Lines and Angles in ACT Math Review and Practice

Lines and Angles in ACT Math Review and Practice SAT / ACT Prep Online Guides and Tips There are several math topics that act as foundations for understanding ACT Math, even though there are not many questions specifically dedicated to the topic. This is most certainly the case for line and angle problems. Though it is rare to see a pure line and angle problem (without the addition of other geometric shapes), you’ll need to know just how lines and angles work and how to solve for all your missing measures before you can take on those more complex problems. This will be your complete guide to lines and angles on the ACT- what they are, how you’ll see them on the test, and how to solve these types of questions to maximize your points on test day. Properties of Lines and Angles Before we get into how lines and angles function, let’s define our terms. A line is a completely straight marker, meaning it has no curvature. It can either have termination points (and will be called a â€Å"line segment†) or go on infinitely. Its degree measure is always 180 °. Parallel lines are two or more lines that are a set distance apart (equidistant) and never meet. They travel in the same direction continuously. Perpendicular lines meet each other at 90 degree angles. An angle is the meeting of two lines. The measure of how they meet is expressed in degrees, and the point at which they intersect is called the angle’s â€Å"vertex.† Line and Angle Equalities Most of what you’ll need to know about lines and angles on the ACT is how to identify when and how they will be equal or supplementary to one another. Equal angles (or lines) are angles (or lines) that have the same measurement. Supplementary angles are angles that add up to 180 degrees. Because all these angles form a straight line and a straight line equals 180 degrees, the three angles are supplementary. Opposite Angles When two (or more) lines intersect, they form a series of opposite angles. Angles that are exactly opposite will always be equal to one another. Both sets of opposite angles will be equal. Opposite Interior Angles When there are two parallel lines that are crossed by another line (called a transversal), the angles on alternate interiors will be equal to one another. And the angles that are on the same side of the transversal line and the same side of their respective parallel lines will also be equal. That may be difficult to picture, so let’s look at a diagram: The marked angles are all congruent (equal) and the unmarked angles are all congruent. (Note: when you are told that two lines are parallel on ACT Math, the problem will almost always involve opposite interior angles in some way.) Now let’s look at an opposite interior angle ACT problem. Here, the test has made it slightly tricky by asking you for supplementary angles instead of equal ones. But the principle remains the same- we must identify angle measurements/equalities by using opposite interior angle equalities. We can see straight away that $x$ lies on a straight line with both 1 and 2, so angles 1 and 2 will be supplementary with $x$. We can also see that angles 1 and 10 are opposite interior angles and so will be equal to one another. And angle 9 is opposite angle 10 and thus will also be equal. This means that angle $1 = 2 = 9 = 10$ and all are supplementary to $x$. Finally, we can ignore the angles 4, 5, 6, 7 and 12, 13, 14, 15. Why? Because lines $c$ and $d$ are not parallel and so do not have opposite interior angle equalities. This means that $x$ is only supplementary to angles 1, 2, 9, 10. Our final answer is H. Equal lines and equal angles can be quite disorientingin the right hands. Typical Line and Angle Problems Almost every line and angle problem on the ACT is given to you as a diagram problem. You will be presented with a series of givens and then told to find a missing value of some kind. Almost always, this requires multiple steps and the use of multiple pieces of line/angle knowledge. The other notable feature of lines and angle problems on the ACT is that you will be given a â€Å"pure† line and angle problem very rarely. Most of them involve other geometric shapes in some way, most commonly triangles. The good news is that you will generally not need to know more than the fact that all the interior angles in a triangle add up to 180 degrees, but check out our guide to ACT triangles if you are unfamiliar with or unused to working with triangles. Now, we are told that two lines are parallel, so there’s a good chance we’ll need to use our opposite interior angle knowledge. With that in mind, let us expand the drawing we are given so that we can see our opposite interior angles more clearly. Using our opposite interior angles, we know that angle BAC is 82, which means that angle ACX must also be 82 degrees. We can also see that angles ACX and ACD make a straight line. Their sum must therefore be 180 degrees. $ACX + ACD = 180$ $82 + ACD = 180$ $ACD = 98$ We are also told that lines AE and CE are bisectors, which means they cut their respective angles exactly in half. This means that angle EAC = $82/2 = 41$ And angle ECA = $98/2 = 49$ Now, we also know that a the interior angles of a triangle add up to 180 degrees, so we are able to find our angle measure AEC by: $AEC + EAC + ECA = 180$ $AEC + 41 + 49 = 180$ $AEC + 90 = 180$ $AEC = 90$ Our final answer is C, angle AEC is 90 degrees. As we said before, this question is representative of most line and angle problems you’ll see on the test. Based on your givens, you must use your knowledge of opposite interior angles (opposite interiors are equal) and your knowledge of the degree measure of a line (a line is 180 degrees) in order to put together all the clues and solve your problem. And yet, in addition to understanding the properties of lines and angles by themselves, you must also understand the basics of triangles. Because many ACT problems that involve lines and angles also use triangles, your knowledge of lines and angles should definitely be supplemented with triangle study. So don’t forget to brush up on your ACT triangles! Now let's check out our angle tips and tricks. Tips for Solving a Line and/or Angle Problem Most of the time, you must solve a line and angle question piece by piece in order to unlock the final solution. This means you must be careful and vigilant that you keep not only your facts and equalities straight, but your variables as well. As you go through this process, keep in mind these three tips: Tip 1: Write in your givens If you are given a diagram in which your givens are NOT written in, then write them in yourself! Sometimes, seeing the numbers on the page can make all the difference in the world between a difficult problem and an easy one. You’ll also be far less likely to mix up your numbers and variables if you keep your work on the page instead of in your head. Tip 2: Work from your givens to find the next puzzle piece Sometimes, it can be tricky to know where or when or in what order to work through a problem. Take a moment to find what you can before you worry about how to go forward. If you have opposite angles, write in the measure of the angle opposite your given. If you have angles that make a straight line, find the value of the missing variable. Immediately find the missing pieces that you can, and that bounty of information will often lead you straight to your solution. Tip 3: If necessary, use plugging in answers or plugging in numbers If you find yourself stuck (or there is literally no other way to solve the problem), then whip out your PIA or PIN knowledge. Sometimes the process can be slower than a straight solve, but these strategies will almost always get you where you need to go and so can be worth the extra seconds. Ready to put your knowledge to the test? Test Your Knowledge 1. 2. 3. 4. Answers: C, J, B, B Answer Explanations: 1. This problem requires multiple steps, so definitely write in your angle measurements as you find them. In order to find out how many angles measure 50 degrees, we must find the measures of all our angles, so let's go through the process. To begin with, we can see that the 130 degree angle lies on a straight line, so its supplementary angle will be: $180 - 130 = 50$ degrees. Now, we also know that opposite angles are equal, so the angle opposite 50 degrees must also be 50 degrees. We also know that a triangle adds up to be 180 degrees and that our figure in the center is a triangle. So: $180 - 80 - 50 = 50$ degrees. This means that the missing value in our triangle is also 50 degrees. Again, we know that opposite angles equal one another, so the angle opposite this 50 degrees will also be 50 degrees. Based on opposite interior angle equalities, the full angle at the opposite 130 degrees will also be 130 degrees. Because the full angle is 130 degrees and part of it is made up of an 80 degree angle, which means that we can find the other angle by saying: $130 - 80 = 50$ And again, the angle opposite this 50 degree angle will also be 50 degrees. We can also see that the 80 degree angle, plus the 50 degree angle, plus one of the unmarked angles will equal 180 degrees, since they make up a straight line. So we can find the unmarked angle by saying: $180 - 80 - 50 = 50$ Finally, we can use opposite angle equalities to find the last unmarked angle. We have found all our angle equalities, so all that's left is to count how many angles are equal to 50 degrees. There are a total of 8, 50 degree angles. Our final answer is C, 8. 2. For this question, we must use our knowledge that both straight lines and the sum of the interior angles in a triangle equal 180 degrees. First, let us find the measure of angle $y$. Angle $y$ makes a straight line with the 72 degree angle, so: $y + 72 = 180$ $y = 108$ Now, we can use the same process to find angle $x$, which forms a straight line with the 57 degree angle. $x + 57 = 180$ $x = 123$ Now, let us find angle $z$ by first finding the third, unknown, angle in the triangle (which we will call angle $a$). The interior angles in a triangle add up to 180 degrees, so: $a + 57 + 72 = 180$ $a + 129 = 180$ $a = 51$ Now, let’s use that angle to find $z$. The two angles make a straight line, so their sum will be 180. $a + z = 180$ $51 + z = 180$ $z = 129$ (Note: you may notice that the sum of the two non-adjacent interior angles of the triangle is equal to the exterior angle. This is not a coincidence and is in fact one of the many rules of triangles. But don’t worry about having to memorize this rule- you can always find the exterior angles using the properties of straight lines just how we did!) Now, we must find the sum of angles $x, y,$ and $z$, so let’s add our values together. $108 + 123 + 129$ $360$ Our final answer is J, 360. 3. Here, we are dealing with several bisecting angles. This means that the angles are cut exactly in half. This means that angle ABD = DBE and angle DBE = EBC. And because DBE is equal to both ABD and EBC, it means that angles ABD and EBC are also equal. This means that we have three equal angles, all making one line. And we know a line equals 180 degrees, so: $x + x + x = 180$ $3x = 180$ $x = 60$ Each angle measure is 60 degrees, which means that angle DBE is 60 degrees. Our final answer is B, 60 degrees. 4. We can see that angle BAC is part of a triangle. And we know that we need two angle measures of a triangle in order to determine the third. But we can also see that the 45 degree angle is opposite one of our unknown interior triangle angles. Because opposite angles are equal, this means that our second unknown interior angle of the triangle is 45 degrees. We now have two angle measures of the triangle, so let us find the measure of BAC. $BAC + 35 + 45 = 180$ $BAC + 80 = 180$ $BAC = 100$ Measure BAC is 100 degrees. Our final answer is B, 100 degrees. These problems require multiple steps, but the process is often simpler than it looks. So don't tire yourself out prematurely. The Take-Aways The trickiest aspect about line and angles questions is the fact that they require multiple steps and several different numbers and measurements. It can be easy to mix-up your solutions and your work due to careless error, so make sure you take steps to avoid doing so. Remember your equalities, keep your work organized, and do your best to avoid careless errors. Once you’ve locked down lines and angles, you will be well equipped to take on the more and more complex geometry problems the ACT will throw at you over the course of the test. What’s Next? Now that you've learned all about your lines and angles, make sure you're up to speed on the rest of your must-know math topics and formulas for the ACT. Look to our ACT Math tag for all of our guides to ACT Math, including ratios, solid geometry, and more. Studying last minute? Check out our tips for making your time count before test day. Running out of time on the ACT math section? Make sure you review how to buy yourself extra time as you go through your test. Looking to get a perfect score? Perfection is far from unobtainable, so check out our article on how to get a 36 on ACT Math, written by a perfect scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

Understanding of English 200 course Essay Example | Topics and Well Written Essays - 1000 words

Understanding of English 200 course - Essay Example Understanding of English 200 course In a more coherent and well argued out basis, this paper aims at reflecting upon my learning as an English 200 student, and to subsequently put into focus the various English knowledge and related works. For the purposes of this significant analysis, I will put my arguments within the scope of the English 200 syllabus. Within the larger description, English 200 is suitable designed to help students write for a variety of purposes that cuts across various English genres, including research essay and theoretical analysis. While interacting with the course content and course material, many emphases placed to rhetorical challenges in knowledge generation from literary materials and texts and for such I undertook personal and well researched literary essays to demonstrate my understanding of the subject matter. Of importance, my original literary compositions and analysis identified as The Ceremony, Curiosity killed the cat, The Mirror, and a critique of the famous play by Sophocles entit led, Antigone. From the onset of my English classes, I have always been a critical thinker; my subsequent and regular interaction with the right course content and materials in English 200 class has further improved my analytical skills as a critical thinker when examining literary texts. My desire for knowledge acquisition in English 200 influenced more as I constantly look at the ‘why’ platform of an author’s literary text rather than just focusing on the author’s literal meaning as depicted in the text. ... equent and regular interaction with the right course content and materials in English 200 class has further improved my analytical skills as a critical thinker when examining literary texts. My desire for knowledge acquisition in English 200 influenced more as I constantly look at the ‘why’ platform of an author’s literary text rather than just focusing on the author’s literal meaning as depicted in the text. Subsequently, my exposure to rhetorical literary analysis, essay research, close reading, critical analysis, and to a larger extent creative thinking have enabled me to gain insightful rich knowledge into different writing styles such that am able to continuously and with much ease create a sustained arguments in any given literary text for a harmonious understanding of any literary text. Moving in a progressive manner throughout the English 200 class in literary analysis from presenting simple facts to building a sustained argument of the various lite rary components and intentions within various literary complexities, I have indeed expanded my reasoning faculties and mental abilities. At the earlier inception stages of this course, I undertake an in depth and informative discussions concerning critical literary analysis. This whole learning process proceeded through critical essay composition, related theories, pedagogical writing of the critique essay, group discussions, and conference presentations of literary review process. At the end, I submitted a well-researched paper on Antigone with special emphasis on 442BC classic writing. Within this literary analysis, deliberate efforts made in connecting the literary intentions of the earlier literary writing to a modern audience while unearthing the intentions of Sophocles in discussing kinship and family

Enterprise and entrepreneurial management Essay

Enterprise and entrepreneurial management - Essay Example The competition in business industry has grown to a very different level (Chambers, 2008). The laundry business started will operate in London area; laundry and dry cleaning are the components of fashion and textile sector according to the national career service. The level of employment in the field has remained in a stable trend even under the current economic swings. Laundry and dry cleaning industry expects growth and increased employment in the coming years. The region where the business will operate is one of the largest regions in laundry and dry cleaning services in the United Kingdom. The business is launched because, in early childhood days, clothes washing took place at home but there were laundry services around the area. Washing and dry machines mostly considered expensive and hard to maintain. Although, the clothes were clean and smelled fresh the time taken and labor used remained high. According to statistics from the national association of laundry industry, laundry providers have decreased over the past two decades. In the early 1980s, the number was twelve thousand five hundred, but has since decreased by a margin of three thousand. The main reason cited by people in the industry is the cost of starting up a laundry service. The cost of launching a launderette ranges from sixty thousand to a hundred thousand pounds. The cost has minimized of competitors in the industry by a great extent. The family will provide financial support for starting the business through borrowing. The firm’s selling points include the modernization of laundry services from the common traditional forms. Reinvention and innovation are the key factors in the launch of the business. Equipping the business with flat screen televisions, introduction of gaming systems for the kids and having a cafe that serves food and beverages are some of the ways the firm will attract clients. People in the region are used to the traditional laundry services and bringing a new ide a through innovation and creativity will help in establishing a clientele base. Technological advance from the coin slots machine to use of top up cards and credit cards will attract everybody both the young and old. The move from coin slot machines is to enhance customer convenience and confidentiality. The product, price, location and promotion are some of the key ideas factored in the firms launch. Establishing a difference in the factors from the rest of laundry service providers will help in the creation of a differential factor from the rest of providers. SWOT analysis will become handy in the determination of the firms strengths, weaknesses, opportunities and threats. The firm will operate in a sole proprietorship, mainly to reduce the time used in setting up the firm (Chell, 2001). The business workers will come from the family members, and they will offer free service until the firm establishes. The firm requires a Rota that will ensure staff members are constantly availabl e, and the firm is not under or overstaffed. The owner with the help of an accountant friend performs the firm’s bookkeeping when it comes to tax returns. Business plan Keys to success The firm has several keys that promise its success, and they include location, convenience, environment and reputation. The location of the firm is strategic such that people will have a glance at it while walking at

Mao's China and Beyond Essay Example | Topics and Well Written Essays - 1250 words

Mao's China and Beyond - Essay Example At any point when a nation and its people are faced with times of change, such evolution can be hectic as it moves forward to approach whatever issues, would need to be handled. Each national party and their leader(s), along with the citizenry themselves, would have unique interpretations of what should and shouldn't be there.These changes can and often times do, take many shapes. Such as, resulting issues over social welfare, economic standing, along with the resulting political unrest that transpires alongside everything else. For the citizens of China, they would encounter ramifications of their own, as a result of the advancement of the Communist movement. Over time, the influence of the movement would be determined. According to Maoism, "Deliberate organizing of mass military and economic power was deemed necessary to defend the revolutionary threat, while centralization kept corruption under supervision," ("Communism", p.15). This in itself would appear to be a positive step, b ut only time would tell how much. Any nation, or civilization, possesses cultural structures, for which they would be proud of. The structures that would be set to distinguish themselves from one another and in the process, would act as a unifier for the general masses. From the social standpoint, "As with the New Culture movement, Mao believed that all vestiges of Chinese traditional culture needed to be overturned. These included hsiao, or filial piety, Confucianism, monarchism, ancestor worship, religion, and the authority of elders," (Hooker, p.2). The movement of Mao's ideology, would further be translated politically as well. In viewing the political philosophy set forth, it would appear as if a contradiction in meaning. When most view proposed democracy, they view it in terms similar, if not exact, to the present US structure of government. In essence of this, "Mao himself referred to "New Democracy" as "democratic centralism"," (Hooker, p.3). With every revolution, comes the hope of a new beginning and the progression from old ideas, to new and what may be seen as better ones. The problem would potentially be that, "Democratic centralism essence a dictatorship- "a dictatorship of all revolutionary classes," in Mao's words- power would be concentrated in the hands of a few in order to guarantee that all class interests are represented," (Hooker, p.3). In further study, it would be discovered that part of Mao's policy, would be making both the financial institutions and general industry more on a national scale. Also there would be re-allocation of land coming from the wealthier owners and going to those who would have been at the very bottom of the economic class system. After Mao assumed his power hold in 1949, he re-named the previously mentioned principle of democratic thinking that he saw as being new, to something called the People's Democratic Dictatorship. While the general idea would further go on to make mention of the strength of the people's convictions and what they wanted to be handled by the ruling government, it would still place power within one central force. Question: What was the historical context of the Hundred Flowers

All About Screw Pumps Engineering Essay

All About Screw Pumps Engineering Essay Screw pumps are rotary, positive displacement pumps that can have one or more screws to transfer high or low viscosity fluids along an axis.   A classic example of screw pumps is the Archimedes screw pump that is still used in irrigation and agricultural applications.   Although progressive cavity pumps can be referred to as a single screw pumps, typically screw pumps have two or more intermeshing screws rotating axially clockwise or counterclockwise.   Each screw thread is matched to carry a specific volume of fluid.   Like gear pumps, screw pumps may include a stationary screw with a rotating screw or screws.   Fluid is transferred through successive contact between the housing and the screw flights from one thread to the next.   Geometries can vary.   Screw pumps provide a specific volume with each cycle and can be dependable in metering applications.   The geometries of the single or multiple screws and the drive speed will affect the pumping action required.   The capacity of screw pumps can be calculated based on the dimensions of the pump, the dimensions of the surface of the screws, and the rotational speed of the rotor since a specific volume is transferred with each revolution.   In applications where multiple rotors are used, the load is divided between a number of rotating screws.   The casing acts as the stator when two or more rotors are used.   Based upon the needs of the application, timed or untimed rotors may be chosen. Untimed rotors are simpler in design.   The combination of factors relating to the drive speed, flow, and the characteristics of the fluid transferred may affect the flow rate and volume fed through each cavity. In water and wastewater treatment applications, a less viscous solution will require a lower power drive compared to untreated sewage, excess sludge, or concentrated slurries, which may require a higher power motor.   The viscosity of the fluid transferred and the lift required may affect the speed and power required.   Indicators of pump malfunction include decrease in flow rate or increased noise. The efficiency of screw pumps requires that each rotor turns at a rate that allows each cavity to fill completely in order to work at full capacity.   Theory Screw pumps are a unique type of rotary positive displacement pump in which the flow through the pumping elements is truly axial. The liquid is carried between the screw threads on one or more rotors. The liquid is then displaced axially as the screws rotate and mesh. In other types of rotary pumps, the liquid is forced to travel circumferentially, however the screw pump has an axial flow pattern and low internal velocities. It provides a number of advantages in many applications where liquid agitation or churning is objectionable. Screw pumps are classified as two different types: the single rotor and the multiple rotor. The multiple rotor is further divided into timed and untimed categories. Timed rotors rely on outside means for phasing the mesh of the threads and for supporting the forces acting on the rotors. Untimed rotors rely on precision and accuracy of the screw forms for proper mesh and transmission of rotation (Fraser, et. al., 1986.). History: The screw pump is the oldest type of pump. The first applications, dating back to the third century B.C., included irrigation and land drainage. The screw pump is thought to have been first used in Egypt (Ewbank, 1972). After several other types of pumps were invented, the screw pump was not used as much because these other pumps could handle higher head capacities. However, later it was found that these pumps could not handle wastewater like the screw pump could. Because of this, the screw pump became widely used for such an application. The Dutch were the first to design a spiral lift screw in 1955. After this, double screw units were put into operation for flood control in the Netherlands and in municipal sewage installations in Europe. Based on excellent results from the pumps used in Europe, the trend extended to Canada and United States and are currently used today (Cheremisinoff, et. al., 1992) [2]. How a Screw Pump Works: Screw pumps for power transmission systems are generally used only on submarines. Although low in efficiency and expensive, the screw pump is suitable for high   pressures   (3000   psi),   and delivers   Ã‚  fluid   Ã‚  with   Ã‚  little   Ã‚  noise   Ã‚  or   Ã‚  pressure pulsation. Screw   pumps   are   available   in   several   different designs;   however,   they   all   operate   in   a   similar manner.   In   a   fixed-displacement   rotary-type   screw pump (fig. 1, view A), fluid is propelled axially in   a   constant,   uniform   flow   through   the   action of just three moving parts-a power rotor and two idler   rotors.   The   power   rotor   is   the   only   driven element,   extending   outside   the   pump   casing   for power   connections   to   an   electrical   motor.   The idler  rotors   are   turned   by   the   power   rotor   throu gh the   Ã‚  action   Ã‚  of   Ã‚  the   Ã‚  meshing   Ã‚  threads.   Ã‚  The   Ã‚  fluid pumped   between   the   meshing   helical   threads   of the idler and power rotors provides a protective film to prevent metal-to-metal contact. The idler rotors   perform   no   work;   therefore,   they   do   not need to be connected by gears to transmit power. The   enclosures   formed   by   the   meshing   of   the rotors inside the close clearance housing contain the fluid being pumped. As the rotors turn, these enclosures   move   axially,   providing   a   continuous flow.   Effective performance   is   based   on   the following   Ã‚  factors: The rolling action obtained with the thread design   of   the   rotors   is   responsible   for   the   very quiet pump operation. The symmetrical pressure loading   around   the   power   rotor   eliminates   the need   for   radial   bearings   because   there   are   no radial   loads.   The   cartridge-type   ball   bearing   in   the pump   positions   the   power   rotor   for   proper   seal operation.   The   axial   loads   on   the   rotors   created by discharge pressure are hydraulically balanced. The key to screw pump performance is the operation   of   the   idler   rotors   in   their   housing bores. The idler rotors generate a hydrodynamic film   to   support   themselves   in   their   bores   like journal bearings. Since this film is self-generated, it   depends   on   three   operating   characteristics   of the   pump-speed,   discharge   pressure,   and   fluid viscosity. The strength of the film is increased by increasing   the   operating   speed,   by   decreasing pressure, or by increasing the fluid viscosity. This is why screw pump performance capabilities are based   on   pump   speed,   discharge   pressure,   and fluid   viscosity. The supply line is connected at the center of the pump housing in some pumps (fig. 1, view B).   Fluid   enters   into   the   pumps   suction   port, which   opens   into   chambers   at   the   ends   of   the screw assembly. As the screws turn, the fluid flows between the threads at each end of the assembly. The   threads   carry   the   fluid   along   within   the housing   toward   the   center   of   the   pump to the discharge port [1]. Three Basic Types : Single Screw The single screw pump is more commonly known as the Archimedean screw. It is quite large; typical dimensions include a diameter of 12 inches or greater, and a length up to about 50 feet. It is normally used as a water-raising pump with the screw arranged at an angle of 30 degrees. It can also be used for handling liquids containing solids in suspension with either vertical lift or horizontal transport. The design of single screw pumps allows very little fracturing of particles and little abrasion damage to the pump. One disadvantage is the considerable bulk necessary to achieve high capacities since rotational speeds are of the order of 30-60 rpm (Warring, 1984) [5]. Intermeshing Screw Pump The intermeshing screw pump is commonly called a rigid-screw pump. This type of pump is suitable for a wide range of sizes, and can be run at high speeds. The larger screw pumps are used for bulk handling of oils and similar fluids. The basic type is suitable for handling most clean fluids with low flow velocities and at low heads (Warring, 1984)[5]. Eccentric screw pump The eccentric screw pump is versatile. It is capable of handling a variety of liquids and products with high efficiency. It comprises of a rigid screw form rotor rolling in a resilient internal helical stator of hard or soft rubber with a moderately eccentric motion. It can handle viscous liquids, slurries, pastes, solids in suspension, and delicate products. This is because of the low flow velocities through the pump (Warring, 1984)[5]. Applications: There are several applications of the screw pump that include a wide range of markets: utilities fuel oil service, industrial oil burners, lubricating oil service, chemical processes, petroleum and crude oil industries, power hydraulics, and many others (Fraser, et. al., 1986). Listed below are some typical situations where a screw pump is used. The benefits of using a screw pump in each of these situations are discussed (Cheremisinoff, et. al., 1992)[2]. Raw sewage lift stations: Can handle variety of raw sewage influent, are non-clogging, require little attention, are resistant to motor overloads, and are not affected by running dry Sewage plant lift stations: Used for sewage lifts up to 40 feet and have self-regulating lift capacity (Normal lifts are 30 feet, while high lifts are 40 feet high.) Return activated sludge: Little floc disintegration, nonturbulent discharge into effluent channel, low horsepower requirements, improved activated sludge treatment. Stormwater pumping: Are ideal because of large capacity at low heads, no prescreening necessary Land Drainage: Used for flood control, can pump large volumes of water over levees. Capacity : The delivered capacity of any screw pump is the theoretical capacity minus the internal leakage. In order to find the capacity of a screw pump the speed of the pump must be known. The delivered capacity of any rotary screw pump can be increased several different ways. The capacity can be increased by simply increasing the speed, increasing the viscosity, or decreasing the differential pressure. The capacity of the pump depends on several factors (Cheremisinoff, et. al., 1992)[2]: Diameter of the screw Speed of the screw Number of flights mounted on the screw shaft Flights: Single, double, and triple flights are often used. Flights are also known as helixes. With each increase in flights, there is a 20% increase in capacity. Therefore, a single flight pump has a capacity that is 80% of a double flight pump, which in turn has a capacity that is 80% of a triple flight capacity. The three-flight pump can handle the most capacity in the least amount of space. Angle of inclination of the screw The greater the angle of inclination, the lower the output. The output lowers approximately 3% for every degree increase over a 22 inclination. Level of influent in the influent chamber Ratio of the diameter of the screw shaft to the outside diameter of the screw flights Clearance between screw flights and trough Advantages : Wide range of flows and pressures Wide range of liquids and viscosities Built-in variable capacity High speed capability allowing freedom of driver selection Low internal velocities Self-priming with good suction characteristics High tolerance for entrained air and other gases Minimum churning or foaming Low mechanical vibration, pulsation-free flow, and quiet operation Rugged, compact design easy to install and maintain High tolerance to contamination in comparison with other rotary pumps (Fraser, et. al., 1986)[4]. Disadvantages : Relatively high cost because of close tolerances and running clearances Performance characteristics sensitive to viscosity change High pressure capability requires long pumping elements (Fraser, et. al., 1986)[4]. Characteristics and Efficiency of Screw Pumps: The screw pump has a number of very important advantages compared with centrifugal due to recovery of velocity head at the discharge pumps. In order, however, to appreciate fully pipe are not as great, what the screw pump will do as compared with the centrifugal pump, particularly for low head operation, it is necessary to have a thorough knowledge of the characteristic curves of both types of pumps. The three curves which are reproduced here show an actual comparison between a screw pump and a 36-in. centrifugal pump. A great deal of care has been taken to make this comparison as fair as possible; but owing to the dissimilarity of the characteristics of the two pumps, a perfect comparison is practically impossible. For this reason , wherever it is impossible to make the conditions coincide exactly for the two different pumps, the centrifugal pump has been given every advantage, yet even under rather severe handicaps, the screw still maintains its supremacy under low head conditions. The combined curve shown in Fig. 3 illustrates that at all heads lower than 12.6 ft. the screw pump is the more efficient of the two pumps. It will be noticed that the 42-in. centrifugal has not been compared with the 42-in. screw pump because the screw pumps are designed for such very low heads that the suction and discharge sizes are made larger than the connections for centrifugal pumps which handle the same capacity. In other words, the 42-in. centrifugal pump would have a capacity so much greater than that of the 42-in. screw that comparison would be impossible. All of the total heads which are shown in the three curves are total dynamic heads, and this includes the velocity head. Therefore, the water delivered from the screw pump is moving at a lower velocity because of the size of pipe, and hence it is in a more usable form. The entrance losses of the suction pipe and the losses due to recovery of velocity head at the discharge pipe are not as great. It has often been stated that the speed of a screw pump can be much higher than that of a centrifugal operating under the same conditions. These curves demonstrate this beyond a doubt. It will be noted that the centrifugal pump operates at 224 r.p.m., while the screw pump operates at a speed more than 50 per cent in excess of this, namely, 360 r.p.m. The advantage in the cost and the efficiency of a motor for operating these two pumps is distinctly in favor of the screw pump. Furthermore, the screw pump is a much lighter pump, requiring less expensive foundations, and it is easier to install. The 42-in. screw pump weighs 9,000 pounds, while the 36-in. centrifugal pump weighs 21,000 pounds. This shows that the body of the screw pump is much smaller than that of the centrifugal pump in spite of the fact that the pipe sizes are larger than the latter. In addition to this, the arrangement for pumping over levees, or between canals at different levels, is much more simple for the screw pu mp than for the centrifugal pump. The property through which the canal runs is always long and narrow and the screw pump, together with its prime mover, makes a long narrow installation which lends itself to the shape of the property in which it is to be installed. The centrifugal pump is usually a more costly pump to produce than the screw pump, and this is especially true of the pump with the characteristics shown in Fig. 2 because of the fact that this 36-in. pump has a Francis runner. The Francis runner is known for its efficiency at low heads and in this case the curve reaches the unusually high maximum point of 90 per cent. This is partly due to the special design and partly due to the very careful workmanship and careful testing of the unit in question. The screw pump, on the other hand, had a caststeel runner whose surfaces were only partially smooth. No great effort was made to bring up its point of maximum efficiency, and therefore it does not exceed 76 per cent at any point. Yet, even in the face of these handicaps of workmanship and finish on the particular units which were selected for this comparison, the screw pump is shown to be inherently a more efficient pump at low heads. It does not take a great deal of imagination to see how the screw pump efficiency curve of Fig. 3 would compare with the centrifugal pump efficiency curve had its blades been made of bronze and highly polished so as to reach a maximum point somewhere above 80 per cent. The curves shown in Fig. 3 are out of the ordinary in that they are plotted against the total head rather than against the conventional gallons per minute. This is done because the comparisons are at low heads rather than at a given capacity. By using this method of plotting, it can readily be observed that at low heads the efficiencies of the two pumps can be read directly from the chart. For example, at a head of 6 ft. the efficiency of the screw pump is 57 per cent while that of the centrifugal pump is only 42 per cent. This same information could be taken from the other curves but it would be inconvenient to do so. To get the efficiency from Fig. 1 it is necessary first to read the capacity. At 6 ft. the capacity is approximately 37,000 g.p.m. The efficiency is quite indefinite on account of the steepness of the curve; but it is apparent that it checks approximately with the reading given in Fig. 3; namely, 57 per cent. Also in Fig. 2 it is necessary first to read the capacity and then the efficiency, which checks with Fig. 3 and is 42 per cent. In addition to this, Fig. 1 and Fig. 2 would not make a graphical comparison even if plotted on the same sheet. The important point which should be kept in mind is that these curves may not show up the screw pump to advantage when read in their entirety but that at the extreme right where the points of low working heads exist the advantages of the screw pump begin to assert themselves. It is under these conditions that a screw pump should be used. In general, these curves have demonstrated, directly or indirectly, most of the advantages of the screw pump over the centrifugal as follows: Higher efficiency at low heads, higher speed, lighter weight, smaller dimensions, lower first cost, lower cost of installation, cheaper motor, more efficient motor, low head installation. [6].

Homosexuals and James Baldwins Role in the Civil Rights Movement Essay

During the Civil Rights Movement, James Baldwin wrote many articles and essays on racial issues. His unique and powerful style invoked the thoughts of many people. What also made Baldwin stand out from others was his homosexuality. Baldwin wrote several essays and novels that had a homosexual theme rooted within the story. It was through this method that Baldwin was able to express his homosexuality and at the same time present a view of black culture that was highly unacceptable during that time period. His works gave him much widespread attention but essentially he was not recognized as a prominent leader of the movement. This was a result of stereotyped images of homosexuals and the desire for African American men to align themselves with the image of being powerful and very masculine. Because African Americans were in the struggle for equality and power here in America, to have a homosexual, who is stereotyped to have effeminate features, might prove detrimenta l in the drive for equality. There were a lot of things going on during the 1960s. The Civil Rights Movement was in full steam and the push for African American quality was greater than ever. The mass of appeal for protest was overwhelming and it spread to other causes as well. Movement could be found in other minority groups, women, and homosexuals as well. This period in time was unique because change was being encouraged and many people took advantage of it. James Baldwin was no exception to this motion of change. During this time period he produced many essays and novels, some of which contained a homosexual theme. He was bold in his move because he was one of a few among many who dealt with the topic. It was only until r... ...among other writers in the literary circle and in a sense became a leader that way. In more recent times, Baldwin has been given much praise for his work, he fueled other writers to follow suit and write about issues like race and sexuality. Hopefully his works will continue to be passed on to others and will open the minds and hearts of many. Works Cited Boykin, Keith. One More River to Cross New York: Anchor Books/Doubleday, 1996. Holland, Sharon P. â€Å"(Pro)Creating Imaginative Spaces and Other Queer Acts: Randall Kenan’s A Visitation of Spirits and Its Revival of James Bladwin’s Absent Black Gay Man in Giovanni’s Room.† McBride 265-87. McBride, Dwight A., ed. James Baldwin Now. New York: New York U P, 1999. Spurlin, William J. â€Å"Culture, Rhetoric, and Queer Identity: James Baldwin and the Identity Politics of Race and Sexuality.† McBride 103-21.

Fahrenheit 451 Equality Essay

Why is equality impossible? In both Fahrenheit 451 by Ray Bradbury and â€Å"Harrison Bergeron† by Kurt Vonnegut, the government’s try to suppress freedom by calling it equality. Both the characters, Guy Montag and Harrison Bergeron try to oppose their government’s idea of equality. They show that there will always be individuals who rebel, are not the same, and try to start their own society to fight against the government. In these readings, both authors, Bradbury and Vonnegut, suggest that equality is unattainable because there will constantly be individuals that challenge the idea of people being the same in everyway possible. Even as the government concealed knowledge in both readings, individuals rebelled in order to obtain knowledge. Harrison Bergeron challenged the government, all while he wore a tremendous pair of earphones that mentally handicaps intelligent people. Nonetheless he refused to sit still and live his life like everyone else in the world. Instead he wanted to be emperor of the world and fought until his death trying to achieve his vision. Harrison proclaims on television, â€Å"‘I am the emperor! †¦ Do you hear? I am the emperor†¦ Even as I stand here†¦ crippled, hobbled, sickened- I am a greater ruler than any man who ever lived! ’†(Vonnegut 3). Despite the fact that Harrison is only fourteen years old and carried three hundred pounds, he rebelled against the government on account that he loathed the world he currently is in. This shows that even if the government forces people into being equal, people will rise up and rebel against them. In Fahrenheit 451, Guy Montag also rebelled against his government. He was not allowed to read or owned books since it was against the law. Knowing this, Guy still rebelled by smuggling books home from his fireman job. Bradbury writes, â€Å" Without looking at [the book, Guy] dropped it to the floor†¦ He kept moving his hand and dropping books on the floor†¦When he was done he looked down upon some twenty books lying at his wife’s feet† (65-66). Though Guy was a fireman and books for a living, he began to doubt and rebel against his government’s idea of equality. As the government burnt books, citizens that normally obeyed the law began to rebel against it and collected books. This shows that even people who enforce the law might rebel against it, if they begin the doubt it. No matter how hard the governments try to suppress knowledge, everyday citizens who want knowledge will find a way to obtain it. Even in the world where everyone is allegedly equal, there will be people that are above others. In â€Å"Harrison Bergeron†, everyone in the world is the same, no one is prettier than anyone else and no one is smarter than anyone else. This is untrue because Diana Moon Glampers, the United States Handicap General, is able kill people. Vonnegut writes, â€Å" Diana Moon Glampers, the Handicap General, came into the studio with a double- barreled ten-gauge shotgun. She fired twice, and the Emperor and the Empress were dead before they hit the floor† (Vonnegut 4). Even though everyone is supposedly equal, the Handicap General has more power than everyone else. She holds the power of life and death in her hands because she is not the same as the other citizens. This shows that there will always be someone that has more power than the rest; thus proving that people will never be perfectly equal. In Fahrenheit 451, the government prevents any person to possess more intelligence than the rest of the population. People who try to gain more knowledge through books are sent to an asylum and their books are burnt to the ground. Montag asks, â€Å"‘ I-I’ve been thinking. About the fire last week. About the man whose library we fixed. What happened to him? ’ [Beatty answers] ‘They took him screaming off to the asylum’† (Bradbury 33). When people try to learn more than others, the government makes sure that they are removed so that no one is smarter than anyone else. Even though they send people in possession of books to an asylum, it does not stop people who want to obtain knowledge from collecting books. This shows that no matter how much the government tries to enforce equality, there will be people that strive to obtain knowledge. No matter how much censorship is used to make everyone the same, certain individuals will always have more knowledge and power than others. As people disagreed with the government’s idea of equality, they band together and form their own society. In â€Å"Harrsion Bergeron†, Harrison Burgeron wanted to start his own empire. He disagreed with the current government and wanted to rule the world. Harrison Bergeron states, â€Å"‘I am the emperor! †¦ I am a greater ruler than any man’†(Vonnegut 3). This shows that Harrison Burgeron wants to create his own world. He opposes the government’s law and plans on creating a different society before he was shot down. Harrsison Bergeron shows that even in the most controlled world, humans who want difference will try to make their own world. When Guy Montag ran away from the society he knew, he encountered a group of people that opposed the way the government works. This group thought that books and knowledge are important unlike the government. Granger says, â€Å"‘We’ll pass the books on to our children, by word of mouth, and let our children wait, in turn, on the other people’† (Bradbury 153). Granger and his group felt that books are important and that individual knowledge is more important than everyone being perfectly equal. They thought that the world is not ready for their knowledge. By having their own group with different ideas from the government’s, they have started a society where people can appreciate books instead of burning them. They have created a society that directly contradicts what he government is trying to accomplish. When people do not agree with the government, they will band together and form a society hoping to overthrow the law. Equality is an unachievable idea due to the fact that there are people who will rebel, be smarter or more powerful than others, and people that band together to form their own ideal society. The more a government forces their citizens to be equal, the more likely people will oppose what the government is doing. In both â€Å"Harrison Bergeron† and Fahrenheit 451, the government tries to censor the amount of freedom and knowledge every individual has, by calling it equality, but people had still rebelled against the government. Both stories show that equality is a truly impossible because certain individuals will always challenge what equality truly is.