on today’s residents, trend setting innovation and understudies ought to find out about another progress that is truly known yet not instructed in schools thus that individuals considering Mayans find out about the legacy. Today, the galactic and innovative advances originated from the Mayan progress. Space experts from the Mayan human progress made schedules that are increasingly precise t hen those of present day society. They have around eighteen unique schedules that was made on the development of the moon, the planets and the sun.In request to get this going, they additionally made numerical hypotheses. With these hypotheses, they had the option to follow the way of the planets. Mayan developments have a large number of archeological destinations across Belize, Honduras, Guatemala, and Southern Mexico. (www. authenticmaya. com) There is an association between the Latino/Hispanics understudy in Massachusetts and in the Mayan development. There is 15. 4% of individuals in the province of Massachusetts who distinguish themselves as Latinos/Hispanic. â€Å"Mayan development arrived at its stature somewhere in the range of 300 and 900 A. D†¦During this time, Mayan culture spread over quite a bit of Mesoamerica, including some portion of present-day Sothern Mexico, Belize, a large portion of Guatemala, and parts of Honduras and El Salvador. † (Bower and Lobd ell) There are things that we eat here that began in Mayan human advancement. We eat things like maize, maize cobs and corn cob and different veggies. (www. foodtimeline. organization) With those things we made things like Tamales or Tortilla, which were acclaimed in Mayan human advancement. There are a couple Mexican and Central American eateries around and they all began from the impact they had on Lynn. What befell the Mayan Civilization?Why did they vanish? Mayan human progress is a riddle in light of the fact that nobody realizes how could they vanish or what befell them. Finding out about Mayan progress will help with school things in light of the fact that your insight will develop. With these inquiries understudies can research further and discover more data o the human progress. Every one of these inquiries keep individuals pondering and it can begin drawing in conversations among others. Having the ability to take part in a conversation is an incredible expertise, addition ally in the event that you are pondering every one of these inquiries you will most likely do some examination on the human advancement and you will know you more than other.Mayan progress must be educated in schools in Massachusetts. Present day society can become familiar with mechanical and cosmic advances on the grounds that the Mayan human advancement has affected us as of now with certain advances. About 15% of understudies in Massachusetts are Hispanic/Latinos. They have numerous likenesses with individuals from the Mayan civic establishments. Mayan civic establishments showed us a great deal of things and they helped give us thoughts to do things certain ways. Thoughts like schedules originated from them.

SCRUM

SCRUM SCRUM is an informal product development methodology, used to guide the product from design to completion. The process advances incrementally, and is often iterative. The guidelines that define the process are very basic and product development occurs in small pieces. Each completed piece is built upon by the next stage. The process remains flexible, since an important principle is the understanding that the customer requirements are fluid and ever changing. This means that a stage completed may need to be revisited occasionally and repeatedly.This process challenges the traditional product development approach, which is usually sequential in nature with requirements locked down in the initial goal setting stages. Instead, the aim is address new and unpredictable challenges throughout the process and allow the development team to efficiently deliver deadlines and respond to new challenges. © Shutterstock.com | SakaidasanIn this article, we look at 1) SCRUM values, 2) history of  SCRUM, 3)  how  SCRUM works, 4) major roles, 5) advantages of  SCRUM, 6) disadvantages of  SCRUM, 7) benefits of  SCRUM, and 8) challenges with  SCRUM.SCRUM  VALUESSCRUM is one of the Agile software development methodologies which are all based on the same principles as mentioned already. The Agile Movement has revolutionized modern software development and engineering through its values principles, champions and philosophies. SCRUM remains the most widely recognized and used of these methodologies and the Agile principles directly govern it. These are:Individuals and Interactions over Processes and ToolsThough necessary, processes and tools will be useless if the team does not have a strong relationship of trust and communications. It is the team’s responsibility to identify challenges and resolve them as well as to work closely with other teams within the organization to work on issues bey ond immediate team control.Working Software over Comprehensive DocumentationFor SCRUM to be successful, there needs to be a functional working result at the end of each incremental step. Though necessary design, analysis and testing needs to be properly documented, it is critical for the product to be ready to feed into the next stage of development.Customer Collaboration over Contract NegotiationIt is vital to involve the customer as part of the solution and the team and not view them as just a means to financial reward. The SCRUM product owner needs to act as a bridge between the team and the customer and create a strong collaborative environment.Response to Change over Following a PlanAll necessary information regarding the product and progress is available for the entire team to view and work on. Any problems that are creating a backlog or are emerging need to be discussed openly and worked on immediately. This is a vital element to the success of the process.These core Agile pr inciples then develop further into the core SCRUM Values, which are:Focus â€" The team focuses on only the key issues at one time and works towards delivering timely resultsCourage â€" Support, collaboration and teamwork allows the team to courageously take on greater challengesOpenness â€" The open and supportive environment allows discussion and sharing of concerns, allowing issues to be resolved quickly and efficientlyCommitment â€" The collaborative way of work allows team members to feel in control of their own areas and strengthens their commitment to the goalRespect â€" Shared successes and joint failures encourage mutual respect and an appreciation of each other.HISTORY OF SCRUMThe first definition of SCRUM came from Hirotaka Takeuchi and Ikujiro Nonaka in 1986. They described it as means to increase speed and flexibility in commercial product development. They used the terms holistic or rugby approach to describe it. In the game of rugby, scrum is used to describe the proce ss where the game begins again after a small violation of the rules. The methodology was first employed by Ken Schwaber at his company (Advanced Development Methods) in the 1990s. Eventually the term was standardized when Jeff Sutherland, John Scumniotales and Jeff McKenna worked on it at Easel Corporation. Schwaber and Sutherland worked together to combine their papers and experiences into the body of knowledge that is SCRUM.The Scrum Alliance and Scrum.org were formed to provide certifications and work on the methodology to improve quality and effectiveness.HOW SCRUM WORKSThe Scrum framework is an orderly and organized set of basic principles which allow the team to focus on core product development without being bogged down with non-essential tasks and activities.PhasesThe Scrum process can be broken down into three major phases.1. PlanningAt this point, work is done on basic project planning and rudimentary design decisions.2. Sprint CycleThe basic unit in the Scrum process is t he sprint. A sprint is one iteration of a specific duration. With basic planning complete, work begins on product development through an iterative cycle of generally three or four weeks. Sprint cycles are a repetitive process, and continue till the development process concludes. A basic principle of the Scrum process dictates that the product demonstrated at the end of each sprint be in complete working condition.The Sprint cycle may involve a number of meetings to ensure collaboration and encourage communication. These are:Sprint Planning Meeting â€" Here, the team decides the work to be done in a particular sprint cycle. The work to be completed is identified and the process for getting it done is identified and communicated. This meeting should not last more than 8 hours.Daily Scrum Meeting â€" These are conducted every day to encourage communication and ensure that everyone is on the same page. Specific rules govern this meeting such as team preparedness, punctuality, fixed meet ing location and time and fixed meeting duration.Sprint Review Meeting â€" In this meeting, results of the current sprint cycle are demonstrated along with a review of the process. Any work left incomplete is also discussed. If changes need to be made to any process step, then those are discussed and incorporated. This meeting also has a time limitSprint Retrospective â€" In this meeting, the concluded sprint is discussed among the team members with an aim to work on continuous process improvement. Best practices may be noted as well as areas of improvement.  3. ClosureOnce all required sprint cycles are concluded, the project itself is brought to a closure and the product prepared for release.MAJOR ROLESThe Scrum team consists of three core roles and may also include several supporting roles. Scrum only defines core roles however, as these are the individuals dedicated to the process and tasked with actually producing the product being developed.Product OwnerThe product owner is th e individual closest to the business end of the project. They are responsible for creating a bridge between the development team and all relevant stakeholders and have the responsibility of satisfying all relevant parties.This complicated task is achieved by managing the flow of work and identifying what areas and items need to be worked on in a particular sprint. This information is contained in a product backlog, which the product owner will maintain and communicate to the team to ensure clear understanding of priorities and roles.Since Scrum is centered on a close knit team, everyone has the responsibility to be productive and ask relevant questions to ensure the best possible outcome. Despite this support, this is a unique role and needs to be taken on by one nominated individual.A major responsibility of the product owner is to create a clear channel of communication. Expectations and priorities need to be conveyed from the stakeholders to the team and back from the team to the stakeholders. They will be responsible for demonstrations to stakeholders, announcement of important releases, progress reports on team status and milestones, updates to stakeholders on the process, and negotiations regarding priority shifts, funding and timelines.The product owner needs to be empathetic and should be able to speak the language of different stakeholders, given differing roles, backgrounds and levels of understanding.Development TeamThe development team is cross functional and made up of a variety of backgrounds and skill sets. The team may consist of between 3 to 9 people and these are the people who perform the actual development work on the product. This ranges from initial analysis to design, technical communications and testing among various other roles.The development team needs to be self-organized and dedicated to the project full time. The team has the task to deliver on each sprint cycle goal as planned and agreed upon. A list of tasks is drawn up and the team assesses how much can be completed in one cycle and what method will be used to reach this development goal.Scrum MasterThe final core role is that of a Scrum Master, who is a member tasked with supporting and helping team members follow processes. This person needs to be well versed in the Scrum methodology and terminology and should be able to impart this knowledge to others.The Scrum Master may also have the responsibility to remove roadblocks from the team’s path. These may be external to the team or any issues within the team. Despite this onus, he needs to foster a sense of self sufficiency within the team that allows them to address any issues and resolve them.Interestingly, this is not a traditional team leader role but more of a buffer between the team and distracting external influences. This buffer system helps ensure that a pure scrum framework remains in place, is understood by all and works smoothly to achieve each sprint goal.ADVANTAGES OF SCRUMThere are many a dvantages of the Scrum methodology. Some of these are:If the nature of the product allows, each sprint cycle results in a complete product that may be ready to market. This may help a company operating in a competitive industry to reduce time to marketThe sprint review requires product demonstrations and review at the end of each sprint cycle. This is a built in step by step testing mechanism and may allow for changes in scope or nature of the product development.Project requirements remain open to change and any new information or requests can be added along the way, ensuring a relevant and updated end product.DISADVANTAGES OF SCRUMAs with all frameworks, there are points to be wary of as well. These include:Planning and organization of the project may become a challenge if the initial goals provided are unclear or lack direction.If the end date is also flexible, there may be a tendency to prolong the development process beyond an optimum point with constant new design demands. Thi s may also cause problems with defined timelines and resource allocations.New requirements and uncertainty may create an intense project cycle with tight deadlines and high levels of stress.The requirement for frequent meetings with set guidelines require resources and time.The scrum team needs to be mature and dedicated and willing to look at their work critically. The team should also be strong communicators and foster trust within the team.BENEFITS OF SCRUM FORThe Scrum process holds a variety of benefits for each unique stakeholder. Some of these are:CustomersAs a customer, the responsive nature of the team may be a highly valued function. Instead of long processes and requests to change initial requirements, changes may be welcomed and quickly incorporated. Additionally, product life cycles are reduced with each cycle offering a somewhat complete product that is tested and demonstrated.VendorsThis process may allow vendors to invest in only highly specific materials and reduce overhead costs as well as time to market. This will result in more satisfied customers and higher retention rates and advocacyDevelopment TeamsSince all tasks are clear and directed, unproductive work is eliminated and there is more time to dedicate to work that makes a difference and is valued by all stakeholders. Product ManagersThese managers are generally the product owners in a Scrum framework and are able to ensure a satisfied customer since the process is aligned for customer needs and requirements. There is ample opportunity to prioritize and deliver true value. Project ManagersProject managers who may take on the role of Scrum Master have the benefit of simpler and more realistic planning and tracking of the project. They are exposed to task level progress and this awareness makes all the difference in successful and timely project monitoring. This in turn allows issues to be identified and addressed efficiently. CHALLENGES WITH SCRUMScrum requires close collaboration and c onstant communication within the team. It also attempts to address certain basic challenges of a more traditional development process. Some of these challenges are:Emergent RequirementsMost traditional approaches to product development set goals and note requirements at the very initial stages of the process with little room for adjustment. However, the requirements of any project generally remain fluid and can often change drastically during the course of the development process.Time, Cost, and Quality EstimatesTraditionally, timelines and resource requirements for a project are estimated at the beginning of the process. It is then decided how much can be achieved within these requirements. Or, based on requirements, time and resources may be loosely estimated often proving too optimistic or more than needed. This is often an inaccurate prediction.Incorrect Progress ReportingWith inaccurate estimates on all major aspects of the project, the development team may be faced with the di fficult situation of reporting incorrect levels of process or constantly battle with the management on progress.Though it is often used in a software development context, Scrum has actually been used successfully by various companies in a number of different fields showing its transferability and adaptability as an important product development concept. The basic nature of the governing principles is one reason for this variety of use and allows Scrum to be used both on its own and as guiding methodology for other product development methods.Intro to SCRUM in under 10 Minutes The Scrum framework offers a unique point of view in product development processes. Whether used independently or as an accompaniment to other methodologies, it can offer tremendous benefits and advantages. Though simple and basic, the scrum framework should be understood and implemented completely to ensure that maximum utility is devised for the product development.

The Relationship Between Substance Abuse and Crime Essay

â€Å"Drugs and Alcohol abuse†, are phrases we hear commonly on the radio, television or in discussions of social problems. People believe it is the user’s personal choice however; it is not only a personal problem that dramatically affects individuals’ life but is a major social problem that affects society as whole. It has become one of the biggest problems in United States today. Alcohol or Drug abuse nearly automatically is linked with criminal acts. The statistical association between alcohol or drug abuse with crime seems to be convincing when examined at the first glance; however, it is not possible to make a conclusion concerning a distinct cause and effect association between the two aspects. Accordingly, this paper will examine†¦show more content†¦According to the data from U.S. Department of transportation, about 1.5 million drunk drivers are arrested every year. In response to an annual national survey conducted by the Bureau of Justic e, in which the sample was offenders serving jail terms for various crimes committed; 36% of the offenders indicated that they committed their crimes under the influence of alcohol or drug (http://bjs.ojp.usdoj.gov). This percentage accounts for nearly one million of convictions carried out yearly. However, there are some variations in substance abuse among state and federal offenders. A lot of people link drug abuse with crime, at times even with violent crime. This association comes from psychopharmacological association that imply that people may engage in criminal acts after taking some kind of substance known to undermine their judgment as well as self-control result in paranoid thoughts and distortion of inhibitions (Sewell, Poling and Sofuoglu, 189). Though all substances that affect the central nervous system might result in this kind of relationships, scientific information indicates that some type of drugs have a more strong effect than others. Such drugs are alcohol, cocaine, phencyclidine and amphetamines (McCauley, Ruggiero, Resnick and Kilpatrick, 136). Inversely, cannabis and heroin are less associated with desire to commitShow MoreRelatedThe Relationship Between Substance Abuse and Crime2406 Words   |  10 PagesSCH150. 6782 LaGuardia Community College Paper #2: The Relationship Between Substance Abuse and Crime December 11, 2012 Do you know someone who has done drugs? Well of course you do, we all do. Drugs are defined as â€Å"a substance that has a physiological effect when ingested or otherwise introduced into the body†, according to the Merriam-Webster dictionary. Researchers are focusing their attention on the aspect of drug addiction and drug abuse. Creating an outlet to drug awareness is the government’sRead MoreWhat Factors Affect Crime Occurrence? Essay1733 Words   |  7 PagesAccording to the Oxford Dictionary crime is an action or omission which constitutes an offense and is punishable by law . Throughout the decade’s crime has been viewed differently and punished in an unjust way. It was not until the mid-18th century that individuals started to study what is now known as criminology. A main concept of criminology is what is crime and why does it occur. Crime happens every single day for many different reasons that are hard to explain. Today many people accept thatRead Mo reTeens Top Reasons for Taking Drugs Essay614 Words   |  3 PagesThe relationship between teens and drugs has been around for decades; however, this is not what you would call positive. Substance abusing (which is using drugs or alcohol in ways than can cause physical harm) is often associated with crime. But why do youths take drugs? Youth take drugs for the following reasons: social disorganization, peer pressure, family factors, emotional, or rational choice. Social disorganization deals with drug abuse to poverty and disorganized urban environment. Read MoreEssay about The Effects of Domestic Violence on Children1448 Words   |  6 Pages How does domestic violence between parents and parental figures affect the children who witness it? This is a question often asked by Sociologists and Psychologists alike. There have been studies that prove that children who witness domestic inter-parental violence experience mental health problems, issues with gender roles, substance abuse, the committing of crimes and suicide/suicide attempts later in their lives. This paper will explore all five of these effects of domestic violence on childrenRead MoreThe Effects Of Drug Abuse On The United States1717 Words   |  7 PagesIn an attempt to demonstrate the absurdity of the drug abuse problems in the United States, it s hould be brought to light that the 2014 National Survey on Drug Use Health estimated that â€Å"27 million people aged 12 or older have used an illicit drug in the past 30 days† (Hedden, Kennet, Lipari, Medley, Tice, 2015). As gun violence has become a popular topic in America over the past few years due to its’ related deaths, many Americans’ fail to realize that more people are dying from drug overdoseRead MoreRelationship Between Drug And Crime1050 Words   |  5 PagesIs There a Relationship between drug and crime? Is there a relationship between drug and crime? My topic is deliberately based on whether or not there is a relationship between drug crime. My reasoning and facts should persuade you to believe that crime drug are related. My essay will have quotes, facts, and reasoning, which will all revolve on my essential question. Drug related offenses and a drug-using lifestyle are major contributors to the U.S crime problem. Provisional data from 1991 showRead MoreSubstance Abuse : A Social Problem1608 Words   |  7 Pages we must also take substance abuse into consideration because it is all too often neglected. According to the World Health Organization, substance abuse â€Å"refers to the harmful or hazardous use of psychoactive substances, including alcohol and illicit drugs† (Substance). Individuals who become victims of substance abuse become dependent on and overindulge in substances such as drugs and alcohol. The outside forces in our world today influence behaviors including substance abuse, ultimately displayingRead MorePrescription Opioid Abuse And Its Effects On Heroin Use Essay1550 Words   |  7 PagesNonmedical Prescription-Opioid abuse in the United States and Michigan has continued to rise, and with it, the devastating results that accompany it. Research has shown that increased op ioid abuse leads to an increase in overdose and death, increases in crime and increased incidences of costly blood borne diseases like HIV, AIDS and Hepatitis. It also leads to increased societal costs, such as an increasing number of children in foster care and increased healthcare, workplace and criminal justiceRead MoreThe Effects Of Substance Abuse On A Person s Life Essay1528 Words   |  7 Pagesknow people who have used or been around substances during their lifetime. We can even categorize these people as the person who is having a good time at a party, or the person who is a drunk and or drug dealer. It also doesn’t come as a shock to us when we find out these people taking the substances too far are now in rehab. But what distinguishes this fine line between the person socializing at a party to the person withdrawing in rehab? As certain substances are generally known to create an addictionRead MoreSchizophrenia And Its Effects On Mental Illness1388 Words   |   6 Pagesillness that contribute to this? According to Fazel, Guati, Linsell, Geddes and Grahn (2009), before the 1980’s many people made no connection between the disorder of schizophrenia and being violent. However, since more in depth and large research studies has been carried out to look at this connection, it has now been proven that there is a relationship between schizophrenia and violence. Schizophrenia can either be interpreted as a unitary disorder with various sub-types or as a disorder where each

Religion In Dantes Inferno By Dante Alighieri And Song Of...

Religion is defined as the belief in and worship of a superhuman controlling power, especially a personal God or gods. Religion is also known as a particular system of faith and worship. In this paper, I will be discussing how important religion is in two works respectively. The two works that I have chosen is, Inferno by Dante Alighieri and Song of Roland by Unknown author. The pursuit or interest to which both of the main characters ascribed to as supreme importance is Jesus Christ of Nazareth through Christianity. Christianity is based on the Bible as sacred scripture, and professed by Eastern, Roman Catholic and protestant bodies. According to the class lecture notes, â€Å"Much of Christianity includes sacraments like baptism and the†¦show more content†¦In other words, you are not allowed to take part in the things of the world but you are forced to set yourself apart from those who dont believe. According to the Bible, which is the holy book that Christians refer to, Romans 12:2 says, â€Å"Do not be conformed to this world, but be transformed by the renewal of your mind, that by testing you may discern what is the will of God, what is good and acceptable and perfect†. Most Christians believed that you must sacrifice your life spiritually because Christ gave himself physically. Dante’s moral system prioritized not human happiness or harmony on Earth but rather God’s will in Heaven. Furthermore, the structure of laws promotes discipline within the lives of its followers. With Dante going through hell to get to heaven, it was very important for him not to sin based on his religion. Transgressions are acts that go against a law, a rule, or code of conduct, an offense. According to Inferno, transgressions included limbo, lust, gluttony, greed, anger, heresy, fraud, and treachery. Abiding by the bible appointed laws helped Dante to help others do the same in their life. This was important to him, otherwise the inspiration to write Inferno would have been 3 irrelevant. Inferno was his way to warn others of the eternal damnation that they could face. It was important for him to warn others about the punishment of hell. As an example, one large and important group of punishments in the tours of hell

Hydraulic Machines Free Essays

30 CHAPTER 5 TURBINES 5. 1 Introduction Hydraulic turbines are the machines which use the energy of water and convert it to mechanical energy. The mechanical energy developed by a turbine is used in running an electric generator which is directly coupled to the shaft of the turbine. We will write a custom essay sample on Hydraulic Machines or any similar topic only for you Order Now The electric generator thus develops electric power, which is known as hydro-electric power. 5. 2 Elements of Hydraulic Power Plants Fig. 5. 1 General Layout of a Hydraulic Power Plant 31 Fig. 5. 1 shows a general layout of hydraulic power plant, in which an artificial storage reservoir formed by constructing a dam has been shown. 5. 3 General Classification of Turbines Turbines are hydraulic machines that convert energy into rotating mechanical energy which in turn generators to produce electrical energy. Originally developed from the water wheels, hydraulic turbines are the prime mortars of importance in modern water power development. According to their hydraulic action, turbines are broadly divided into two classes. (1) Impulse Turbine: Impulse turbines are more efficient for high heads. At the inlet to the turbine runner, pressure head can be completely converted into kinetic head in the form of a jet of water issuing from one or more nozzles. The free jet will be at atmospheric pressure before as well as after striking the vanes. The turbines are regulated by nozzles which may be a simple straight flow type or a deflector type. The impulse turbines are commonly represented by Pelton Wheels. Turgo turbine is also an impulse turbine but with different buckets, when compared with pelton. Turgo and cross flow turbines are relatively new developments in this class. The main advantages of these turbines are: †¢ They can be easily adopted to power variation with almost constant efficiency. †¢ The penstock overpressure and the runner overspeed control are easier. †¢ The turbine enables an easier maintenance. †¢ Due to the jet the manufacturer of these turbines impose a better solid particle control, conducting, consequently, to a lower abrasion effect. (2) Reaction Turbine: A turbine can be made to rotate under the action of water flowing under pressure through the runner. In such turbines the penstocks, the inlet passage to the runner, passage between the runner vanes, all form a continuous passage for the flow under a pressure which continuously decreases from inlet to outlet. The turbine runner directly converts both kinetic energy as well as the pressure energy into mechanical energy. Reaction turbines are represented in modern practice by two principal types: the Francis turbine where the flow is directed radial to the runner axis and the Propeller type 32 where the flow is axial to the runner axis. Propeller turbines may be fixed blade or adjustable blade types. Kaplan turbine has adjustable blades. The main advantages of these turbines are: †¢ It needs lesser installation space. †¢ It provides a greater net head and a better protection against downstream high flood levels. It can have greater runner speed. †¢ It can attain greater efficiencies for high power values. In order to distinguish different turbines, the hydraulically salient features like pressure, head, flow direction and magnitude, speed and power etc. The general classification of hydraulic turbines is illustrated in Fig. 5. 2. Hydraulic Turbines Impulse Turbines Pelton Tur go Reaction Turbines Cross-Flow Fixed -Blade Propeller Kaplan Francis Tubular Deriaz Bulb Fig. 5. 2 General Classification of Turbines 5. 4 Number of Units It is normally cost effective to have a minimum number of units at a given small ydropower installation. Multiple units may, however, be necessary from the operational point of view so that even one unit breaks down or is in the routine maintenance, the power generation can be achieved to a certain extent. The efficiency curves of turbines show that the 33 efficiency of power generation from hydraulic turbines considerably decreases at low flow ratios or power ratios. In multiple units, it is possible to maintain the higher efficiency even in low flows and the low loads by running a certain number of the units at a time depending upon the available discharge and the load demand. Multiple units thus, make the most effective use of water where the flow as well as the load variations are significant. 5. 5 Limits of Use of Turbine Types The selection of best turbines for any particular small hydropower site depends on the site characteristics, the dominant beings the head and the available flow. There are some limits on the range of these parameters in the selection of turbines. Each turbine type is best suited to a certain range of pressure head and the flow rate. For instance, Pelton wheels operate with low flows discharged under great pressures where as Propeller turbines are effective in high flows under low heads. Francis turbines fall in the medium category covering a wide range of different heads and discharges. The common practice of SHP systems is to develop standard unit sizes of equipment that will operate over a range of heads and flows. Either charts or nomographs are used to select appropriate units for site specific application. One such chart showing the head-flow range of normal SHP schemes applicable to each type of turbine is given in Fig5. 3. The graph also indicates the approximate power generation for each combination of the head and the discharge applicable to SHP schemes. Fig. . 3 Head-Flow Ranges for Different Turbines 34 5. 6 Pelton Wheel Pelton wheel is well suited for operating under high heads. A pelton turbine has one or more nozzles discharging jets of water which strike a series of buckets mounted on the periphery of a circular disc. The runner consists of a circular disc with a number of buckets evenly spaced round its periphery. The buckets have a shape of a double semi-ellipsoidal cups. The pelton bucket is designed to deflect the jet back through 165 ° which is the maximum angle possible without the return jet interfering with the next bucket. Fig. 5. 4 Pelton bucket General arrangement of a pelton wheel is shown in the Fig. 5. 5. For SHP schemes, Pelton wheels are easier to fabricate and are relatively cheaper. The turbines are in general, not subjected to the cavitation effect. The turbines have access to working parts so that the maintenance or repairs can be effected in a shorter time. Fig. 5. 5 General Arrangement of a Pelton Wheel 35 Traditionally, micro hydro pelton wheels were always single jet because of the complexity and the cost of flow control governing of more than one jet. Advantages of multi-jet: -Higher rotational speed -Smaller runner -Less chance of blockage Disadvantages of multi-jet: -Possibility of jet interference on incorrectly designed systems -Complexity of manifolds 5. 7 Francis Turbine Francis turbine is a mixed flow type, in which water enters the runner radially at its outer periphery and leaves axially at its center. Fig. 5. 6 illustrates the Francis turbine. The runner blades are profiled in a complex manner and the casing is scrolled to distribute water around the entire perimeter of the runner. The water from the penstock enters a scroll case which completely surrounds the runner. The purpose of the scroll case is to provide an even distribution of water around the circumference of the turbine runner, maintaining an approximately constant velocity for the water so distributed. The function of guide vane is to regulate the quantity of water supplied to the runner and to direct water on to the runner at an angle appropriate design. A draft tube is a pipe or passage of gradually increasing cross sectional area which connects the runner exit to the tail race. Fig. 5. 6 Francis Turbine 36 . 8 Kaplan Turbine It is an axial flow turbine which is suitable for relatively low heads. From Fig. 5. 7, it will be seen that the main components of Kaplan turbine such as scroll casing, guide vanes, and the draft tube are similar to those of a Francis turbine. Fig. 5. 7 5. 9 Kaplan Turbine Specific Speed The specific speed of any turbine is the speed in r. p. m of a turbine geometrically sim ilar to the actual turbine but of such a size that under corresponding conditions it will develop 1 metric horsepower when working under unit head. Ns = NP H5/ 4 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 1) where Ns = specific speed P = power in HP 5. 10 Characteristic Curves The turbines are generally designed to work at particular values of H,Q,P,N and ? o which are known as the designed conditions. It is essential to determine exact behaviour of the turbines under the varying conditions by carrying out tests either on the actual turbines or on their small scale models. The results of these tests are usually graphically represented and the resulting curves are known as characteristic curves. 37 -constant head characteristic curves -constant speed characteristic curves -constant efficiency characteristic curves In order to obtain constant head characteristics curves the tests are performed on the turbine by maintaining a constant head and a constant gate opening and the speed is varied by changing the load on the turbine. A series of values of N are thus obtained and corresponding to each value of N, discharge Q and the output power P are measured. A series of such tests are performed by varying the gate opening, the head being maintained constant at the previous value. From the data of the tests the values of Qu, Pu, nu and ? o are computed for each gate opening. Then with Nu as abscissa the values of Qu, Pu and ? o for each gate opening are plotted. The curves thus obtained for pelton wheel and the reaction turbines for four different gate openings are shown in Fig. 5. 8. Fig. 5. 8 Constant head characteristics for Pelton wheel and reaction turbines 38 5. 11 Cavitation in turbines When the pressure in any part of the turbine reaches the vapour pressure of the flowing water, it boils and small bubbles of vapour form in large numbers. These bubbles are carried along by the flow, and on reaching the high pressure zones these bubbles suddenly collapse as the vapour condenses to liquid again. The alternate formation and collapse of vapour bubbles may cause severe damage to the surface which ultimately fails to fatigue and the surface becomes badly scored and pitted. This phenomenon is known as cavitation. In order to determine whether cavitation will occur in any portion of the turbine, D. Thomas has developed a dimensionless parameter called Thomas’cavitation factor ? which is expressed as ?= Ha ? Hv ? Hs H †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 2) where Ha = atmospheric pressure head Hv = vapour pressure head Hs = suction pressure head For Francis turbines: Critical cavitation factor ? c = 0. 625 (Ns/444)2 †¦Ã¢â‚¬ ¦.. (5. 3) For Propeller turbines: ? c = 0. 28 + [ Example 5. 1 1 Ns 3 ( )] 7. 5 444 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. (5. 4) Estimate the maximum height of straight conical draft tube of a 18000 h. p. Francis turbine running at 150 r. p. m under a net head of 27 m. The turbine is installed at a station where the effective atmospheric pressure is 10. 6 m of water. The draft tube must sink at least 0. 77 m below the tail race. Ns = NP H5/ 4 = 327 39 ?c = 0. 625 (Ns/444)2 = 0. 339 Cavitation factor ? = Ha -Hv -Hs H Ha -Hv = 10. 6 m, H =27 m 0. 339 = 10. 6 -Hs 27 Hs = 1. 45 m Max length of the draft tube = 1. 45 + 0. 7 = 2. 22 m 5. 12 Governing of Turbines All the modern turbines are directly coupled to the electric generators. The generators are always required to run at constant speed irrespective of the variations in the load. This constant speed N of the generator is given by the expression N= 60 f p †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. (5. 5) where f = frequency (usually 50) p = numbers of pairs of poles 5. 13 Water Hammer A gate or valve at the end of the penstock pipe controls the discharge to the turbine. As soon as this governor regulated gate opening is altered, the pipe flow has to be adjusted to the new magnitude of flow. In doing so, there are rapid pressure oscillations in the pipe, often accompanied by a hammering like sound. Hence this phenomenon is called as water hammer. 5. 14 Jet Speed The velocity of flow of the jet depends upon the total net head H at the base of the nozzle and is given by the nozzle equation: v = C v ? 2gH where the discharge coefficient velocity of the nozzle is taken as 0. 95. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 6) 40 5. 15 Bucket speed V= ? DN 60 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 7) The bucket speed should be half of the jet speed. In practice, losses in the turbine cause the maximum efficiency to occur at slightly less than a half, typically 0. 46. V =0. 6 v 5. 16 Design of Pelton Wheel Runner diameter: Runner diameter can be found out from the rpm equation. D= 38 ? H N †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. (5. 8) where N = runner speed(rpm) H = net head Nozzle diameter: The nozzle diameter is given by the nozzle equation: d = 0. 54 ? Q 0. 5 1 ? 0. 25 H n jet †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. (5. 9) Je t ratio: Jet ratio D/d is a size parameter for the turbine. It has a value in a range of 10 to 24. For the high efficiency Pelton wheel design, the ratio of the runner diameter to the nozzle should be more than 9. Number of buckets: The number of buckets required for the efficient operation of the Pelton turbine is calculated as: N buc = 0. 5 ? D + 15 d †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. (5. 10) In practice, the selection and the detail design of the turbine units are carried out by the manufactures based on the model performances. 41 Example 5. 2 Powerhouse is equipped with a vertical shaft pelton turbine. The generator is provided with 6 pairs of poles. Design discharge is 1. 4 m3/s and net head is 425 m. The turbine will provide 6500 hp. Take coefficient of nozzle as 0. 95. Determine (a) the specific speed (b) velocity of jet (c) jet diameter (d) pitch circle diameter of the wheel (e) number of buckets (a) N= 60 f p = 60 x 50/6 = 500 rpm Ns = = NP H5/ 4 500 6500 4255 / 4 = 20. 9 Use single jet pelton turbine (b) velocity of jet v = C v ? 2gH = 0. 95 ? 2Ãâ€"9. 81Ãâ€"425 = 86. 75 m/s (c) jet diameter d = 0. 54 ? = 0. 54 ? Q 0. 5 1 ? 0. 25 H n jet 1. 4 0. 5 425 0. 25 ? = 0. 14 m =14 cm 1 1 42 (d) pitch circle diameter D= 38 ? H N = 1. 57 m (e) Number of buckets N buc = 0. 5 ? N buc = 0. 5 ? D + 15 d 1. 57 + 15 0. 14 = 20. 6 = 21 5. 17 Work done of Pelton Wheel In turbines, the water flows on to the runner, which itself is rotating with a certain speed. The water flows over the runner and leaves the runner at its outlet point. We can speak of absolute velocity of water before it flows in the runner, the relative velocity of water w. r. t the runner and again the absolute velocity of water after it has left the runner. In order to ascertain the relationship between these velocities, the velocity vector diagram prove to be very useful. Fig. 5. 9 shows the velocity triangles at the tips of the bucket of a pelton wheel. At the outlet tip velocity triangles are different depending upon the magnitude of u corresponding to which it is slow, medium or fast runner. Inlet velocity diagram V Vri Vai =Vwi 43 Outlet velocity diagram V Vwo ? ? Vfo Vro Vao Fig. 5. 9 Velocity triangles V = bucket velocity Vai = absolute velocity of jet at inlet tip Vai = Cv 2 gH1 Vao = absolute velocity of jet at outlet tip Vri = relative velocity of jet at inlet = Vai-V Vro = relative velocity of jet at outlet = k. Vri Vwi = velocity of whirl at inlet =Vai Vwo = velocity of whirl at outlet = V-VroCos ? Vfo = velocity of flow at outlet Mass/sec m =? Q =? a Vai=? ?/4 d2 Vai †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 11) Workdone on the bucket/sec (power developed by turbine) P = m (Vwi -Vwo) V †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 12) Maximum hydraulic efficiency ? h max = 1 (1 + kCos? ) 2 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(5. 13) The hydraulic efficiency is maximum when the bucket speed is equal to half of the velocity of jet. 44 Example 5. 3 The head available at entrance to the nozzle supplying a pelton wheel is 300 m and the coefficient of velocity for the nozzle is 0. 98. The wheel diameter is 1. 8 m and the nozzle diameter is 125 mm. The buckets deflect the jet through 165 °. Assuming the relative velocity of the jet is reduced by 16%, calculate the theoretical speed in rev per min for the maximum hydraulic efficiency. What is the hydraulic efficiency when running at this speed, and what is the power developed? Deflection angle =165 ° = (180- ? ) ? = 15 ° k = 0. 84 hf hn H’=Vai2/2g H For max hydraulic efficiency V/Vai =0. 5 Vai = Cvv2gH1 = 75 m/s V =Vai/2 = 37. 5 m/s V =? DN/60 N =60V/? D = 398 rpm ?hmax = 1/2 (1+ k Cos ? ) = 90. 55 % mass/sec = m = ? Q = ? ?/4 d2 Vai = 920 kg/sec H1 45 Inlet diagram: V Vri From velocity diagram Vwi = Vai =75 m/s Vri = Vai- V =37. 5 m/s Vwi = Vai Outlet diagram: Vwo = V -Vro Cos ? V = V – k Vri Cos ? Vwo Vro Power = m V ( Vwi -Vwo) = 234600 Watts Vao =7 m/s 46 CHAPTER 6 CENTRIFUGAL PUMP 6. 1 Introduction Centrifugal pumps are classified as rotodynamic type of pumps in which dynamic pressure is developed which enables the lifting of liquids from a lower to a higher level. The basic principle on which a centrifugal works is that when a certain mass of liquid is made to rotate by an external force, it is thrown away from the central axis of rotation and a centrifugal head is impressed which enable it to rise to a higher level. Now, if more liquid is constantly made available at the centre of rotation, a continuous supply of liquid at a higher level may be ensured. Since in these pumps the lifting of the liquid is due to centrifugal action, these pumps are called ‘centrifugal pumps’. 6. 2 Advantages of centrifugal pumps over reciprocating pumps The main advantage of a centrifugal pump is that its discharging capacity is very much greater than a reciprocating pump which can handle relatively small quantity of liquid only. A centrifugal pump can be operated at very high speeds without any danger of separation and cavitation . The maintenance cost of a centrifugal pump is low and only periodical check up is sufficient . But for a reciprocating pump the maintenance cost is high because the parts such as valves etc. , may need frequent replacement. 6. 3 Component Parts of a Centrifugal Pump The main component parts of a centrifugal pump are: -impeller -casing -suction pipe -delivery pipe 47 Fig. 6. 1 Component part of a centrifugal pump 6. 4 Workdone by the Impeller The expression of the workdone by the impeller of a centrifugal pump on the liquid flowing through it may be derived in the same way as for a turbine. The liquid enters the impeller at its centre and leaves at its periphery. Fig. 6. shows a portion of the impeller of a centrifugal pump with one vane and the velocity triangles at the inlet and outlet tips of the vane. V is absolute velocity of liquid, u is tangential velocity of the impeller, Vr is relative velocity of liquid, Vf is velocity of flow of liquid, and Vw is velocity of whirl of the liquid at the entrance to the impeller. Similarly V1,u1,Vr1,Vf1 and Vw1 represent their counterpa rts at the exit point of the impeller. 48 Fig. 6. 2 Velocity triangles for an impeller vane ? = the impeller vane angle at the entrance ? = the impeller vane angle at the outlet = the angle between the directions of the absolute velocity of entering liquid and the peripheral velocity of the impeller at the entrance ? = the angle between the absolute velocity of leaving liquid and the peripheral velocity of the impeller at the exit point Work done per second by the impeller on the liquid may be written as Work done = W ( Vw1 u1 – Vw u) ————-(6. 1) g where W kg of liquid per second passes through the impeller. Since the liquid enters the impeller radially ? = 90 and hence Vw = 0. Thus equation (6. 1) becomes Work done = W (Vw1u1) ————-(6. ) g 6. 5 Head of a Pump The head of a centrifugal pump may be expressed in the following two ways: (a) Static head (b) Manometric head (or total head or gross head) 49 Fig. 6. 3 Head on a centrifugal pump (a) Static Head Static head is the vertical distance between the liquid surfaces in the pump and the tank to which the liquid is delivered by the pump. Static head (or lift) Hs = hs + hd where hs = static suction lift hd = static delivery lift †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. (6. 3) 50 (b) Manometric Head Manometric head is the total head that must be produced by the pump to satisfy external requirements. If there are no energy losses in the impeller and the casing of the pump, then the manometric head Hm will be equal to the energy given to the liquid by the V ? 1u1 g impeller, i. e Hm = . But if losses occur in the pump then V ? 1u1 ? losses of head in the pump g †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. (6. 4) Applying Bernoulli’s equation between the points, O at the liquid surface in the pump and 1 in the suction pipe just at the inlet to the pump (i. e. , at the centre line of the pump), the following expression is obtained if the liquid surface in the sump is taken as datum. 0= p s Vs2 + + hs + h f s ? 2g ps Vs2 ? [ + hs + h fs ] 2g ? †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. (6. 5) where ps is the pressure at point l ; Vs is the velocity of flow in the suction pipe ; hs is the suction lift and hfs is the head loss in the suction pipe which includes the head loss due to friction and the other minor losses. It may however be pointed out that if the pump is situated below the level of the liquid surface in th e sump, hs will be negative. Equation (6. 5) indicates that at the inlet to the pump there is always a suction or vacuum pressure developed which will be recorded by the vacuum gauge provided at this point as shown in Fig. . 3. The head expressed by equation (6. 5) is called the suction head of the pump. Also, applying Bernoulli’s equation between points 1 and 2, which is just at the outlet of the impeller and is assumed to be at the same level as point 1, then since the impeller imparts a head equal to (Vw1u1/g) to the liquid the following expression is obtained: p s V s2 V? 1u1 p 2 V12 + + = + + hLi ? 2g g ? 2g †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. (6. 6) where p2 is the pressure and V1 is the absolute velocity of the liquid leaving the impeller and hLi is the loss of head in the impeller. 51 6. Specific Speed of Centrifugal Pumps In order to compare the performance of different pumps, it is necessary to have some term which will be common to all centrifugal pumps. The term used for this purpose is the specific speed. The specific speed of a centrifugal pump is the speed at which the specific pump must run to deliver unit quantity against unit head, the efficiency being the same as the actual pump. Ns = NQ H 3/ 4 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦(6. 7) where Ns= specific speed N = rotational speed(rpm) H = total head 6. 7 Performance of Pumps- Characteristic Curves A pump is usually designed for one speed, flow rate and head in actual practice, the operation may be at some other condition of head on flow rate, and for the changed conditions, the behaviour of the pump may be quite different. Therefore, in order to predict the behaviour and performance of a pump under varying conditions, tests are performed and the results of the tests are plotted. The curves thus obtained are known as the characteristic curves of the pump. The following three types of characteristic curves are usually prepared for the centrifugal pumps : a) Main and operating characteristics. (b) Constant efficiency or Muschel curves . (c) Constant head and constant discharge curves. Main and Operating Characteristics In order to obtain the main characteristic curves of a pump it is operated at different speeds. For each speed the rate of flow Q is varied by means of a delivery valve and for the different values of Q the corresponding values of manometric head Hm, shaft H. P. , P , and overall efficiency ? are measured or calculated. The same operation is repeated for different speeds of the pump. Then Q v/s Hm ; Q v/s P and Q v/s ? urves for different speeds are plotted, so that three sets of curves, as shown in Fig. 6. 4 are obtained, which represent the 52 main characteristics of a pump. The main characteristics are useful in indicating the performance of a pump at different speeds. During operation a pump is normally required to run at a constant speed, which is its designed speed, (same as the speed of the driving motor). As such that particular set of main characteristics which corresponds to the designed speed is mostly used in the operations of a pump and is, therefore, known as the operating characteristics. A typical set of such characteristics of a pump is shown in Fig. 6. 5 Fig. 6. 4 Main characteristics of a centrifugal pump Fig. 6. 5 Operating characteristic curves of a centrifugal pump 53 6. 8 Parallel or Series Operation of Pumps Pumps in series Centrifugal pumps generate a relatively low head delivering a fairly high rate of discharge. Normally a pump with a single impeller can be used to deliver the required discharge against a maximum head of about 100 m. But if the liquid is required to be delivered against a still larger head then it can be done by using two or more pumps in series. Fig. 6. 6 Three stage centrifugal pump If the required head is more than that can be provided by one pump, the pumps are connected in series. The same discharge passes through both pumps but the head developed by one pump add the other. The total head developed is obtained by adding together the value of the head of each pump corresponding to the relevant discharge. Pumps in Parallel The multi-stage pumps or the pumps in series as described earlier are employed for delivering a relatively small quantity of liquid against very high heads. However, when a large quantity of liquid is required to be pumped against a relatively small head, then it may 4 not be possible for a single pump to deliver the required discharge. In such cases two or more pumps are used which are so arranged that each of these pumps working separately lift the liquid from a common sump and deliver it to a common collecting pipe through which it is carried to the required height Fig. 6. 7. Since in this case each of the pumps deliver the liquid against the same head, the arrangement is known as pumps in parallel. If Q1, Q2, Q3†¦.. , Qn are the discharging capacities of n pumps arranged in parallel then the total discharge delivered by these pumps will be Qt = (Q1+Q2+Q3+†¦Ã¢â‚¬ ¦+Qn) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. (6. 8) If the discharging capacity of all the n pumps is same, equal to Q , then the total discharge delivered by these pumps will be Qt = nQ Fig. 6. 7 Two centrifugal pumps arranged in parallel 55 A centrifugal pump, having four stages in parallel, delivers 11m3/min of Example 6. 1 liquid against a head of 24. 7m, the diameter of the impeller being 225mm and the speed 1700 rpm. A pump is to be made up with a number of identical stages in series, of similar constriction to those in the first pump, to run at 1250 rpm, and to deliver 14. 5 m3/min, against a head of 248m. Find the number of stages required for the second pump. 1st Pump 2nd Pump Q = 11m3/min Q = 14. 5m3/min H = 24. 7 m H = 248 m N = 1700 rpm N =1250 rpm D = 225 mm Specific speed N s = NQ H 3/ 4 Q for one pump = 11/4 = 2. 75 m3/min Ns = 1700 2. 75 24. 7 3 / 4 = 254 For 2nd pump, with identical stages in series i. e multi-stage pump, if each stage is similar to those of each stage is similar to those of the first pump. The specific speed of each stage Ns = 254 Ns = 254 = NQ H 3/ 4 1250 14. 5 H 3/ 4 H = 49. 64 m Total head required = 248 m No of stages required = 248/49. 64 = 5 stages 56 CHAPTER 7 DIMENSIONAL ANALYSIS, HYDRAULIC SIMILITUDE AND MODEL INVESTIGATION 7. 1 Dimensional Analysis Dimensional analysis is a mathematical method of obtaining the equations, changing units, determining a convenient arrangement of variable of a physical relation. In an equation expressing a physical relationship between quantities, absolute numerical and dimensional equality must exit. In general, all such physical relationships can be reduced to the fundamental quantities of mass M, length L and time T. It is a based on the assumption that the phenomenon can be expressed by a dimensionally homogeneous equation, with certain variable. The dimensional analysis is widely used in research work for developing design criteria and also for conducting model tests. 7. 2 Dimensions and Units All physical quantities are measured by comparison. This comparison is always made with respect to some arbitrarily fixed value for each independent quantity, called dimension(e. g. , length, mass, time, etc. ). Since there is no direct relationship between these dimensions, they are called fundamental dimensions. Some other quantities such as area, volume, velocity, force etc. can not be expressed in terms of fundamental dimensions and thus may be alled derived dimensions. There are two systems for fundamental dimensions namely FLT (i. e force, length, time) and MLT (i. e. , mass, length, time). One common system employed in dimensional analysis is the M,L,T system. Table is a listing of some of the quantities used in fluid flow, together with their symbols and dimensions. 57 Quantity Symbol Dimensional Form Length l L Time t T Mass m M Velocity v L T-1 Acceleration a L T-2 Force F M L T-2 Pressure P M L-1 T-2 Discharge Q L3 T-1 Power P M L2 T-3 W,E M L2 T-2 Density ? M L-3 Dynamic viscosity  µ M L-1 T-1 Kinematic viscosity ? L2 T-1 Surface tension M T-2 Work,energy 7. 3 Methods of Dimensional Analysis The methods of dimensional analysis are: -Buckingham’s ? theorem -Ralyeigh’s method Buckingham’s ? Theorem If there are ‘n’ variables in a dimensionally homogeneous equation, and if these variables contain ‘m’ fundamental dimensions such as (M,L,T) , they may be grouped into (nm) non-dimensional independent ? terms. Mathematically, if a variable x1 depends upon independent variables x2, x3,x4, †¦. ,xn, the functional equation may be written as x1 = f (x2, x3, x4, †¦. , xn) The equation may be written in its general form as 58 f1 ( x1, x2, x3,†¦Ã¢â‚¬ ¦. xn) = C In this equation there are ‘n’ variables. If there are ‘m’ fundime ntal dimensions, the according to ? theorem f2 ( ? 1,? 2,? 3,†¦.. , ? n-m ) = C1 e. g Q = f (d,H, µ,? ,g) f1 (Q, d, H,  µ, ? , g) = C n = 6; m = 3; (n-m) = 3 f2 ( ? 1, ? 2, ? 3) = C1 Procedure 1. First of all, write the functional relationship with the given data. 2. Then write the equation in its general form. 3. Choose ‘m’ repeating variables and write separate expressions for each term. Every ? term will contain the repeating variables and one of the remaining variables. The repeating variables are written in exponential form. 4. With the help of the principle of dimensional homogeneity, find out the values of the exponents by obtaining simultaneous equations. 5. Substitute the value of these exponents in the ? term. 6. After the ? terms are obtained, write the functional relation in the required form. e. g Q = f ( d, H,  µ, ? , g) f1 (Q, d, H,  µ, ? , g) =C n = 6 , m = 3 , (n-m) = 3 f2 (? 1,? 2,? 3)=C1 Choose ? , g, d as repeating variable, ?1 = ? a1 gb1 dc1 Q ? 2 = ? a2 gb2 d c2 H ? 3 = ? a3 gb3 dc3  µ 59 Selection of Repeating Variable 1. The variables should be such that none of them is dimensionless. 2. No two variables should have the same dimensions. . Independent variables should be as far as possible, be selected as repeating variable. ? fluid property ? flow characteristics l geometric characteristics Example 7. 1 A V-notch weir is a vertical plate with a notch angle ? cut into the top of it and placed across an open channel. The liquid in the channel is backed up and forced to flow through the notch. The discharge Q is some function of the elevation H of upstream liquid surface above the bottom of the notch. In addition it depends upon gravity and upon the velocity of approach Vo to the weir. Determine the form of discharge equation: ?V ? Q = gH 5/2 f ? ,? ? ? gH ? ? ? Q = f (H, g , Vo , ? ) f1 ( Q, H ,g ,Vo, ? ) = C Choose g and H as repeating variables n = 5; n-m =3 ; m=2 ?1 = Ha1 gb1 Q = (L)a1 (LT-2)b1 L3 T-1 ?2 =Ha2 gb2 Vo = (L)a2 (LT-2)b2 LT-1 ?3 = ? (M)o (L)o (T)o = (L)a1 (LT-2)b1 L3 T-1 a1+b1+3 =0 ? a1 = -5/2 -2b1-1 =0 ? b1 = -1/2 ?1 = H-5/2 g-1/2 Q = Q vg H 5/2 (M)o (L)o (T)o = (L)a2 (LT-2)b2 L T-1 a2 = -1/2 60 b2 = -1/2 ?2 =H-1/2 g-1/2 Vo= Vo vgH Q f2 ( gH 5/ 2 Q gH 5/ 2 , Vo ,? gH ) = C1 Vo ,? gH ) Vo ,? gH ) =f( Q = gH 5/2 f ( Example 7. 2 Q = VD 2 f [ Prove that the discharge over a spillway is given by the relation gD H ,] V D where V= velocity of flow D = depth of throat H = Head of water g = Acceleration due to gravity Q= f (V,D,H,G) f1 (Q,V,D,H,G) = C Choose V and D as repeating variables n = 5, m =2, n-m =3 ?1= Va1 Db1 Q = (LT-1)a1 (L)b1 (L3T-1) ?2 = Va2 Db2 H = (LT-1)a2 (L)b2 (L) ?3 = Va3 Db3 g = (LT-1)a3 (L)b3 (LT-2) M0L0T 0 = (LT-1)a1 (L)b1 (L3T-1) 0 = -a1-1 ; a1 = -1 0 = a1+b1+3 ; b1= -2 ?1 = V -1 D -2 Q 61 ?1 = Q VD2 M0L0T 0 =(LT-1)a2 (L)b2 (L) 0 = -a2 a2+b2+1 =0 ; b2 = -1 ?2 = V0 D-1 H = H/D M0L0T 0 = (LT-1)a3 (L)b3 (LT-2) 0 = -a3-2 ; a3 = -2 0 = a3+b3+1 ; b3 =1 ?3 = V-2 D g gD V = f2 ( gD H , )=0 VD 2 D V Q VD 2 Q , = f( gD H ,) V D Q = VD 2 f ( 7. 4 D H ,) V D HYDRAULIC MODELS Hydraulic models, in general, may be either true models or distorted models. True models have all the significant characteristics of the prototype reproduced to scale (geometrically similar) and satisfy design restrictions (kinematic and dynamic similitude). Model-prototype comparisons have clearly shown that the correspondence of behaviour is oft en well beyond expected limitations, as has been attested by the successful operation of many structures designed from model tests. 7. 5 Hydraulic Similitude To know the complete working and behaviour of the prototype, from its model, there hould be a complete similarity between the prototype and its scale model. This similarity is 62 known as hydraulic similitude. From the subject point of view, the following three types of hydraulic similitude are important. (1) Geometric similitude (2) Kinematic similitude (3) Dynamic similitude GEOMETRIC SIMILITUDE The model and the prototype are identical in shape, but differ only in size. (The ratios of all the corresponding linear dimensions are equal) . Let L = Length of the prototype B = Breadth of the prototype D = Depth of the prototype l,b,d = corresponding values of the model L Linear ratio Lr = Area ratio Ar = ( Volume ratio Vr = ( l = BD = bd L B D )2 = ( )2 = ( )2 l b d L B D ) 3 = ( ) 3 = ( )3 l b d KINEMATIC SIMILITUDE The model and the prototype have identical motions. ( The ratios of the velocities at corresponding points are equal) Let V1 = velocity of liquid in prototype at point 1 V 2 = velocity of liquid in prototype at point 2 v1,v2 = corresponding values of the model Velocity ratio Vr = V1 V2 = = †¦.. v1 v 2 DYNAMIC SIMILITUDE The model and prototype have identical forces. (The ratios of the corresponding forces acting at corresponding points are equal). F Force ratio Fr = 1 = f1 F2 †¦.. f2 63 7. 6 CLASSIFICATION OF MODELS (1) Undistorted model (2) Distorted model Undistorted model A model which is geometrically similar to the prototype is known as undistorted model. Distorted model Model does not have complete geometric similarity with the prototype, is known as distorted model. 7. 7 Comparison of an Undistorted Model and the Prototype If the model is to be overall similar to the prototype, then all the three similarities (i. e, geometric, kinematic, dynamic ) should exist. But this is not possible in actual practice, as it is difficult to exist two types of similarities simultaneously. In general, and undistorted model of a prototype is made keeping in view the geometric similarity only and the remaining similarities are then compared for the scale ratio. 7. 8 Velocity of Water in Prototype for the Given Velocity of an Undistorted Model Consider an undistorted model geometrically similar to a proposed prototype like a weir, dam, spillway etc. Let h = head of water over the model v = velocity of water at a point in the model H,V = corresponding values for the prototype 1/s = scale ratio of the model to the prototype Velocity of water in the model v = Cv v2gh Velocity of water on the corresponding point in the prototype V = Cv v2gH C v 2 gh v = = V C v 2 gH h 1 = H s V = v vs Example 7. 3 The velocity at a point on a spillway model of a dam is 1. 3m/sec for a prototype of model ratio 1:10. What is the velocity at the corresponding point in the prototype? 64 Velocity in the model v = 1. 3 m/s Model ratio, 1/s = 1/10 s = 10 Velocity in the prototype V = v vs V =1. 3 x v10 = 4. 11 m/sec 65 References: 1. Hydraulics and Fluid Mechanics P. N. Modi and S. M. Seth 2. Hydraulics, Fluid Mechanics and Hydraulic Machines R. S. Khurmi 3. Fluid Mechanics Victor L. Streeter How to cite Hydraulic Machines, Essay examples

Why the New West Indies Federation Failed free essay sample

The West Indian Federation began in the twentieth century. A fedration is an organization within which smaller divisions have some internal independence. The West Indian Federation was one of the first attempts at federation in the Caribbean. This occurred from the year 1958-1962. The West Indies agreed to come together because this was the only way they could prove to Britain that they were ready for their independence. However, before they could prove this to Britain the Federation had gone done in history as a failure. Many factors led to the failure of the federation including its weakness, conflict among the states and the unwillingness of the large islands to be burdened by the smaller islands. One of the main reasons why the federation failed is because it was weak. The federation was only given powers over its internal affairs and any foreign matters were dealt with by England. In addition, the member states had different views on what the federation should entail. We will write a custom essay sample on Why the New West Indies Federation Failed or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Eric Williams of Trinidad wanted a strong federation with the power to levy taxes, control economic development and set up custom union. The federal Prime Minister, Grantley Adams of Barbados was in support of this. Jamaica on the other hand, opposed all of this and wanted a weak federation that did not have the power of taxation. (Greenwood 1991) Jamaica and Trinidads disagreement on this point was not good for the federation. Eventually, this led to the breakdown of the federation. Conflict between individual member states and the federal government was a key reason for the breakdown of the West Indian federation. The idea of free movement within the units of the federation was not supported by Trinidad. Trinidad according to Greenwood and Hamber (2003) opposed the idea because her per capita income was twice that of the next richest country. In comparism to places like Barbados, Trinidad was under-populated and thus it was feared that immigrants would flock to the islands and take the Jobs of its citizens which would lead to an increase in unemployment. This was one reason for Trinidads withdrawal from the federation. According to Elizabeth Wallace (1996) Eric Williams strong objection to allowing free entry to other west Indians increased his existing hostility to the federation. Trinidad also encountered problems with the federation over Chaguaramas, the site for the federal capital which had been leased to the United States by Britain for 99 years. Trinidad negotiated for the capital and Grantley Adam felt this was wrong since the issue was a federal case and had to be dealt with by the federation. Jamaica was at loggerheads with the federation when it disagreed with customs union since that was the main earner of revenue. Therefore, when it was evident that the customs union would pull through Jamaica withdrew from the federation. In addition, Jamaica ave tax concession to an oil company which forced the federal prime minister to threaten retroactive taxation. Finally, the federation broke up because the large islands did not want to be burdened by the small islands. From the outset Jamaica and Trinidad thought that Britain supported the federation because she wanted to transfer responsibility for the smaller states on them. According to Elizabeth Wallace the striking imbalances among the territories in size, wealth were major reasons for the breakdown of the federation. Therefore, as soon as it was known that these two pted out. In theory the federation was ideal but in practice it was so overwhelming that it ended in 1962. Several factors worked in conjunction to bring about the demise of the federation namely the unwillingness of the larger islands to be burdened by the smaller islands, conflict between member states and the fact that the federation was weak from the beginning. Thus the federation was as Premier Barrow of Barbados stated an Unfederable federation from the beginning. Bibliography Ashdown, P. Humphreys, F. Caribbean Revision History For CXC, Oxford: Macmillan