How to Develop a Smart GMAT Study Plan

The GMAT is a challenging test. If you want to do well, youre going to need a study plan that will help you prepare in an efficient and effective manner. A structured study plan breaks the huge task of preparation into manageable tasks and achievable goals. Lets explore some of the steps you can take to develop a smart GMAT study plan based on your individual needs. Get Familiar With Test Structure Knowing the answers to the questions on the GMAT is important, but knowing how  to read and answer GMAT questions is even more important. The first step in your study plan is to study the GMAT itself. Learn how the test is structured, how questions are formatted, and how the test is scored. This will make it easier for you to understand the method behind the madness so to speak. Take a Practice Test Knowing where youre at will help you decide where you need to go. So the next thing you should do is take a GMAT practice test to assess your verbal, quantitative, and analytical writing skills. Since the real GMAT is a timed test, you should also time yourself when you take the practice test. Try not to be discouraged if you get a bad score on the practice test. Most people don’t do very well on this test the first time around — thats why everyone takes so long to prepare for it! Determine How Long You Plan to Study Giving yourself enough time to prepare for the GMAT is really important. If you rush through the test prep process, it will hurt your score. The people who score the highest on the GMAT tend to spend a large amount of time preparing for the test (120 hours or more according to most surveys). However, the amount of time that should be devoted to preparing for the GMAT comes down to individuals needs. Here are a few questions you need to ask yourself: What is my target GMAT score? Most business schools publish class profiles that contain an average GMAT score or score range for students who have been accepted to the program. Look up the average score for students at the business school youre applying to. This score should be your target GMAT score. If you have a high target GMAT score, youre going to need to study more than the average test taker.How well did I score on the practice GMAT? Take the score you got on the practice GMAT and compare it to your target score. The larger the gap, the longer you are going to need to study to close it.When do I need to take the GMAT? Determine how long you have before you need to take the test. You don’t want to wait too long into the application process to take the GMAT. It is important to give yourself enough time to retake it just in case. So think about the application deadlines for the schools you are applying to and plan accordingly. Use your answers to the above questions to determine how long you need to study for the GMAT. At a minimum, you should plan at least one month to prepare for the GMAT. Planning to spend two to three months would be even better. If you will only be devoting an hour or less each day to prep and need a top score, you should plan on studying for four to five months. Get Support A lot of people choose to take a GMAT prep course as a way of studying for the GMAT. Prep courses can be really helpful. They are typically taught by individuals who are familiar with the test and full of tips on how to score high. GMAT prep courses are also very structured. They will teach you how to study for the test so that you can use your time efficiently and effectively. Unfortunately, GMAT prep courses can be expensive. They might also require a significant time commitment (100 hours or more). If you cant afford a GMAT prep course, you should seek out free GMAT prep books from your local library. Practice, Practice, Practice The GMAT is not the kind of test that you cram for. You should stretch your prep out and work on it a little bit each day. This means doing practice drills on a consistent basis. Use your study plan to determine how many drills to do each day. For example, if you plan to study for 120 hours over four months, you should do one hour of practice questions every single day. If you plan to study for 120 hours over two months, youll need to do two hours worth of practice questions each day. And remember, the test is timed, so you should time yourself when doing drills so that you can train yourself to answer every question in just a minute or two.

Enron the Nigerian Barge Deal - 2218 Words

April 4, 2006 0 1 Introduction: The Nigerian Barge Deal Enron Corporation was an energy company based in Texas and created when InterNorth acquired Houston Natural Gas Company in 1985. Enrons growth was fast, it was named \Americas Most Innovative Company for six consecutive years and it soon became the seventh largest company in the United States, until its bankruptcy was declared in 2001. Accounting fraud, money laundering and conspiracy are some of the charges which Enron stood accused of in a series of scandals that nally came to a head in the largest bankruptcy in history. One of these scandals was named the Nigerian Barges case ([Fleischer1, 2005]). Enron tried to sell an interest in three power-generating barges in the coast of†¦show more content†¦Merrill Lynchs main interest was to accommodate a very important client, as Enron paid millions in fees to Merrill 2 Lynch ([Glisan, 2003]). Furthermore, it can be considered that there was an agreement between Enron and Merrill Lynch in this contract, since the latter accepted the o er and all the conditions of the former. The second requirement that needs to be fullled by the parties in the contract is the consideration, which species what is exchanged, i.e., as commented in [Cornell, 2005], \the bene t or detriment which a party receives which reasonably and fairly induces them to make the promise/contract. Consideration can involve a wide group of things, everything that has a value and is involved in the contract. Money is one of the main factors. The contract between Enron and Merrill Lynch allowed Enron to perceive seven million dollars from Merrill Lynch, which acquired an interest in the three barges in Nigeria. Those millions of dollars helped Enron to in ate its earnings since that transaction was considered by Enron as a sale, and not as a loan. This constitutes the main problem of the contract, since the prosecutors were essentially charged for not following basic accounting rules. Consideration of the contract also includes the interest that Merrill Lynch purchased, including the 22:5% of prot that Merrill Lynch made. Finally, Andrew FastowsShow MoreRelatedThe Corporate Culture Of Enron1474 Words   |  6 PagesHow did the corporate culture of Enron contribute to its bankruptcy? The Enron Corporation was an energy trading and utilities company that eventually failed due to the discovery that Enron was hiding large debts and losses in financial documents. â€Å"Through its subsidiaries and numerous affiliates, the company provided products and services related to natural gas, electricity, and communications for its wholesale and retail customers† (Ferrell, Fraedrich Ferrell, 2015, p. 486). A company’s corporateRead MoreEnron Corporation : The Biggest Gas Transmission System Essay1081 Words   |  5 Pages The Enron Corporation started in 1985 by Kenneth Lay and was the result of a merger between Houston Natural Gas and InterNorth Corporation (Madsen Vance, 2009). Enron had the biggest gas transmission system in the U.S which consisted of a network of 38,000 miles of pipeline (Giroux, 2008). After the addition of Jeffrey Skilling, Enron transformed itself from a producer and distributor of natural gas to a trading company (Chandra, 2003). Enron lobbied hard for deregulation and was capableRead MoreEnron And Corporate Culture Of Enron1322 Words   |  6 PagesIntroduction In 1985 The Enron Corporation came into existence after a successful merger between two gas pipeline companies. The company nurtured a very competitive culture, which encouraged employees to win at any means necessary. 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That s because they were at the bottom of the investing food chain.† In July of 1985, Houston Natural Gas merged with InterNorth, to create Enron, and Kenneth Lay became CEO the following year. In 1989, Enron began trading natural gas commodities. In 1997, Andrew Fastow devised the first steps to hide debts and i nflate profits and one yearRead MoreEnron And Its Impact On Enron s Corporate Bankruptcy Essay1811 Words   |  8 Pages Enron was founded in 1985 by Kenneth Lay and by the mid 90s under the tutelage of Jeff Skilling, it was being touted as a revolutionary company that was destined to change the face of business and the energy industry. However, by 2001 it became clear that Enron’s astronomical growth and sustained profitability was built upon fraudulent grounds. The company was stashing debt but continued to report profits. 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Native son 2 Essay Example For Students

Native son 2 Essay Native Son by Richard Wright is a novel written about a black boy trying to grow up in a white mans world. Bigger, the main charter, is growing up in a typical black neighborhood. He is the only man of the house so he must help his mother support them. In this novel it is important to understand that Bigger is prone to violence. In every tough situation he gets stuck in he refers to a violent action. This can be seen by the way he treats his friends and family. Richard Nathaniel Wright was born on September 4, 1908 on a Mississippi plantation. During Wrights childhood he was often hungry. This allowed Wright to write passionately and eloquently about the meaning of suffering in the lives of oppressed and exploited people because that suffering was an integral part of his own life. The Communist Party had been the only one to take a deep interest in Wrights life and had at one time offered to teach him to write. Richard Wright died on November 28, 1960, at the age of 52 in Paris. Choose a person who had the most influence on Bigger. I feel that Max had the most influence on Bigger. Max helped Bigger realize what he had done wrong and how that not all white people were out to get the black man. At times Bigger felt that Max was only trying to hurt him but I think that deep down inside, Bigger knew Max was only there to help him. A wave of excited voices swept over the room. Biggers fingers gripped the arms of the chair. Maxs hand touched his shoulder, Bigger turned and Max whispered,Sit stillMr. Coroner?Yes?In the capacity of Bigger Thomas lawyer. Id like to state that he does not wish to testify here (328). This quote shows that Max was looking out for Biggers best wishes. Max knew that if Bigger had testified the lawyers would have pounded him with questions and made him seem more guilty that he already was. I also think that it showed Bigger that Max cared about him and showed Bigger that he was going to help him though the trial. Your honor, I have no desire to be disrespectful to this court, but I must be honest. A mans life is at stake. And not only this man a criminal, but he is also a black criminal. And such he comes into this court under a handicap, notwithstanding our pretensions thatall are equal before the law (382). Max is showing not only the court, but the nation as a whole, that there is no way that Bigger can receive a fair trial. Bigger and Max both know this. I also think that Bigger knows he is going to die Max is the only one trying to help him. Max is trying to do the impossible. That is make a black man innocent in a white mans court. Max not only had a major influence on Bigger, but he was one of the only people that cared about him and did not judge him by the color of his skin. I think that Max had a significant influence on the judge even though Bigger did receive the death penalty. Look at Jan and tell whether he is a realistic charter or not. I feel that Jan could be a realistic person but his views on topics are too exaggerated and Jan is too forgiving. In the pale yellow sheen of the street lamp they faced each other . . . Bigger had his hand insidehis shirt pocket on his gunWhat all this about, Bigger? I havent done anything to you Bigger. Jans presence condemned him it was Jans innocence that made anger rise in him (171). .u7b1dd7e8fbef693920cb8322580dd420 , .u7b1dd7e8fbef693920cb8322580dd420 .postImageUrl , .u7b1dd7e8fbef693920cb8322580dd420 .centered-text-area { min-height: 80px; position: relative; } .u7b1dd7e8fbef693920cb8322580dd420 , .u7b1dd7e8fbef693920cb8322580dd420:hover , .u7b1dd7e8fbef693920cb8322580dd420:visited , .u7b1dd7e8fbef693920cb8322580dd420:active { border:0!important; } .u7b1dd7e8fbef693920cb8322580dd420 .clearfix:after { content: ""; display: table; clear: both; } .u7b1dd7e8fbef693920cb8322580dd420 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u7b1dd7e8fbef693920cb8322580dd420:active , .u7b1dd7e8fbef693920cb8322580dd420:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u7b1dd7e8fbef693920cb8322580dd420 .centered-text-area { width: 100%; position: relative ; } .u7b1dd7e8fbef693920cb8322580dd420 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u7b1dd7e8fbef693920cb8322580dd420 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u7b1dd7e8fbef693920cb8322580dd420 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u7b1dd7e8fbef693920cb8322580dd420:hover .ctaButton { background-color: #34495E!important; } .u7b1dd7e8fbef693920cb8322580dd420 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u7b1dd7e8fbef693920cb8322580dd420 .u7b1dd7e8fbef693920cb8322580dd420-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u7b1dd7e8fbef693920cb8322580dd420:after { content: ""; display: block; clear: both; } READ: Criminology EssayJan, I think, is too forgiving to be realistic. How can a man that was just lied about be questioning his accuser on what was said about him? If I were Jan, I would want to kill Bigger for making up the whole story and lying about me. Jan not only forgives Bigger, but he wants to help Bigger by getting him a lawyer to defend Bigger in court. Let me be on your side, Bigger Jan said. I can fight this thing with you, just like youve started it. I can come from all of those white people and stand here with you. I got a friend his name is Max. He wants to help you (289). Jan wants to have his friend Max help him in court. How could any human being be this forgiving? Jan was not only accused of the crime but he was directly involved in it because of Mary being his girlfriend. Discuss two themes and choose which one you like the best. The two themes that I am going to discuss are: How Bigger awakes to the fact that he killed Mary and How Bigger thinks that it is Bessies and Marys fault that he killed them. At the beginning of Book II Bigger is struggling to come to reality that he has in fact killed Mary. He also must face the fact that he had killed and that he killed a white women. Subconsciously he denies killing Mary but I know that Bigger knows he killed her. He would have to go over his story andmake it foolproof . . . Oh, hell, what had happened had happened and he would stick to his story (126). This quote shows that Bigger knows that he has killed Mary. He is trying to prefect his story to the best of his ability but he is unable to comprehend that this is all very real and that he is in serious trouble. How does Bigger think that the murders he committed were Marys and Bessies fault? Bigger knows that he has killed two people, but for Biggers own sanity he tries to blame the two women. Bigger feels that it was Marys fault and that he had to smother her with a pillow when she came home drunk after making him eat and drink with her after he didnt want to. When he killed Mary, he had to kill her because it was Bessie that kept nagging him to tell her of his scheme. Bigger felt that he had to kill these two women. He was rigid; not moving. This was the way it had to be. Then he took a deep breath and his hand grippedthe brick and shot upward and paused a second and then plunged downward through the darkness (237). For choosing a topic I am going to choose how Bigger felt he had to kill the two women. I think that the murders prove one thing that Bigger can be a man himself. In Biggers life Bessie and Mary are the most meaningful things that ever happened to Bigger Thomas. Compare and contrast Native Son with The Awakening. I think that the two books can be compared in the basis of that in both novels someone was looking for freedom. In The Awakening Edna was looking for freedom from her husband. She was tired of being restricted in what she could do. Edna wanted to be her own person. In Native Son Bigger is looking for freedom in things that he is allowed to do. Bigger wants to be allowed to do the same things as the white man. Bigger has always been told that he cannot hold certain jobs in this world. Both Bigger and Edna wanted things that neither of them would see in their lifetimes. My opinion of this book is very good. I enjoyed reading Native Son. I was amazed with the graphic descriptions of how Richard Wright could describe how Bigger killed Mary and stuffed her in the furnace. Wright captured and held my attention throughout the entire novel. I hated the way the book ended though I thought that somehow it would go on and say that somehow, someway Bigger would get out of the death penalty. I feel that Max in his closing statement made an accurate description of what Bigger was feeling at the time that he murdered both Mary and Bessie.

Weimar Republic Essays (2325 words) - German Revolution Of 191819

Weimar Republic Weimar Republic There were various factors that contributed to the failure of the Weimar Republic of Germany and the ascent of Hitler's National Socialist German Workers Party into power on January 30, 1933. Various conflicting problems were concurrent with the result of a Republic that, from the outset, its first governing body the socialist party (SPD) was forced to contend with. These included the aspect of German imperialism, the unresolved defeat of 1918, financial collapse and the forced struggle against the activities of the National party as well as inflation. Other factors that influenced the failure of Weimar were the structural weaknesses induced by the constitution and the basic lack of support for the Republic among the German people particularly amongst the elite. All in all, these aspects were the major causes that doomed the Weimar republic to ultimate failure and the eventual ascent of Hitler's nationalist party to power. The new socialist government of Weimar (SPD), whose constitution was adopted on July 30, 1919, entered a situation they by no means created. The period during which they were appointed to rule was associated with defeat and misery, and when disorder was nationwide. The situation then, was that of revolution. However, rather than to make it a revolution of there own, they co-operated with the liberals and with the catholic centre party to lead Germany in a reformed version of her old self. In June 1919, they voted to comply with the treaty of Versailles. However, the signing of the Treaty served to promote protest and unrest amongst the soldiers, sailors and the German people generally, and democracy thus resulted in becoming an alien device. The imperial army, for instance, never got over the humiliation of surrender, which they felt, was a 'stab in the back' by their own countrymen. The sailors at Kiel mutinied in a last desperate effort on October 28 and on November 9 1919, the streets were filled with crowds marching to demonstrate at the center of Berlin. Furthermore, compliance with the Treaty of Versailles meant that Germany would have to make reparation payments it could scarcely afford. This fact placed a heavy strain on the already suffering economy of Germany which was bankrupted by four years of war thus ensuing in the ascend of inflation and the occasioning of the respite of payments by Germany in 1922. The French reacted by occupying the Ruhr, a major industrial area of Germany, in January 1923. This was felt a grave humiliation by the German people and eventuated in widespread discontent. Germany's currency was already fragile, and in face of the occurring circumstances consequent to the Ruhr invasion and the overprinting of currency, the Mark fell to chronic levels, eventually reaching the value of four billion against the US dollar, which therefore generated massive hyperinflation. The economic instability, on top of the disillusionment and resent caused by the humiliating peace settlement, resulted in vast sections of German society feeling alienated by the Republic. They responded by attacking the democracy and as a consequence it became impossible to control the hostility and discontent. The deteriorating economic and social situation also managed to wreak havoc on the political atmosphere of the time and the Republic wound up having no positive friends and too many enemies. The Republic faced opposition from the extreme left by Spartacists who resorted to force in efforts to overturn the Republic. In March 1920, the Freikorps who in Berlin launched a pro-Monarchist putsch in an attempt to install Wolfgang Kapp as Chancellor also challenged the Republic from the right. During this incident troops both refused to defend the Republic or take action against Freikorps. In protest the working classes then responded by organizing a general strike in Berlin, which had the effect of frustrating this putsch. The present regime was able to survive despite the numerous threats. Extremism remained to pollute the atmosphere, the evidence being represented in the alarming amount of political assassinations that continued occurring. In evidence, according to an estimate of the Minister of Justice, rightists committed 354 murders between 1919 and 1923. During this time, when the Republic was suffering most and was being threatened, practically from all sides, Hitler had been making affective attempts to capitalize on the resultant circumstances. He exploited the economic collapse by blaming it on all those he wished to portray as enemies. These were the same enemies he declared as the 'November criminals' who had brought about Germany's defeat in 1918. Hitler's plan was to seize power in Munich, and, with Bavaria as his base, to launch a march on Berlin not unlike

From Element to Riches essays

From Element to Riches essays A diamond in a sense is the most communal, elegantly, used jewel used in circulation today. Do people in actuality understand the concept and edifice of this mineral? A diamond is known as the hardest rock in existence and to most of the world it is a piece of jewelry, but do we know what the chemical composition of a rock and how is it formed? A diamond in actuality is carbon in its most concentrated form. While a few diamonds may have trace impurities such as boron or nitrogen, most diamonds are composed mostly of carbon. Carbon is a chemical that is fundamental in the process of life and used in various amounts of ways on the Earths surface. In diamonds, carbon atoms share all four valance electrons with adjacent carbon atoms, which form a tetrahedral unit. The covalent bond that is formed in this process is responsible for many of the diamonds superlative properties. As a result of the highly symmetrical arrangement of eight atoms that are fundamentally arranged in a repeating structural unit diamond crystals can form a variety of different shapes known as crystal habits. The octahedron is the most common of these crystal habits, but others include cubes dodecahedra and combinations of theses shapes. All however, are manifestations of the cubic crystal system to which the mineral diamond belongs. Diamond crystals that are real do not have entirely smooth faces which can be seen in the trigons that reflect the subtle changes of height in the diamonds face. However some raised trigons that point the same direction as the crystal face can occur from dissolution, etching, and the crystals natural growth. Another notable property that the diamond is well known for is its hardness. Diamonds are the hardest substance known, receiving a ten on Mohs hardness scale. While diamonds are not fragile or prone to breaking they can fracture or shatter. The best place for splitting a diamond is along one of its lines of cleavage as the cr...

Heavy Metals in Science - Definition and Examples

Heavy Metals in Science s In science, a  heavy metal is a metallic element which is toxic and has a high density, specific gravity or atomic weight. However, the term means something slightly different in common usage, referring to any metal capable of causing health problems or environmental damage. Examples of Heavy Metals Examples of heavy metals include lead, mercury and cadmium. Less commonly, any metal with a potential negative health effect or environmental impact may be termed a heavy metal, such as cobalt, chromium, lithium and even iron. Dispute over Heavy Metal Term According to the International Union of Pure and Applied Chemistry or IUPAC, the term heavy metal may be a meaningless term because there is no standardized definition for a heavy metal. Some light metals or metalloids are toxic, while some high-density metals are not. For example, cadmium generally is considered a heavy metal, with an atomic number of 48 and specific gravity of 8.65, while gold typically is not toxic, even though it has an atomic number of 79 and specific gravity of 18.88. For a given metal, the toxicity varies widely depending on the allotrope or oxidation state of the metal. Hexavalent chromium is deadly; trivalent chromium is nutritionally significant in many organisms, including humans. Certain metals, such as copper, cobalt, chromium, iron, zinc, manganese, magnesium, selenium, and molybenum, may be dense and/or toxic, yet are required micronutrients for humans or other organisms. The essential heavy metals may be needed to support key enzymes, act as cofactors, or act in oxidation-reduction reactions. While necessary for health and nutrition, excess exposure to the elements can cause cellular damage and disease. Specifically, excess metal ions can interact with DNA, proteins, and cellular components, altering the cell cycle, leading to carcinogenesis, or causing cell death. Heavy Metals of Significance to Public Health Exactly how dangerous a metal is depends on several factors, including the dose and means of exposure. Metals affect species differently. Within a single species, age, gender, and genetic predisposition all play a role in toxicity. However, certain heavy metals are of grave concern because they can damage multiple organ systems, even at low exposure levels. These metals include: ArsenicCadmiumChromiumLeadMercury In addition to being toxic, these elemental metals are also known or probable carcinogens. These metals are common in the environment, occurring in air, food, and water. They occur naturally in water and soil. Additionally, they are released into the environment from industrial processes. Source: Heavy Metals Toxicity and the Environment, P.B. Tchounwou, C.G. Yedjou, A.J. Patlolla, D.J. Sutton, Molecular, Clinical and Environmental Toxicology  Volume 101 of the series  Experientia Supplementum  pp 133-164. Heavy metals a meaningless term? (IUPAC Technical Report)  John H. Duffus,  Pure Appl. Chem., 2002, Vol. 74, No. 5, pp. 793-807

Government Essay Example | Topics and Well Written Essays - 750 words

Government - Essay Example strialized City in heart of this country, a highway was constructed, cutting across the major watershed supporting the City’s underground water supply to reduce into half the travel time from the Export Processing Zone to the International Ship-building Yard on the other side of the island. Hundreds of trees were cut to give way to the approximately 100-kilometer road traversing the mountain ridges. Since, the mountains were already cleared and accessible to motor vehicles, affluent City dwellers started building houses on the cleared areas. Soon, a large portion of the watershed turned into a housing and commercial district. A couple of years after the opening of the highway, water supply seriously dropped. It was estimated that with the current rate of extraction will soon overtake the recharging rate and fresh water supply will be gone in less than 15 years. An alarming level of E. Coli bacteria brought about by fecal contamination was also found in the water. This sad reality happening is not only happening in developing countries like the Philippines. Even developed countries have problems of similar nature. A serious review of water governance policies is in order. Water supply plays a vital role for sustainable development, be it in developed countries or developing countries. The use and abuse of water supply and the blatant disregard or ignorance of its management can cost a city even an entire country a fortune. Water shortages and water quality degradation are seriously affecting prospects for economic and social development in countries all over the world. However, most of these fatal mistakes can easily be avoided with a good water governance system. Water governance refers to the range of political, social, economic and administrative systems that are in place to regulate the development and management of water resources and provision of water services at different levels of society. This must be instituted at the regional, national and local

Modern methods of teaching English Language Essay

Modern methods of teaching English Language - Essay Example Moreover, English is one of the most widespread languages of the planet serving as the means of politics, business, and economics communication for world leaders. With the help of the technological innovation and Internet English vocabulary enriches with new words every day. However, there are also degrading process in the language, some grammar rules get redundant and there appear new on their place. Therefore, teaching English demands close attention to all the changes. Every teacher knows that despite general requirements he/she must elaborate personal approach to the teaching and choose among the numerous methods. It is possible to base the choice on the experience received at school or University, or follow already existing methods. There exist numerous techniques of teaching English Language. Some of them become outdated with the development of new technologies, and some get substituted with more efficient. It is hardly possible to choose one method that could be applied for ev ery situation as each technique has its own purpose. It is necessary to know advantages and disadvantages of each method and be able to utilize them according to the situation. There are numerous innovations in English language teaching which appeared in the past century. Many schools, teachers, and applied linguists strived to find the optimal and the most efficient methods of language teaching basing on their understanding of the learning mechanisms. Traditional methods were mostly concentrated on teacher`s explanation of the material, practicing of lexical and grammatical material, and skills development. Modern methods of English language teaching are more student-oriented comparing to the old methods, they encourage students to learn rather than make them learning. A student becomes involved in a half-natural process of interaction with a techer.

Reliability Issues †Centrifugal Slurry Pumps Essay Example for Free

Reliability Issues – Centrifugal Slurry Pumps Essay Introduction Pumps were probably the first machine ever developed, and are now the second most common machine in use around the world, out-numbered only by the electric motor. The very earliest type of pump is now known as a water wheel, Persian wheel or â€Å"noria†, consisting of a wheel of buckets that rotates to pick up water from a stream and dump it into a trough. Another early pump was the â€Å"Archimedean screw†, similar to the modern screw conveyor except that the flights were often fixed to the tube so that the whole arrangement would turn together. Both of these devices are still used, most commonly in basic agricultural applications. Pumps are now produced in an enormous range of types and sizes, for a very wide scope of applications, and this makes it difficult for any individual reference document or organisation to cover â€Å"pumps and pumping† as a general topic. So the broad field of pumping is classified into sub-divisions and then dealt with at that level. In the mining industry, the upper end of the pump scale includes impellers with diameters over 2.5m, slurry lines 10km long, particle size up to 100mm, flow rates handling more than 7000tph, and motors over 10MW. Finer slurries of around 1mm particle size are pumped for hundreds of kilometres in some operations. There are many ways to classify pumps. This just one of them. This document only addresses centrifugal pumps, with a focus on single-stage radial-flow slurry pumps. Centrifugal pumps are capable of meeting duties of up to 1.4 m /s at 30MPa, and higher volumes at lower 3 pressures. The maximum flow rate at low discharge pressure is about 180 m /s. Industrial applications requiring high delivery pressures generally use reciprocating fixed-displacement pumps, but they are limited in the amount of flow they can put out per unit. In general purpose applications, where different types of pumps could all deliver the performance sought, centrifugal pumps are usually the preferred choice due to lower lifecycle costs. Basic Requirements for Reliability Assuming correct pump manufacture and installation, the basic requirements for reliable long-term operation of centrifugal pumps are: 1. Continuous operation at best-efficiency point (BEP) 2. Adequate net positive suction head (NPSH) 3. Low velocity fluid flow within the pump and throughout the system 4. Processing of fluids that are benign ie: a) Chemically and physically stable b) At near-ambient temperatures c) Free of particles likely to cause wear or blockage Pumps of a basic design satisfying all these requirements have run for 50 years and more without major component replacement. The first three requirements are satisfied by matching pump performance to expected duty. Where item 4 cannot be addressed through pre-treatment of the fluid, the pump configuration, geometry and materials must be optimised to give best results. Obviously, item 4.c) is a dominating issue for slurry pumps as it cannot be eliminated and must be managed. Centrifugal Pump Construction Centrifugal pumps have two main sub-assemblies – the rotating parts (impeller, shaft, bearings), and the fixed parts (casing, piping connections, stand, foundations. Pumps of all types may be single stage or multi-stage. Multiple stages are used where it is not practical to generate the necessary discharge pressure using a single impeller. The simplest way to imagine a multi-stage pump is as one pump with its discharge feeding straight into the suction of a second pump so that the overall discharge pressure is increased while the flow rate stays the same. However, this arrangement is properly described as â€Å"single stage pumps in series†. A true multi-stage pump consists of multiple impellers mounted on a single shaft, positioned in a single casing made up of multiple chambers. Multi-stage pumps of this type are not used with slurries, but sometimes slurry pumps are mounted in series. Casing There are two types of casing designs â€Å"volute† and â€Å"diffuser†. A volute casing has a snail’s shell shape, while a diffuser casing has internal vanes. Diffuser casings are rarely used on single-stage radial pumps, and are not commonly used for handling slurries due to the flow restriction and high wear rates that would result. Slurry pumps have volute casings which house the impeller and have a spiral-shaped outer volume that extends 360 degrees and increases in cross-sectional area as it approaches the discharge flange. At full circle the volute overlaps itself, creating the cut-point, also known as â€Å"cut-water point† or â€Å"tongue†. The ideal shape is to have a steady linear increase in cross-sectional area for 360 degrees around the circumference starting from the cut-water point, but this can be difficult to manufacture. Compared to a clear water pump, a slurry pump has a much larger radial gap between cut-water point and impelle r, to reduce risk of blockage. Where a pump is identified as oversize for its duty, and is suffering high recirculation wear, it may be possible to fit liners with an extended cut-water point that throttles the flow. In theory, when a pump operates at its best efficiency point (BEP), the pressure acting on the impeller and casing are uniform. However, in practice the pressure is rarely completely uniform, and if a pump is operating away from its BEP the imbalanced in the radial forces acting on the impeller become significant. These forces are larger for bigger pumps operating at higher pressures. Running a large pump below rated capacity can create unbalanced radial forces that may (over time) damage the bearings or snap the shaft. If it is known that a pump may need to occasionally operate well away from its BEP, the manufacturer should include an oversize shaft arrangement in the design, but with commercial competition driving purchase decisions this may have to be specifically requested. Another option for reducing imbalanced radial forces is to use a twin-volute design, which consists of a wall splitting the volute in half for about half its circumference, ending after the cut-point but before the discharge flange. This is not practical for most slurry applications. Casings must be designed to allow the impeller to be installed inside, and so are manufactured in at least two parts. Solid casings have a removable cover, either on the suction side or shaft side or both, but the volute shape is a one-piece casting. Casings may also be split, either axially or radially. Axially split housings make inspection easier because the upper piece can usually be removed without disturbing the shaft or piping too much. Split casings may tend to â€Å"breathe† at high pressures, resulting in leakage, air entrainment, vibration, misalignment etc. Casings are normally provided with ribbing at the location of highest stresses, to minimise this. Open or semi-open impellers require close clearances against the casing to ensure pumping efficiency. The casings generally include a side-plate that can be adjusted for minimal clearance using jacking screws or shims, especially in wearing applications eg slurries. Impeller Impellers are classified according to their design features ie: ï‚ · Suction flow orientation o Single suction ie inlet on one side only o Double suction ie inlet on both sides ï‚ · The direction of exit flow relative to the shaft axis ie: o Radial flow o Axial flow o Mixed flow ï‚ · Vane shape ie: o Single curvature vanes, also called straight vanes – the impeller surfaces that accelerate the fluid are straight and parallel to the axis of rotation o Francis or screw vane – the surfaces that accelerate the fluid are curved in relation to the axis of rotation ï‚ · Mechanical construction o Enclosed ie with side walls or â€Å"shrouds† o Open ie no shrouds o Semi-open ie shroud on one side only o Partially shrouded ie shroud not extending to impeller tips The open area through which the fluid flows into the impeller is called the suction eye. For a closed-shroud impeller, this is simply the hole in the shroud. The suction eye area is an important featur e of the pump design. The area taken up by the shaft, if it protrudes through the eye, is deducted when calculating eye area. Impellers can be single suction or double suction. A single suction impeller has an inlet eye on one side only, with the shaft extending out the opposite side so the impeller overhangs. A double suction impeller can be thought of as two mirror-image single suction impellers mounted back-to-back. They accept fluid from both sides and usually have a shaft that extends straight through the impeller with bearings providing support on both sides. Double suction impellers are usually fed fluid from a single inlet flange, with the fluid flow being split into two streams by channelling inside the casing. Double suction units provide advantages in reduced fluid velocity at the impeller eye, and better balancing of axial hydraulic forces, while single suction units are simpler in design, manufacture and maintenance. Most if not all slurry pumps are single suction type. Some pumps may have an inducer, which is an axial flow impeller with a few blades installed between the suction inlet and the main impeller, intended to improve the suction head seen by the main impeller. Impeller shrouds often incorporate thin â€Å"pump-out vanes† cast into the outside of the shrouds. Their purpose is to help clear any solids from the back hub of the impeller (opposite the inlet eye), reduce pressure at the seal area, reduce axial thrust, and discourage recirculation. Some impellers have similar vanes on the eye side as well as the shaft side – in this case, those on the shaft side are usually called â€Å"expeller vanes†. In clear water pumps, a cylindrical ring is usually cast or machined into the outside surface of the shrouds, coinciding with a matching feature in the casing, to help seal off the discharge fluid from the suction fluid and prevent internal circulation. Clearances here are tight in order to ensure pumping efficiency – typically around 0.25mm on radius for most common sizes of industrial pumps. In larger pumps the casing (and sometimes also the impeller) is usually protected at this point by replaceable â€Å"wear rings†, which may be high-wear items, and need to be replaced before efficiencies fall too low. It is good practice to replace wear rings once the clearance reaches twice the original specification. Wear rings are provided in a wide range of designs and materials according to the pressures, speeds and fluids involved. The wear rings on impeller and casing are often made from differing materials that are not subject to galling, to reduce problems should contact occur. Wear ring features may include labyrinths, water injection, inspection ports, adjustment mechanisms etc. Pumps handling light slurries may make use of wear rings, sometimes with water injection to reduce wear from the slurry. Pumps handling heavier slurries usually just use pump-out vanes. Slurry pump impellers must be designed to resist wear and tear, and this requires some pumping efficiency features to be sacrificed. For example, vane edges will be blunter, vanes and shrouds will be generally thicker, and the number of vanes will be decreased in order to open up the channels between them. Passages through slurry pumps, including impeller vane spacing, are larger than for clear water pumps. Open impellers are sometimes used for very stringy materials, but tend to be weak and wear quickly, and so are not very common. Vane shape is obviously a major element of impeller design. Two critical factors are the blade entry angle (ß1) and blade exit angle (ß2), as measured between the centre-line of the vane and a tangent to the inner or outer diameter (respectively) drawn from their tips, in the oppo site direction to rotation. Most modern pumps have impellers with ß2 smaller than ninety degrees – ie backward-curved blades. Theoretically, a forward-curved blade would give higher head, but at less efficiency. Some pumps have ß2 at ninety degrees, and these are sometimes referred to as â€Å"expellers†. Many clear-water impeller designs rely on close running clearances between vane tips and casing to minimise recirculation from one â€Å"vane chamber† to the next, and maximise efficiency. Even small amounts of vane tip wear can have an effect on head and overall efficiency. The outer and inner vane tips should be sharp, not rounded or chamfered. Replacing a pump which is too large for its duty can be a major exercise. It usually requires changes to the foundations, drive arrangement and piping, spares holdings, and so on. A model of the ideal size may be just not available. As an alternative, in some cases it may viable to install a reduced-diameter impeller without changing other components. If done correctly, trimming the impeller will move the pump’s BEP to match the actual system operating point. The efficiency at the new BEP will be lower than the BEP with the original impeller, but higher than was being achieved in practice when operating well away from the original BEP. The performance variation can be estimated using the â€Å"affinity laws† which often apply to a specific impeller before and after machining: Flow rate: Pump head: Motor power: Q1 / Q2 = n1 D1 / n2 D2 H1 / H2 = (n1 D1 / n2 D2) P1 / P2 = (n1 D1 / n2 D2) 2 So if running at the same speed, trimming an impeller by a certain proportion will result in a corresponding drop in flow rate, a greater decrease in head produced, and an even greater decrease in the motor power consumed. However, these equations are based on several assumptions and some caution is called for. Impellers are complex three-dimensional objects and their effects on the liquid are due to other factors that are also affected by machining, beyond just the outside diameter – eg open area, discharge blade angle and so on. The following considerations should apply. ï‚ · Diameter reductions should not exceed 10%. Reductions beyond 20% are generally considered extreme. Some references state 30% as the maximum reduction advisable. ï‚ · Some overlap in the vanes should be retained. ï‚ · The angle between the vane centreline and the tangent to the outer diameter drawn at its tip should be restored to original by filing, with most filing occurring on the trailing si de of the vane.   The vanes will probably be thicker after cutting, and should be filed back to original shape, by filing on the traling side of the vane. ï‚ · Vane tips should be kept sharp, not rounded or chamfered. Outer tips should be sharpened by filing on the trailing side, and inner tips by filing mostly on the leading side.   Inefficiencies will take the form of increased disc friction, increased flow path length within the casing, and more recirculation across vane tips. Impellers apply forces to the fluid and are subject to the equal and opposite forces themselves. The typical single-suction impeller engages with fluid entering the pump and at first accelerates it axially into the pump, before diverting it into the radial direction. The impeller pushes the fluid into the pump, and at the same time pushes itself axially back toward the inlet point. Another way of looking at this effect is to consider that the impeller is mostly exposed to pressurised fluid all over the shroud surfaces, but not at the eye on the suction side. The thrust on the impeller must be resisted by the shaft arrangement, which must always include bearings capable of serious thrust loading. Double-suction pumps typically have less axial loading, but can still experience axial thrust, especially if flow is restricted more on one side due to internal differences in the pump, or restrictions in fluid supply on one side. Clean water pump designs may incorporate features to reduce this imbalance, such as having wear rings on both sides of the impeller, with the pressure within t he volume they enclose largely equalised by â€Å"balancing holes† passing right through the impeller. Another method is the use of a balancing disc. This is a disc mounted on the shaft in a separate chamber, with a geometry and clearances designed to counterbalance thrust effects. However, these are not practical for slurry pumps, which may use pump-out vanes instead, to lower the pressure toward the inner area of the non-suction shroud. Axial thrust loads usually consist of a steady state component plus dynamic fluctuations. Heavy axial loading is often associated with recirculation. Where failure occurs it is usually a result of overloading and over-heating of bearing components. Measures to correct excessive axial loading include:   Restoring BEP operating conditions (which may include selecting a more appropriate pump size or trimming the impeller)   Ensuring internal clearances / wear are not excessive ï‚ · Verifying correct bearing type and installation including clearances / pre-load To further complicate this issue of axial thrust, single-suction pumps handling fluids with a high suction head may experience thrust on the impeller in the opposite direction, away from the inlet. And then there are pumps with highly variable duties and suction conditions that may experience impeller thrust in different directions at different times. Shaft The shaft transmits mechanical power to the impeller from the driving motor or engine. It must also support the impeller and restrict its axial and radial movement. The loads on the shaft include self-weight of the rotating components, torque, and forces transmitted to / from the fluid. Design of a shaft requires consideration of maximum allowable deflection, the span or overhang, the location and direction of all loads, any temperature variations, and the critical speed. Loads are normally at their maximum on start-up. All objects have a natural frequency at which they will vibrate after being struck. Machines made of several components with complex shapes normally have several natural frequencies, some of which dominate. In the case of pumps, if the rotational speed of the impeller matches a dominant natural frequency, small imbalances may be amplified to a level where they interfere with operation and/or reliability. These are known as â€Å"critical speeds†. Steady operating speeds between 75% and 120% of the first critical speed should be avoided. Pumps with longer overhang on the shafts have lower critical speeds. Shafts are referred to as rigid or flexible, according to whether the running speed is lower or higher than the first critical speed. Pumps with a flexible shaft must pass through a critical speed on each start-up. This is not usually a problem because frictional forces with the fluid and the bearings act as dampers for a period sufficient for transition through the critical speed. Pumps with speeds below 1750rpm, which includes most slurry pumps, are usually of the rigid-shaft design. The shaft must be designed so that any deflection will not bring moving parts into contact, for example at wearing rings, or cause non-concentricity in critical areas such as the shaft seal. As a general rule, shaft deflection should not exceed 0.15mm even under the most extreme conditions. Deflection and critical speed are related stiffening a shaft to reduce deflection will also raise its critical speed. For pumps with overhung impellers, as is the case for most slurry pumps, this often results in the shaft diameter between bearings being quite large. The fluid passing through a pump creates a hydrodynamic bearing effect, known as the â€Å"Lomakin Effect†. That is, to some extent, the impeller rotating in the casing with fluid present is like a shaft rotating in a journal bearing with oil present. The result is that the shaft is better supported when running than when idle, so that the shaft deflection will be less, and the critical speed of the shaft assembly will be higher. However, the Lomakin Effect varies with pump head and internal clearances, both of which diminish with wear. Therefore the effective critical speed may be expected to decrease with time in service. To allow assembly, shafts step up in diameter from coupling to bearing to impeller, so tha t any torque problems are very likely to appear first at the coupling rather than the impeller, at least in single stage pumps. Shaft Seal and Sleeve The shaft connects the drive to the impeller, and so must pass through the pressurised casing. Achieving a reliable seal between shaft and casing is one of the most problematic areas in pumping. Centrifugal pumps have two types of seals – mechanical seals and packing seals. Many designs of mechanical seals have been attempted for slurry pumps, without comprehensive success, and the remainder of this discussion concentrates mainly on packing seals and stuffing boxes. Note, however, that packing is only suitable within pressure and temperature limitations. Depending on pump design and duty, the seal may need to prevent either air ingress into the casing, or fluid egress out of the casing or both of these at different times, if operation is variable. Many casings are designed with the seal area built into a compartment configured to improve sealing performance. For mechanical seals, this compartment is usually referred to as the â€Å"seal chamber†, while for packing seal s, it is known as the â€Å"stuffing box†. Slurry pump seals usually consist of several rings of packing fitted in a stuffing box around the shaft, often with provision for grease lubrication or water injection to reduce friction and provide additional sealing (particularly for when the pump is stopped). There are many stuffing box design variations and many types and configurations of packing. Stuffing boxes will accept a number of rings of packing, with a packing ring or throat bush preventing extrusion into the casing, and a gland (sometimes called a â€Å"follower†) used to adjust packing compression. A lantern ring may be substituted for one of the packing rings, to cater for injection of grease or sealing water, water being particularly required if air would otherwise be sucked into the fluid stream at this point. Sealing water (or an alternative clean liquid) is usually required for: Slurries   Liquids for which leakage is not acceptable   Liquids that are not suitable for sealing purposes   Suction lifts greater than 4.5m (air ingress may interfere with priming)   Discharge pressures above 70kPa The packing must be placed under some compression and this tends to result in wear on the shaft, which is often sleeved to avoid having to replace the entire shaft once wear is advanced. There are numerous designs of shaft sleeves. The shaft sleeve must be resistant to friction and heat, and several different materials and surface treatments are available – eg hardened high-chrome stainless steel, ceramic, plasma spray or tungsten carbide coating etc. To prevent chipping, coatings should not extend to the edges of the sleeve. The sleeve does not contribute to strength, so the shaft itself must be large enough to carry all the loads, and this means that including a sleeve in the design enlarges the seal diameter. For small pumps, this may decrease pumping efficiency and raise the purchase cost to the point that sleeves may be abandoned and a stainless steel shaft used instead. Glands may be solid, or split to allow replacement without disassembly of pump or bearing assembly. They are usually made of bronze, cast iron or steel. Special designs are used to improve safety if the fluid is hazardous. The leakage of fluid past the packing is controlled by tightening the gland, compressing the packing axially and expands it radially so that leakage paths along the shaft sleeve are constrained. However, some fluid flow between packing and sleeve is usually needed to avoid overheating the packing and damaging the sleeve surface. Once the sleeve surface is damaged, the sealing efficiency decreases and more tightening is required, further damaging the sleeve, and so on. The secret is to provide a configuration of packing and seal water injection that suits the application, and then avoid over-adjustment. To further reduce the pressure at the shaft seal area, where the rear pump-out vanes are not sufficient, some slurry pumps are fitted with a second smaller open-faced impeller, usually called an â€Å"expeller†. Many different designs have been tried. If sealing water is used, there will be a design intention regarding the ratio of water to pass in to the volute compared to out past the gland follower. This can be controlled using the number of packing rings on each side of the lantern ring, but the lantern ring must be installed at the injection point. For clean water pumps, this seal water is sometimes provided from the pump discharge. Clean water must be used to avoid contaminating the packing with grit – filtration or cycloning may be necessary if the water contains some grit. When managing sealing arrangements, thought must be given to what happens when the pump is stopped. The pressure in the stuffing box changes to static conditions, which may result in slurry leaking into the packing and contaminating it, causing rapid sleeve wear on re-starting. But if sealing water continues to be applied, the slurry may be diluted, and eventually a sump can be filled with sealing water if left idle for a long time. For prolonged stoppages, sumps may be best dropped, for various reasons. On restarting, sealing water supply should start before the pump starts. Stuffing boxes in extreme applications may be provided with galleries through which cooling water can pass to prevent excessive temperatures around the packing. In applications where leakage must be more precisely controlled, or where elevated temperatures in the seal area must be avoided (for example where the fluid is volatile), mechanical seals may be suitable, provided that the fluid is not damaging to the seal components. A comparison between mechanical seals and packing seals is given below. ï‚ · Packing seals: o Low initial cost o Tend to deteriorate gradually o Easily replaced when necessary o Can handle large axial shaft movements o Always some leakage required o Require regular adjustment o Not suitable for hazardous / volatile fluids o Often cause progressive shaft sleeve wear o Can result in significant shaft power losses o Limited to low pressures and speeds ï‚ · Mechanical seals: o Minimal or zero leakage o No adjustments required o Suitable for hazardous / volat ile fluids o No shaft wear o Do not consume significant shaft power o Can handle high pressures and speeds o Tend to fail suddenly o Replacement requires pump disassembly o High initial cost Packing seals work as a result of axial compression, so that the packing rings extrude outward and apply radial pressure to the adjacent components, these being the static surface of the stuffing box, and the rotating shaft sleeve. A dynamic seal is formed between the packing rings and the sleeve surface, with some fluid flow between the two being necessary for lubrication and cooling. For clean water pumps, this fluid may be supplied from the inner end of the stuffing box, or from the discharge pipe via small diameter piping. In the case of slurries, grit in the fluid would add to friction and wear, so the lubricating and cooling fluid is usually injected from a separate clean water supply. The injection pressure should be 10 to 25psi greater than that at the inside end of the stuffing box, and this figure should be available from the pump designer. A rule of thumb is to set the gland feed water pressure to between 35 and 70kPa above pump discharge pressure. Pressure regulation is often helpful. In theory, some slurry pumps should operate with a pressure at the inside of the stuffing box which is below atmospheric pressure, so that the packing is required only to prevent air ingress into the pump. However, when the pump is turned off, or in abnormal operating conditions, slurry can pass back into the seal and contaminate the packing with grit, so these situations still call for water injection. Grease or oil may be used instead of water in some applications. Packing material must be able to withstand the operating environment and remain resilient to perform satisfactorily despite minor shaft misalignment, run-out, wear and thermal expansion / contraction. Packing is available in a huge range of materials (lubricant, binder and fibre / matrix) and in many sizes, shapes, and constructions, to suit different applications – particularly size, shaft speed, temperature, pressure, and chemical resistance. The number of packing rings varies between applications, the most common arrangement being throat bush or ring, three inner packing rings, lantern ring, two more packing rings, and gland follower. The lantern ring may be placed further in, to reduce slurry ingress. Packing size is usually proportional to shaft / sleeve outer diameter, as follows: Shaft / Sleeve OD (mm) 15 to 30 30 to 50 50 to 75 75 to 120 120 to 305 Packing Size (mm) 6 8 10 12.5 16 Shaft sleeve finish needs to be at least 0.4micron CLA to avoid excessive rotational friction, and the finish in the stuffing box bore needs to be at least 1.65 micron CLA to allow even compression during adjustment. The sleeve must be harder than the packing, and chemically resistant to the fluid pumped and the injection fluid. Any coating on the sleeve must have a good thermal shock resistance. The lantern ring allows for entry and distribution of the lubricant or flushing fluid. Lantern rings are usually split to allow installation and removal without pump disassembly. They were traditionally made from metal such as stainless steel, but lubricant-impregnated plastics are now common. Gland followers are also usually split to allow easy replacement. They are usually bronze but may be steel or cast iron. Special purpose gland followers are used with volatile or hazardous materials, including capacity for diluting and safely flushing away leakage. The axial compression on the packing must be occasionally adjusted to control leakage. The correct leakage rate is one drip per second. Over-tightening should be avoided as it will result in over-heating and shaft wear. Most packing is supplied with impregnated lubricant, and over-tightening will press the lubricant out. Pumps need extra sealing provisions if pressure at the inner end of the stuffing box is greater than 75psi. The use of harder packing material on the inner rings may help. The procedure for replacing packing is: 1. Read the instructions provided by the pump manufacturer and packing supplier. 2. Loosen and remove gland follower. Inspect gland follower for wear, corrosion, warping etc. 3. Remove old packing rings using a packing puller, and the lantern ring. 4. Inspect shaft sleeve surface for deterioration, and clean up where possible. Replace if necessary. 5. Inspect bore of stuffing box for corrosion, wear, scaling etc, and clean up where possible. 6. Verify correct packing size to be used. 7. Tightly wrap the correct number of packing coils around a mandrel of equal diameter to the shaft sleeve. 8. Cut each ring at an oblique angle. 9. Install each ring, staggering the joins 90 degrees on subsequent rings. Suction / Intake Design Centrifugal pumps operate most efficiently when the liquid to be pumped flows into the inlet nozzle in a smooth, uniform manner with minimal turbulence. Suction systems need to be designed to ensure that this happens. The most common problems are: ï‚ · Uneven / turbulent flow ï‚ · Vapour collection ï‚ · Vortex formation Suction piping should be as short and straight as possible to minimise friction, and if unavoidably long, should be of large diameter. The suction line will normally be at least one pipe size larger than the pump inlet flange, requiring fitment of a reducer. A reducer should not change the pipe bore by more than 100mm. Fluid flow should be as uniform as possible right up to the pump inlet flange. There should not be any fittings likely to cause turbulence, sudden changes in flow direction or spin within ten pipe diameters of the pump inlet flange. There should be no short radius elbows at all, and no long radius elbows within three pipe diameters. All suction line connections need thorough sealing to prevent air being drawn in. For suction manifolds serving multiple pumps, all the above points apply, and branches should be angled at 30 or 45 degrees, rather than ninety degrees, and sized so that fluid flow is constant throughout. Flow should not exceed 0.9m/s. Improper suction conditions or designs can result in the fluid swirling as it approaches the pump through the suction pipe. This is called â€Å"pre-rotation†. It causes a drop in pumping efficiency because the pump is designed to process fluid that is entering without rotation, and can cause additional suction pipe wear. Sometimes a radial fin is fitted to the suction pipe or casing to reduce pre-rotation. The suction pipe design should cater for elimination of air from the suction line, and prevention of vapour pockets, in the simplest manner, meaning that: ï‚ · For pumps with the feed being drawn from a level below (eg a dam pump), o Suction pipe should have a slightly upward slope toward the pump o The eccentric reducer should have the flat side on top ï‚ · For pumps with the feed being drawn from a level above (eg a thickener underflow pump), o Suction pipe should have a slightly downward slope toward the pump Vortexing in feed tanks needs to be avoided to prevent air being drawn down into the pump. Baffles may need to be fitted to tank walls. The tank fluid level needs to be kept well above the suction inlet. Bearings Bearings provide axial and lateral restraint to the pump shaft and attached components, while allowing free rotation. Axial loading on pump shafts may be significant as discussed separately, and the bearing arrangement always includes some thrust capability. The bearings most commonly used are deep-groove single row ball bearings, and single or double row angular contact ball bearings. Pumps may be in overhung configuration, where the shaft is supported by bearings on one side only, or have a shaft that passes right throught the casing with bearings on both sides. Most slurry pumps are of the overhung design. The bearings are usually rolling-element, but plain journal bearings are sometimes used on larger pump sizes. The bearings must be lubricated by grease injection or oil bath and may need provisions for cooling as well. This may be by having a cooling water jacket integral with the bearing housing, or by pumping the lubricating oil through a heat exchanger and filter. Oil lubrication is usually recommended rather than grease, if speed exceeds 5000rpm (which is very rare in a slurry pump). Grease-packed bearings should have one third of the chamber filled with grease. Oil baths should be filled to the centre point of the lowest rolling element. Inadequate loading of bearings can result in the rolling elements skating over the race instead of rolling, and this can cause heating and failure. To avoid this, bearing assemblies are usually designed with an assembly configuration, including preload, that ensures all bearings carry some load. Frame and Foundations For large pumps that are directly connected (ie no vee-belt drive), the motor and pump are usually mounted on the same bed-plate, which is fixed to the foundations in a way sufficient for eliminating looseness and distortion. This eliminates some misalignment issues at the source. Foundations including bed-plates should be checked occasionally for deterioration (corrosion, ground subsidence, concrete cracking, loose fasteners, missing grout etc), and the alignment between pump and motor should also be checked if there is any cause for concern. The framework should have provisions for drainage of any spillage and seal leakage etc, so that this does not become trapped and contribute to corrosion etc. Where pumps operate at high temperature (ie above around 100C) the pump casing should be supported at its axial centre-line, to help reduce thermal stresses. It is generally preferred that all suction and discharge piping have its own supports, so that the pump casing and foundations do not carry any significant static or dynamic piping loads, and so that pump components can be independently removed and replaced. Where this is not the case, extra pump and foundation attention may be needed at the design stage. Drive Arrangement Many drive arrangements are possible to suit the circumstances. Electric motor drive is the most popular, followed by internal combustion engines. Variable speed drives are sometimes necessary and often convenient, but always more expensive and less reliable. In minerals handling plants, slurry pumps are most often electric motor driven, with belt drives. Belt drives allow speeds to be changed through minor modifications – ie pulley changes. Short, low head slurry system designs usually provide motors that are 10 to 20% oversized, to cater for any under-estimates in slurry or system characteristics such as viscosity and friction, and to allow for minor system modifications during the service life. Instrumentation Pumps may be controlled to allow: ï‚ · Variation of flow rate, pressure, liquid level ï‚ · Protection against damaging operating conditions ï‚ · Flexibility in matching pumping performance to duty For centrifugal pumps, control is usually accomplished by speed setting (including turning off/on), or valve setting. This may be manual or automatic. For slurries, control by throttling valve is rare due to the wear rates that usually result. Typical instrumentation includes: ï‚ · Tank / sump level switches ï‚ · Pressure sensors ï‚ · Flow sensors ï‚ · Density sensors In each case, protection from damage by the slurry is critical. This is commonly achieved by using sensors that do not need to contact the slurry eg nucleonic density sensors mounted outside the pipe, with source on one side and detector on the other. Ideally, it is good to have instrumentation available, either permanently mounted or portable, to: Verify operation at BEP, by measuring the difference between suction and discharge pressure Determine flow Ensure that NPSH is sufficient to prevent cavitation Compare flow to motor amperage, to identify when impeller adjustment is needed Need to search more on valves for slurry applications. Notes on Material Selection Where there is some chance of parts coming into contact during pump operation, thought should be given towards minimising the damage that may result. An example of this is at the wear-ring / impeller interface. Studies have shown that damage can be minimised by manufacturing adjacent components from materials that:   Are dissimilar, except where known to be resistant to adhesive wear and galling   Have a difference in hardness of at least 10Rc, if either has hardness less than 45Rc Because it may be difficult to always prevent cavitation from occurring, impellers are usually made of cavitationresistant materials such as chrome-manganese austenitic stainless steel, carburised 12% chrome stainless steel, cast nickel-aluminium bronze, etc. Obviously corrosion resistance is another key selection factor that these materials satisfy. Slurry pumps are subject to heavy wear in the form of abrasion and erosion. The aggressiveness of the slurry is determined by the hardness of the particle s in the slurry, their shape (rounded or sharp), the pulp density, and the size distribution. Slurries can become less aggressive as they travel through a minerals processing plant as the sharp edges become rounded off. Velocity and angle of impingment are also very important factors affecting the resultant wear rates, with wear rate being proportional to velocity squared according to some references. The impingement angle associated with maximum wear rate seems to be dependent on the hardness and brittleness of the material being struck. For very hard / brittle materials it is between 65 and 90 degrees, while for more ductile materials it may be around 25 degrees. Pumps handling slurries with greater than 6mm particle size are usually lined with rubber. However, if impeller tip speed exceeds 28m/s, rubber becomes subject to thermal degradation, and this usually restricts the use of rubber to a maximum head of 30m per stage. Metal lined pumps may be used up to 55m head per stage. For wet end components, materials that may be used to resist wear include Ni-resist, carburised and hardened 12% chromium steel, etc. White iron slurry pump components, which includes Ni-Hard, are restricted to impeller tip speeds of about 36m/s to avoid maximum disc stresses. Steel components are softer but can run at higher speeds, up to a tip speed of 45m/s. Centrifugal pumps are subject to cyclic loads due to such things as imbalance, unbalanced radial forces, fluctuating axial thrust, the vibration induced as each vane passes the cut-point, and variations in upstream and downstream fluid pressure and flow. This sets the scene for fatigue loading, which becomes more of an issue if the slurry is corrosive. Fretting may occur between assembled components where looseness is allowed to develop. This is best avoided through the use of correct manufacturing dimensions and surface finishes, good fitting practice etc. The materials commonly used for pump components include:   Impellers (require castability, weldability, and resistance to corrosion, abrasion, and cavitation) o Bronze, for non-corrosive liquids below 120C o Nickel-aluminium bronze, for higher speed and mildly corrosive applications o Cast iron, for small low-cost applications o Martensitic stainless steel, where added resistance to cavitation, wear, corrosion (other than salt water) or high temperatures may be required o Austenitic stainless steel (mostly cast 316 grade), where a higher level of corrosion resistance is needed. Austenitic stainless steel with 6% molybdenum is often used for salt water pumping.   Casings (require strength, castability and machinability, weldability, and resistance to corrosion and wear) o Cast iron o Cast steel, where extra strength is required ie for pressures above 6000kPa (1000psi) and temperatures above 175C. o Austenitic cast irons with 15 to 20% nickel (Ni-Resist) may be used where abrasion and corrosion are issues. o Bronze, for water applications o Stainless steel, where corrosion is a major issue – martensitic for higher pressures in mildly corrosive fluids, austenitic for more aggressively corrosive fluids. ï‚ · Shafts (require resistance to fatigue and corrosion) o Mild steel, where corrosion and fatigue are minor issues Low alloy steel such as 4140 for added strength Martensitic stainless steel, where added strength and corrosion resistance are needed Shafts are usually chrome-plated, and care is needed to avoid this adding to the fatigue susceptibility through micro–cracking and hydrogen embrittlement. Shafts can be shot-peened prior to plating, and heat-treated afterward to reduce these effects. Wear rings (require castability and machinability, and resistance to corrosion, abrasion and galling) o Bronze for clean liquids and temperatures up to 120C o Stainless steel for applications with abrasion, corrosion and high temperatures – but steps must be taken to avoid galling should the rings come into contact eg increased clearances, hardness differences etc. o o o Impellers other than those made from martensitic stainless steel can usually be repaired by welding, although in some cases this needs to be followed by specific heat treatment processes. In all cases, more exotic (and expensive) materials may be used for specific applications. Material selection is often a balancing act between optimising purchase cost and maintenance / operations performance. Where high temperatures are involved, material selection must take into account differences in expansion rates. Unlined slurry pump impellers and casings are often made from abrasion-resistant cast irons as per ASTM A532, which includes Ni-Hard. These materials consist of a martensitic matrix with secondary hard phases of chrome and iron carbides that increase wear resistance. They cannot be machined or welded, and tend to be prone to corrosion, and breakage through mechanical impact and thermal shock. Brittleness may be reduced by annealing, but this reduces wear resistance. Slurry pump impellers and casings may be lined with softer materials like rubber, where high temperatures can be avoided. These can reduce wear rates by absorbing the impact energy of the particles, while resisting corrosion. Problems may arise in bonding of the rubber at the cut water point, and on the impeller. The lining reduces the thickness of the metal section of the component, so stronger materials are usually used eg steel rather than cast iron. Manufacturers develop their own specifications for ideal liner thicknesses based on experience, but one reference suggests a volute liner thickness of 4% to 6% of impeller diameter. Natural rubbers seem well suited for wear liners for use with slurries with less than 6mm particle size for the impeller, and 15mm particle size for the volute. Provided the base materials are suitable, patches of high wear on wet end parts can sometimes be repaired by welding / hard-facing. However, this increases the likelihood of cracking. Also if the welding results in uneven surfaces in critical points, the added turbulence can accelerate further wear. Many types and styles of surface coating have been tried, with some success. These include thermal spray coatings, diffusion surface treatments, spraying and trowelling of epoxies, etc.

The Sisters of Mercy :: Exploratory Essays Research Papers

The Sisters of Mercy   Ã‚  Ã‚  Ã‚  Ã‚   For this assignment, I decided to research the Sisters of Mercy, a Catholic order of nuns.   I never before realized that there is so much behind their amazing devotion to the Catholic Church and God. I must admit that they are beautiful examples of God's teaching, and I feel truly blessed to be involved with the Sisters of Mercy. Each and every one of them has a unique story to tell about her life, but none is more intriguing than that of Sister Mary Joel Hopkinson. Having only heard bits and pieces, and not knowing for sure the steps that each of these women had to take to become who she is today, I asked Sister Mary Joel to share her story with me.    When she was born into a Protestant family in New England, no one could have guessed that Sister Joel would end up becoming a Catholic, let alone a Sister of Mercy. But as it turned out, as Sister Mary Joel Hopkinson says, "There was no way to deny it; this is what God wanted for me." Sister Joel has been a Sister of Mercy for almost fifty years. What is so interesting about her story is that she has been a Catholic for only fifty years. Only a little more than a year after she converted to Catholicism, she found herself looking to enter a convent. She explained that all her life she had had Catholic friends. At one of her jobs, she was the only non-Catholic in the carpool. The Catholic Church intrigued her, and she was of a curious nature, but not until years later did she realize that God was sending her a sign. She puts it rather bluntly when she says, "God pushed me out of the window and into the convent." Sister Joel was not always a businesswoman; in fact, she worke d in a building in Brooklyn, New York, cleaning windows on the second floor. It was a rather old building, and the chains on the windows had been painted over a number of times. Once, while struggling to pull the window down, she lost her footing and fell out the window. The reason she says God pushed her is that the only ambulance on call that day was from St.

Quantum Entanglement and Bell’s Theorem Essay

In the early 20th century, physicists were in need of a new theory to describe the world of the atom and its components. Newtonian mechanics and Einstein’s theory of relativity worked very well at describing the motion of the planets and stars, but when these theories were applied to the atom, they completely broke down. Max Planck discovered that atoms exchange energy in individual packets of specific energy values. Planck called these energy packets â€Å"quanta†, Latin for â€Å"unit of quantity†, hence the name quantum theory. Two pioneers of quantum theory, Werner Heisenberg and Erwin Schrodinger, devised mathematical formulas to describe the atom. Two fundamental principles of quantum mechanics emerged from their equations: the uncertainty principle and the principle of superposition. Superposition states that an atom exists in all possible states until it is measured. The uncertainty principle says that you cannot know a quantum particles location and momentum (momentum is a particles velocity,roughly) at the same time. These principles are important because they reduce predictions of physical object’s position from an absolutes to only a range of probabilities. This is very different from the certainty of classical physics. The strangest phenomenon predicted, however, is quantum entanglement. It predicted that when a particle is split in two, it behaves as if it were still joined, no matter how far they are separated. Change one of the entangled particles and the other reacts instantly. These strange properties described by quantum mechanics were unacceptable to Einstein and many other physicists. Einstein felt that quantum theory itself must be a flawed theory to produce such strange predictions. The bizarre behavior and properties of the atom and sub-atomic particles must be attributable to some other mechanisms, he reasoned. Niels Bohr, another pioneer of quantum theory, deflected Einstein’s criticisms and claimed that quantum theory was a sound theory. The problem, Bohr said, was that we need an entirely new set of words and terminology for the theory because the realm of the atom was so different from our everyday experiences. In 1935 Einstein, along with Boris Poldolsky and Nathan Rosen, submitted a famous paper outlining their criticisms of quantum mechanics titled â€Å"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? †. The EPR paper, as it is known, included an idea for an experiment that would test and prove who was right, classical physics or quantum mechanics. The test, however, was not thought possible. For 30 years the debate between the classical and quantum views continued. Physicist John Bell brilliantly devised a feasible experiment involving entanglement using individual photons, light filters, and photon detectors. He calculated two sets of equations that predict the results: one using classical mechanics, the other using quantum theory. The predictions of classical and quantum theories give very different results. The theory that matches the experimental data must be the correct theory. It would not be until 1980 that the technology existed to perform Bell’s experiment. I am going to greatly simplify how the experiment works for clarity. When a photon is split, each photon retains complementary properties of one another. That is, if a photon starts as â€Å"AB†, the individual halves of the photon become â€Å"A† and â€Å"B â€Å"(â€Å"B† is complementary to â€Å"A† and vice versa). If we measure one of the split photons as being â€Å"A†, the other must be â€Å"B†. In the experiment, the photon is split and the individual photons race through a path in opposite directions. They each go through a filter that polarizes the photons. Simply put, polarization orients the photon in a certain direction. Imagine the photon as a sphere with a pole through it marking as â€Å"north† or â€Å"south†. Polarization flips the direction of the pole. So, polarized light becomes either â€Å"up† (north) or â€Å"down† (south). In this case, the complement of â€Å"up† is â€Å"down† and vice versa. Our photons can be labeled â€Å"A up† or â€Å"B down†; â€Å"A down† or â€Å"B up† depending on how the filter polarizes it which is completely random. If we were to send a pair of photons on separate and opposite directions without a filter, no polarization happens and the detectors would register â€Å"A† on one and â€Å"B† on the other invariably. Add the filters, and the detectors register â€Å"A up†,†B down†,†B up†, or â€Å"A down†. Since the filters completely randomize each photon’s polarization, one detector could indicate an â€Å"A up† and the other could detect an â€Å"B up† for the same set of split photons, right? The Bell tests show that when when one detector registers â€Å"A up†, the other detector shows a â€Å"B down†. It’s not surprising the â€Å"A’s† are opposite to the â€Å"B’s†, it’s that their polarizations are always complementary, or opposite. How does the other photon â€Å"know† what the other polarization will be and act accordingly? Are they still connected somehow? If not, does one photon somehow send information about its state to the other photon so it can act accordingly? If the photons do somehow communicate, the information they send must travel much faster than the speed of light and violate a fundamental physical law. Whatever the case, it shows our understanding of the universe is incomplete. Bell was a proponent of Einstein’s view of reality and didn’t expect quantum theory to be proven right. After witnessing a confirmation of his theory he said â€Å"I have seen the impossible done†. The phenomenon of entanglement has been demonstrated in experiment after experiment and progressively separating the photons at greater distances. Recently in Vienna, an even more stringent test was completed by Professor Anton Zellinger. The tests have sent split photons from one island to another many kilometers away and had the same eerie result. Our whole description of fundamental reality has to be revised. After the latest confirmation of quantum theory in Vienna, Dr. Zellinger and his colleagues posted a help wanted. They are seeking a philosopher to help understand the profound implications.

Should Students Wear Uniforms

Are Uniforms A Good Way to Improve Students Discipline and Motivation? AED 200 Introduction Uniforms have been a big debate for years. Some educators and parents believe feel uniforms are a great addition to the school system while others feel it is not giving student’s freedom of speech by expressing themselves in what they wear. Should Students Wear Uniforms? Should students wear uniforms is the big debate across school districts across the united states today. According to Eduguide. rg, school uniforms are one step that may break the cycle of violence; truancy and disorder by helping young students understand what really counts. Some feel students benefit from uniforms because it boosts their self-esteem. Students also have feel like they are in a fashion show dressing in uniforms makes students realize what on the inside that counts. Uniforms decrease the influence of gangs and are known to make things difficult for weapons being brought in hidden inside of clothes. Unifor ms improve learning.Uniforms reduce distraction and shapes focus on school work and making the classroom a more serious environment. Uniforms improve behavior and increase school attendance. Uniforms save families time and money. Parents report uniforms are cheaper than buying designer clothes or keeping up with the latest trends. Uniforms helps the administrators quickly identify outsiders who could be a danger to the students. Some people believe uniforms shows neatness by requiring students to tuck in their shirts, wear belts and wear shoes similar in color.Students dressing the same decreases teasing about clothing and shoe appearance. Uniforms prepare children for following a dress code for the future when they reach adulthood and join the workforce. Some children form their own groups in school in which wearing a certain thing or color or style. Some children use fashion trends to differentiate the popular ones from the unpopular children according to what they wear. Uniforms make it less possible for kids to be judged based on clothing choices. Uniforms prevent the competition to have the most fashionable clothes.Competition in school causes students to lose focus on schoolwork instead of on who is wearing the latest fashion trends. Uniforms eliminate clothes competiveness. Another article from Proffessorshouse. com states that some people claim that requiring a uniform increase graduation rates and also has an impact on children’s educational experience. Students performed on the uniform debate claim that uniforms encourage discipline, helps prevent social groups from forming opinions based on fashion status, gets rid of economic barriers and makes easily to identify persons at the school who should not be there.The article also talks about how some form of dress codes enforced around 75% of all schools dress codes are in place to outlaws offensive clothing being worn to the school. After reviewing another article from Ezinearticles. com uniform s create a source of identity and provides a sense of belonging according to the article the article some children’s believe the school chosen for them is a sort of achievement and the school uniform is a mark of inclusion, something to brag about and they feel proud and empowered wearing it.It eliminates the child having to worry about what to wear each day. Uniforms also relieve the parent of having to spend money to helping the child to keep up with the latest trends every day. Uniforms allow a sense of unified purpose to develop particular rivalry with other establishments. Uniforms reinforce children’s since of belonging to reassuring communities. In a 1996 Long Beach, Calif. speech, former President Bill Clinton announced his support of that district's uniform initiative.It didn’t get far in the United States but it also helped start the debate. Uniforms also closes the debate on what children are allowed wear to school, then that makes mornings easier for parents and for children. Everyone knows exactly what the kids need to wear, their regulated school uniform. This leads to a decrease in morning arguments. Some experts believe that when the entire student body is dressed in uniforms, they develop a stronger team mentality. When they are all dressed alike, their all-for-one-and-one-for-all attitude is boosted.With parents saving by not having to buy day to day clothes, they can let their children buy a few nicer and more fashionable clothes for weekends and evenings. Wearing a uniform five days a week can make children appreciate their weekend fashions more. Why Students Should Not Wear Uniforms Parents on the opposing side feel uniforms violate the right to freedom of speech and expression; a uniform cost too much for families struggling financially, uniforms are a band aid on the problem of school violence and does not address the real issues behind it.Uniforms hide warning signs that point to problems that maybe going on with th e child. Some feel that uniforms have not been able to prove wither the decreased discipline or violence and uniforms fail to allow children the ability to learn and make good choices based on their own values. Most feel that uniform are not allowing children to be themselves. Some believe that children cannot be themselves clothes are an expression of who they are. Parents feel that uniforms can be more expensive than regular clothes.Some parents may feel they are a big waste of money wither the school paid for them or not. Some feel uniforms made children uncomfortable and made them focus on the uniform rather than focusing on school work. Also uniforms do not change a child’s behavior in school. Wearing uniforms stop children from getting in trouble and acting out in school. Self-expression is an important part of a child’s development and curbing it with uniforms can be determined to children. Some feel if students are not able to express themselves will in another way by excessive make-up or hairstyles or jewelry.Uniform wear delays transitions into adulthood. Some experts feel teenagers to wear uniforms limits their ability to express in their own way in which can delay their transition in adulthood. Studies show uniforms can be a difficult to enforce in public schools. Conclusion Uniforms have many pros and cons, most believe uniforms are a good option for kids while others feel they can compromise who kids are through expressing themselves through the clothes they wear uniforms cuts down on violence and is a solution to economic problems parents may be facing today.My own personal experience with uniforms causes me to look at uniforms in both sides of the issue. I feel uniforms should be forced in middle or high school but voluntary in elementary schools. I feel most kids in elementary school do not notice what each other wear. Middle and high school is the times where students notice what the other person is wearing or form groups based on who they think are popular or the other. Uniforms are a choice based on school officials and it is up to the child or school if uniforms work. References Website: EduGuide. com Website: Ezarticle. com Website: About. com

Sodium Thosulphate essays

Sodium Thosulphate essays Plan an investigation into the rate of reaction between Sodium thiosulphate and hydrochloric acid. The equation for the rate of reaction is 1/time. The rate of reaction measures the speed of reaction. It is a measure of the loss of reactants and gain of products. The faster a reaction takes place, the shorter the time needed for the reaction to finish. An example of a slow reaction is rusting An example of a fast reaction is sodium and water. This predicts what will happen to the speed of a reaction if a variable like surface area, concentration and temperature. This theory says that when particles collide a reaction occurs. With a greater surface area a solid, particles collide far more frequently and as a result the reaction rate is greater. If there is a higher concentration the particles are closer and they have a greater chance of colliding. The more collisions, the faster the reaction. The higher the temperature the faster the particles are going to move. This means that there are many energetic collisions that will speed up the reaction. The word and chemical equation, for this reaction, which takes place in a solution: The variables you can change in this experiment are: The variables that we will be keeping constant are: I predict that the rate of reaction would get faster, if the volume of sodium thiosulphate was increased. This is because a higher concentration of sodium thiosulphate would mean that the particles would be closer together and as a result there would be more collisions, which would make the reaction faster. This can be scientifically proven using the collision theory. For my investigation I will use 1/time for the rate of reaction. I decided to do a preliminary experiment to investi ...