## 1 MECE2320U-THERMODYNAMICS HOMEWORK # 5 Instructor: Dr. Ibrahim Dincer Assignment Date: Thursday, 22 October 2015 Assignment Type: Individual Due Date: Thursday, 29 October 2015 (3.00 pm latest, leave in dropbox 8) 1) As shown in figure, the inlet and outlet conditions of a steam turbine are given. The heat loss from turbine is 35 kJ per kg of steam. a) Show all the state points on T-v diagram b) Write mass and energy balance equations c) Calculate the turbine work 2) As shown in figure, refrigerant R134a enters to a compressor. Write both mass and energy balance equations. Calculate the compressor work and the mass flow rate of refrigerant. 3) As shown in figure, the heat exchanger uses the heat of hot exhaust gases to produce steam. Where, 15% of heat is lost to the surroundings. Exhaust gases enters the heat exchanger at 500°C. Water enters at 15°C as saturated liquid and exit at saturated vapor at 2 MPa. Mass flow rate of water is 0.025 kg/s, and for exhaust gases, it is 0.42 kg/s. The specific heat for exhaust gases is 1.045 kJ/kg K, which can be treated as ideal gas. 1 Turbine 2 ? 1 = 1 ??/? ?1 = 1 ??? ?1 = 300 ℃ ?1 = 40 ?/? ? ??? =? ????? = 35 ??/?? ?2 = 150 ??? ?2 = 0.9 ?2 = 180 ?/? 1 Compressor 2 ???? ???? = 1.3 ?3/??? ?1 = 100 ??? ?1 = −20 ℃ ? ?? =? ? ???? = 3 ?? ?2 = 800 ??? ?2 = 60 ℃ 2 a) Write mass and energy balance equations. b) Calculate the rate of heat transfer to the water. c) Calculate the exhaust gases exit temperature. 4) As shown in figure, two refrigerant R134a streams mix in a mixing chamber. If the mass flow rate of cold stream is twice that of the hot stream. a) Write mass and energy balance equations. b) Calculate the temperature of the mixture at the exit of the mixing chamber c) Calculate the quality at the exit of the mixing chamber 5) As shown in figure, an air conditioning system requires airflow at the main supply duct at a rate of 140 m3/min. The velocity inside circular duct is not to exceed 9 m/s. Assume that the fan converts 85% of electrical energy it consumes into kinetic energy of air. a) Write mass and energy balance equations. b) Calculate the size of electric motor require to drive the fan c) Calculate the diameter of the main duct ?2 = 1 ??? ?2 = 90 ℃ ?1 = 1 ??? ?1 = 30 ℃ ?3 =? ?3 =? 140 ?3/??? 9 ?/? Air Fan

No expert has answered this question yet. You can browse … Read More...

## Project Part 1 Objective Our objective, in this Part 1 of our Project, is to practise solving a problem by composing and testing a Python program using all that we have learnt so far and discovering new things, such as lists of lists, on the way. Project – Hunting worms in our garden! No more turtles! In this project, we shall move on to worms. Indeed, our project is a game in which the player hunts for worms in our garden. Once our garden has been displayed, the player tries to guess where the worms are located by entering the coordinates of a cell in our garden. When the player has located all the worms, the game is over! Of course there are ways of making this game more exciting (hence complicated), but considering that we have 2 weeks for Part 1 and 2 weeks for Part 2, keeping it simple will be our goal. We will implement our game in two parts. In Part 1, we write code that constructs and tests our data structures i.e., our variables. In Part 2, we write code that allows the player to play a complete “worm hunting” game! ? Project – Part 1 – Description Data Structures (variables): As stated above, in Part 1, we write code that constructs our data structures i.e., our variables. In our game program, we will need data structures (variables) to represent: 1. Our garden that is displayed to the player (suggestion: list of lists), 2. The garden that contains all the worms (suggestion: another list of lists), Garden: Our garden in Part 1 of our Project will have a width and a height of 10. Warning: The width and the height of our garden may change in Part 2 of our Project. So, it may be a good idea to create 2 variables and assign the width and the height of our garden to these 2 variables. 3. Our worms and their information. For each worm, we may want to keep the following information: a. worm number, b. the location of the worm, for example, either the coordinates of the cells containing the worm OR the coordinate of the first cell containing the worm, its length and whether the worm is laying horizontally or vertically. Worms: We will create 6 worms of length 3. 4. And other variables as needed. Testing our data structures: ? Suggestion: as we create a data structure (the “displayed” garden, the garden containing the worms, each worm, etc…), print it with a “debug print statement”. Once we are certain the data structure is well constructed, comment out the “debug print statement”. Code: In Part 1, the code we write must include functions and it must include the main section of our program. In other words, in Part 1, the code we write must be a complete program. In terms of functions, here is a list of suggestions. We may have functions that … ? creates a garden (i.e., a garden data structure), ? creates the worms (i.e., the worm data structure), ? places a worm in the garden that is to hold the worms (i.e., another garden data structure), ? displays the garden on the screen for the player to see, ? displays a worm in the displayed garden, ? etc… ? Finally, in Part 1, the code we write must implement the following algorithm: Algorithm: Here is the algorithm for the main section of our game program: ? Welcome the player ? Create an empty “displayed” garden, (“displayed” because this is the garden we display to the player) ? Create the worms (worms’ information) ? Create an empty “hidden” garden Note 1: “hidden” because one can keep track of the worms in this “hidden” garden, which we do not show to the player. This is why it is called “hidden”. Note 2: One can keep track of worm’s locations using a different mechanism or data structure. It does not have to be a list of lists representing a “hidden” garden. We are free to choose how we want to keep track of where our worms are located in our garden. ? Place each worm in the “hidden” garden (or whatever mechanism or data structure we decide to use) ? Display the “displayed” garden on the screen for the player to see ? While the player wants to play, ask the player for a worm number (1 to 6), read this worm number and display this worm on the “displayed” garden. This is not the game. Remember, we shall implement the game itself in Part 2. Here, in this step, we make sure our code works properly, i.e., it can retrieve worm information and display worms properly. Displaying worms properly: Note that when we create worms and display them, it may be the case that worms overlap with other worms and that worms wrap around the garden. These 2 situations are illustrated in the 3 Sample Runs discussed below. At this point, we are ready for Part 2 of our Project. Sample Runs: In order to illustrate the explanations given above of what we are to do in this Part 1 of our Project, 3 sample runs have been posted below the description of this Part 1 of our Project on our course web site. Have a look at these 3 sample runs. The code we create for this Part 1 of our Project must produce exactly the same output as the one shown in these 3 sample runs. Of course, the position of our worms will be different but everything else should be the same. What we see in each of these 3 sample runs is 1 execution of the code we are to create for this Part 1 of our Project. Note about Sample Run 1: In this Sample Run, the player enters the numbers 1 to 8 sequentially. Wrap around: Worm 2 wraps around: it starts at (row 7, column B), (row 7, column A) then wraps around to (row 7, column J). Worm 6 also wraps around: it starts at (row 2, column E), (row 1, column E) then wraps around to (row 10, column E). Overlap: There are some overlapping worms: worms 5 and 6 overlap at (row 1, column E). Note about Sample Run 2: In this Sample Run, the player enters the numbers 1 to 8 sequentially. Wrap around: Worm 3 wraps around: it starts at (row 1, column B) then wraps around to (row 10, column B) and (row 9, column B). Worm 6 also wraps around: it starts at (row 1, column D) then wraps around to (row 10, column D) and (row 9, column D). Overlap: There are some overlapping worms: worms 2 and 4 overlap at (row 3, column H), worms 1 and 2 overlap at (row 3, column G) and worms 2 and 5 overlap at (row 3, column E). Note about Sample Run 3: In this Sample Run, the player enters the numbers in the following sequence: 3, 2, 6, 4, 5, 1, 7, 8. Wrap around: Worm 3 wraps around: it starts at (row 2, column C), (row 1, column C) then wraps around to (row 10, column C). Worm 1 also wraps around: it starts at (row 2, column B), (row 2, column A) then wraps around to (row 2, column J). Overlap: There are some overlapping worms: worms 6 and 3 overlap at (row 1, column C) and (row 2, column C). Other Requirements: Here are a few more requirements the code we are to create for this Part 1 of our Project must satisfy. 1. The location of each worm in the garden must be determined randomly. 2. Whether a worm is lying horizontally or vertically must also be determined randomly. 3. It is acceptable in Part 1 of our Project if worms overlap each other (see Sample Runs) 4. When placing a worm in a garden, the worm must “wrap around” the garden. See Sample Runs for examples of what “wrapping around” signifies. How will we implement this wrapping around? Hint: wrapping around can be achieved using an arithmetic operator we have already seen. 5. We must make use of docstring when we implement our functions (have a look at our textbook for an explanation and an example). 6. Every time we encounter the word must in this description of Part 1 of our Project, we shall look upon that sentence as another requirement. For example, the sentence “The code we create for this Part 1 of our Project must produce exactly the same output as the one shown in these 3 sample runs.”, even though it is not listed below the Other Requirements heading, is also a requirement because of its must.

info@checkyourstudy.com

## The energy absorbed by the BOX in Fig. P1.15 is shown . How much charge enters the box between 0 and 10 millisecond ?

## Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4 A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A B = -15 A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A B = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to . A B A = 2 + 5 ı ^ ^ B = −2 − 4 ı ^ ^ = 175 A B A = −6 + 2 ı ^ ^ B = − − 3 ı ^ ^ = 90 W = = cos F s F s W F s F Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos F 1 It is positive. It is negative. It is zero. There is not enough information to answer the question. = 90 What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F 2 It is positive. It is negative. It is zero. 0 < < 90 cos F 3 positive negative zero 90 < < 180 cos F 4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F 5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F 6 positive negative zero F 7 positive negative zero W = = cos F s F s Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

please email info@checkyourstudy.com

## Assignment 12 Due: 11:59pm on Friday, May 9, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 15.6 A 0.600 -diameter vat of liquid is 2.30 deep. The pressure at the bottom of the vat is 1.30 . Part A What is the mass of the liquid in the vat? Express your answer with the appropriate units. ANSWER: Correct Problem 15.8 A 90-cm-thick layer of oil floats on a 160-cm-thick layer of water. Part A What is the pressure at the bottom of the water layer? Express your answer with the appropriate units. ANSWER: Correct m m atm 876 kg p = 1.25×105 Pa Problem 15.9 A research submarine has a 40.0 -diameter window 9.00 thick. The manufacturer says the window can withstand forces up to 1.20×106 . What is the submarine’s maximum safe depth? Part A The pressure inside the submarine is maintained at 1.0 atm. Express your answer with the appropriate units. ANSWER: Correct Problem 15.13 Part A What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 12 dog off the floor? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 15.40 The 78 student in the figure balances a 1100 elephant on a hydraulic lift. cm cm N 947 m kg d = 3.8 cm kg kg You may want to review ( pages 415 – 419) . For help with math skills, you may want to review: Rearrangement of Equations Involving Multiplication and Division Part A What is the diameter of the piston the student is standing on? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Given that the height of the fluid on the two sides is the same in the figure, how is the pressure of the fluid on the two sides related? What is the definition of pressure? What is the area of the right cylinder? What is the force exerted by the elephant on the right cylinder? What is the additional pressure above atmospheric pressure in the fluid under the elephant? What is the additional pressure above atmospheric pressure under the student in the left cylinder? What is the force exerted by the student on the left cylinder? What is the area of the left cylinder? ANSWER: Correct Part B d = 0.53 m When a second student joins the first, the piston sinks 40 . What is the second student’s mass? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the definition of pressure? How is the height difference between the left and right cylinders related to the pressure difference in the two cylinders? What is the standard value for the density of the oil given in the text? What is the force due to the elephant on the right cylinder? What is the additional pressure above atmospheric pressure in the fluid under the elephant? Given the height difference between the two cylinders and the pressure in the right cylinder, what is the pressure above atmospheric pressure in the left cylinder? What is the force due to both students on the left cylinder? What is the sum of the masses of the students? What is the mass of the second student? ANSWER: Correct Enhanced EOC: Problem 15.17 A 6.80 rock whose density is 4900 is suspended by a string such that half of the rock’s volume is under water. You may want to review ( pages 419 – 423) . For help with math skills, you may want to review: Conversion Factors Part A What is the tension in the string? Express your answer with the appropriate units. Hint 1. How to approach the problem cm m = 80 kg kg kg/m3 What are the three forces acting on the rock? Draw a picture indicating the direction of the forces on the rock and an appropriate coordinate system indicating the positive direction. How is volume related to mass and density? What is the volume of the rock? What is the buoyant force on the rock given that half of the rock is underwater? What is the gravitational force on the rock? Given that the rock is suspended, what is the net force on the rock? Now, determine the tension in the string. ANSWER: Correct Problem 15.15 A block floats in water with its long axis vertical. The length of the block above water is 1.0 . Part A What is the block’s mass density? Express your answer with the appropriate units. ANSWER: Correct Crown of Gold? According to legend, the following challenge led Archimedes to the discovery of his famous principle: Hieron, king of Syracuse, was suspicious that a new crown that he had received from the royal goldsmith was not pure gold, as claimed. Archimedes was ordered to determine whether the crown was in fact made of pure gold, with the condition that only a nondestructive test would be allowed. Rather than answer the problem in the politically most expedient way (or perhaps extract a bribe from the goldsmith), Archimedes thought about the problem scientifically. The legend relates that when 59.8 N 2.0 cm × 2.0 cm × 7.0 cm cm 857 kg m3 Archimedes stepped into his bath and caused it to overflow, he realized that he could answer the challenge by comparing the volume of water displaced by the crown with the volume of water displaced by an amount of pure gold equal in weight to the crown. If the crown was made of pure gold, the two volumes would be equal. If some other (less dense) metal had been substituted for some of the gold, then the crown would displace more water than the pure gold. A similar method of answering the challenge, based on the same physical principle, is to compute the ratio of the actual weight of the crown, , and the apparent weight of the crown when it is submerged in water, . See whether you can follow in Archimedes’ footsteps. The figure shows what is meant by weighing the crown while it is submerged in water. Part A Take the density of the crown to be . What is the ratio of the crown’s apparent weight (in water) to its actual weight ? Express your answer in terms of the density of the crown and the density of water . Hint 1. Find an expression for the actual weight of the crown Assume that the crown has volume . Find the actual weight of the crown. Express in terms of , (the magnitude of the acceleration due to gravity), and . ANSWER: Wactual Wapparent c Wapparent Wactual c w V Wactual Wactual V g c Wactual = cV g Hint 2. Find an expression for the apparent weight of the crown Assume that the crown has volume , and take the density of water to be . Find the apparent weight of the crown submerged in water. Express your answer in terms of , (the magnitude of the acceleration due to gravity), , and . Hint 1. How to approach the problem The apparent weight of the crown when it is submerged in water will be less than its actual weight (weight in air) due to the buoyant force, which opposes gravity. Hint 2. Find an algebraic expression for the buoyant force. Find the magnitude of the buoyant force on the crown when it is completely submerged in water. Express your answer in terms of , , and the gravitational acceleration . ANSWER: ANSWER: ANSWER: Correct Part B Imagine that the apparent weight of the crown in water is , and the actual weight is . Is the crown made of pure (100%) gold? The density of water is V w Wapparent V g w c Fbuoyant w V g Fbuoyant = wV g Wapparent = (c − w)gV = Wapparent Wactual 1 − w c Wapparent = 4.50 N Wactual = 5.00 N grams per cubic centimeter. The density of gold is grams per cubic centimeter. Hint 1. Find the ratio of weights for a crown of pure gold Given the expression you obtained for , what should the ratio of weights be if the crown is made of pure gold? Express your answer numerically, to two decimal places. ANSWER: ANSWER: Correct For the values given, , whereas for pure gold, . Thus, you can conclude that the the crown is not pure gold but contains some less-dense metal. The goldsmith made sure that the crown’s (true) weight was the same as that of the amount of gold he was allocated, but in so doing was forced to make the volume of the crown slightly larger than it would otherwise have been. Problem 15.23 A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. Liquid flows through the first segment at a speed of 9.0 . Part A What is the speed in the second segment? Express your answer with the appropriate units. w = 1.00 g = 19.32 Wapparent Wactual = 0.95 Wapparent Wactual Yes No = 4.50/5.00 = 0.90 Wapparent Wactual = 1 − = 0.95 Wapparent Wactual w g m/s ANSWER: Correct Part B What is the speed in the third segment? Express your answer with the appropriate units. ANSWER: Correct Part C What is the volume flow rate through the pipe? Express your answer with the appropriate units. ANSWER: Correct Understanding Bernoulli’s Equation Bernoulli’s equation is a simple relation that can give useful insight into the balance among fluid pressure, flow speed, and elevation. It applies exclusively to ideal fluids with steady flow, that is, fluids with a constant density and no internal friction forces, whose flow patterns do not change with time. Despite its limitations, however, Bernoulli’s equation is an essential tool in understanding the behavior of fluids in many practical applications, from plumbing systems to the flight of airplanes. 2.25 ms 36.0 ms 7.07×10−4 m3 s For a fluid element of density that flows along a streamline, Bernoulli’s equation states that , where is the pressure, is the flow speed, is the height, is the acceleration due to gravity, and subscripts 1 and 2 refer to any two points along the streamline. The physical interpretation of Bernoulli’s equation becomes clearer if we rearrange the terms of the equation as follows: . The term on the left-hand side represents the total work done on a unit volume of fluid by the pressure forces of the surrounding fluid to move that volume of fluid from point 1 to point 2. The two terms on the right-hand side represent, respectively, the change in potential energy, , and the change in kinetic energy, , of the unit volume during its flow from point 1 to point 2. In other words, Bernoulli’s equation states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the change in potential and kinetic energy per unit volume that occurs during the flow. This is nothing more than the statement of conservation of mechanical energy for an ideal fluid flowing along a streamline. Part A Consider the portion of a flow tube shown in the figure. Point 1 and point 2 are at the same height. An ideal fluid enters the flow tube at point 1 and moves steadily toward point 2. If the cross section of the flow tube at point 1 is greater than that at point 2, what can you say about the pressure at point 2? Hint 1. How to approach the problem Apply Bernoulli’s equation to point 1 and to point 2. Since the points are both at the same height, their elevations cancel out in the equation and you are left with a relation between pressure and flow speeds. Even though the problem does not give direct information on the flow speed along the flow tube, it does tell you that the cross section of the flow tube decreases as the fluid flows toward point 2. Apply the continuity equation to points 1 and 2 and determine whether the flow speed at point 2 is greater than or smaller than the flow speed at point 1. With that information and Bernoulli’s equation, you will be able to determine the pressure at point 2 with respect to the pressure at point 1. Hint 2. Apply Bernoulli’s equation p1 +gh1 + = +g + 1 2 v21 p2 h2 1 2 v22 p v h g p1 − p2 = g(h2 −h1)+ ( − ) 1 2 v22 v21 p1 − p2 g(h2 − h1) 1 ( − ) 2 v22 v21 Apply Bernoulli’s equation to point 1 and to point 2 to complete the expression below. Here and are the pressure and flow speed, respectively, and subscripts 1 and 2 refer to point 1 and point 2. Also, use for elevation with the appropriate subscript, and use for the density of the fluid. Express your answer in terms of some or all of the variables , , , , , , and . Hint 1. Flow along a horizontal streamline Along a horizontal streamline, the change in potential energy of the flowing fluid is zero. In other words, when applying Bernoulli’s equation to any two points of the streamline, and they cancel out. ANSWER: Hint 3. Determine with respect to By applying the continuity equation, determine which of the following is true. Hint 1. The continuity equation The continuity equation expresses conservation of mass for incompressible fluids flowing in a tube. It says that the amount of fluid flowing through a cross section of the tube in a time interval must be the same for all cross sections, or . Therefore, the flow speed must increase when the cross section of the flow tube decreases, and vice versa. ANSWER: p v h p1 v1 h1 p2 v2 h2 h1 = h2 p1 + = 1 2 v21 p2 + v2 2 2 v2 v1 $V A $t $V = = $t A1v1 A2v2 v2 > v1 v2 = v1 v2 < v1 ANSWER: Correct Thus, by combining the continuity equation and Bernoulli's equation, one can characterize the flow of an ideal fluid.When the cross section of the flow tube decreases, the flow speed increases, and therefore the pressure decreases. In other words, if , then and . Part B As you found out in the previous part, Bernoulli's equation tells us that a fluid element that flows through a flow tube with decreasing cross section moves toward a region of lower pressure. Physically, the pressure drop experienced by the fluid element between points 1 and 2 acts on the fluid element as a net force that causes the fluid to __________. Hint 1. Effects from conservation of mass Recall that, if the cross section of the flow tube varies, the flow speed must change to conserve mass. This means that there is a nonzero net force acting on the fluid that causes the fluid to increase or decrease speed depending on whether the fluid is flowing through a portion of the tube with a smaller or larger cross section. ANSWER: Correct Part C Now assume that point 2 is at height with respect to point 1, as shown in the figure. The ends of the flow tube have the same areas as The pressure at point 2 is lower than the pressure at point 1. equal to the pressure at point 1. higher than the pressure at point 1. A2 < A1 v2 > v1 p2 < p1 A v decrease in speed increase in speed remain in equilibrium h the ends of the horizontal flow tube shown in Part A. Since the cross section of the flow tube is decreasing, Bernoulli's equation tells us that a fluid element flowing toward point 2 from point 1 moves toward a region of lower pressure. In this case, what is the pressure drop experienced by the fluid element? Hint 1. How to approach the problem Apply Bernoulli's equation to point 1 and to point 2, as you did in Part A. Note that this time you must take into account the difference in elevation between points 1 and 2. Do you need to add this additional term to the other term representing the pressure drop between the two ends of the flow tube or do you subtract it? ANSWER: Correct Part D From a physical point of view, how do you explain the fact that the pressure drop at the ends of the elevated flow tube from Part C is larger than the pressure drop occurring in the similar but purely horizontal flow from Part A? Hint 1. Physical meaning of the pressure drop in a tube As explained in the introduction, the difference in pressure between the ends of a flow tube represents the total work done on a unit volume of fluid by the pressure forces of the The pressure drop is smaller than the pressure drop occurring in a purely horizontal flow. equal to the pressure drop occurring in a purely horizontal flow. larger than the pressure drop occurring in a purely horizontal flow. p1 − p2 surrounding fluid to move that volume of fluid from one end to the other end of the flow tube. ANSWER: Correct In the case of purely horizontal flow, the difference in pressure between the two ends of the flow tube had to balance only the increase in kinetic energy resulting from the acceleration of the fluid. In an elevated flow tube, the difference in pressure must also balance the increase in potential energy of the fluid; therefore a higher pressure is needed for the flow to occur. Venturi Meter with Two Tubes A pair of vertical, open-ended glass tubes inserted into a horizontal pipe are often used together to measure flow velocity in the pipe, a configuration called a Venturi meter. Consider such an arrangement with a horizontal pipe carrying fluid of density . The fluid rises to heights and in the two open-ended tubes (see figure). The cross-sectional area of the pipe is at the position of tube 1, and at the position of tube 2. A greater amount of work is needed to balance the increase in potential energy from the elevation change. decrease in potential energy from the elevation change. larger increase in kinetic energy. larger decrease in kinetic energy. h1 h2 A1 A2 Part A Find , the gauge pressure at the bottom of tube 1. (Gauge pressure is the pressure in excess of outside atmospheric pressure.) Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. Hint 1. How to approach the problem Use Bernoulli's law to compute the difference in pressure between the top and bottom of tube 1. The pressure at the top of the tube is defined to be atmospheric pressure. Note: Inside the tube, since the fluid is not flowing, the terms involving velocity in Bernoulli's equation can be ignored. Thus, Bernoulli's equation reduces to the formula for pressure as a function of depth in a fluid of uniform density. Hint 2. Simplified Bernoulli's equation For a fluid of uniform density that is not flowing, the pressure at a depth below the surface is given by , where is the pressure at the surface and is the magnitude of the acceleration due to gravity. ANSWER: Correct The fluid is pushed up tube 1 by the pressure of the fluid at the base of the tube, and not by its kinetic energy, since there is no streamline around the sharp edge of the tube. Thus energy is not conserved (there is turbulence at the edge of the tube) at the entrance of the tube. Since Bernoulli's law is essentially a statement of energy conservation, it must be applied separately to the fluid in the tube and the fluid flowing in the main pipe. However, the pressure in the fluid is the same just inside and just outside the tube. Part B Find , the speed of the fluid in the left end of the main pipe. Express your answer in terms of , , , and either and or , which is equal to . Hint 1. How to approach the problem Energy is conserved along the streamlines in the main flow. This means that Bernoulli's law can be applied to obtain a relationship between the fluid pressure and velocity at the bottom of p1 g p h p = p0 + gh p0 g p1 = gh1 v1 h1 h2 g A1 A2 A1 A2 tube 1, and the fluid pressure and velocity at the bottom of tube 2. Hint 2. Find in terms of What is , the pressure at the bottom of tube 2? Express your answer in terms of , , and any other given quantities. Hint 1. Recall Part A Obtain the solution for this part in the same way that you found an expression for in terms of in Part A of this problem. ANSWER: Hint 3. Find in terms of given quantities Find , the fluid pressure at the bottom of tube 2. Express your answer in terms of , , , , and . Hint 1. Find the pressure at the bottom of tube 2 Find , the fluid pressure at the bottom of tube 2. Express your answer in terms of , , and . ANSWER: Hint 2. Find in terms of The fluid is incompressible, so you can use the continuity equation to relate the fluid velocities and in terms of the geometry of the pipe. Find , the fluid velocity at the bottom p2 h2 p2 h2 g p1 h1 p2 = gh2 p2 p2 p1 v1 A1 A2 p2 p1 v1 v2 p2 = p1 + ( − ) 1 2 v1 2 v2 2 v2 v1 v1 v2 v2 of tube 2, in terms of . Your answer may include and , the cross-sectional areas of the pipe. ANSWER: ANSWER: ANSWER: Correct Note that this result depends on the difference between the heights of the fluid in the tubes, a quantity that is more easily measured than the heights themselves. Problem 15.39 The container shown in the figure is filled with oil. It is open to the atmosphere on the left. v1 A1 A2 v2 = A1 A2 v1 p2 = p1 + ( )(1 − ) 1 2 v1 2 ( ) A1 A2 2 v1 = 2g h1−h2 ( ) −1 A1 A2 2 −−−−−−−−−−−−−− Part A What is the pressure at point A? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the pressure difference between points A and B? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the pressure difference between points A and C? PA = 106 kPa PB − PA = 4.4 kPa Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 15.48 You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads 32.4 . If you then lower the statue into a tub of water, so that it is completely submerged, the scale reads 17 . Part A What is the density? Express your answer with the appropriate units. ANSWER: Correct Problem 15.60 Water flows from the pipe shown in the figure with a speed of 7.0 . PC − PA = 4.4 kPa N N statue = 2100 kg m3 m/s Part A What is the water pressure as it exits into the air? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the height of the standing column of water? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 99.9%. You received 93.92 out of a possible total of 94 points. P = 1.0×105 Pa h h = 5.9 m

please email info@checkyourstudy.com

## Assignment 12 Due: 11:59pm on Friday, May 9, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 15.6 A 2.00 -diameter vat of liquid is 2.90 deep. The pressure at the bottom of the vat is 1.20 . Part A What is the mass of the liquid in the vat? Express your answer with the appropriate units. ANSWER: Correct Problem 15.8 A 120-cm-thick layer of oil floats on a 130-cm-thick layer of water. Part A What is the pressure at the bottom of the water layer? Express your answer with the appropriate units. ANSWER: Correct m m atm 6490 kg p = 1.25×105 Pa Problem 15.9 A research submarine has a 40.0 -diameter window 8.00 thick. The manufacturer says the window can withstand forces up to 1.20×106 . What is the submarine’s maximum safe depth? Part A The pressure inside the submarine is maintained at 1.0 atm. Express your answer with the appropriate units. ANSWER: Correct Problem 15.13 Part A What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 13 dog off the floor? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 15.40 The 80 student in the figure balances a 1300 elephant on a hydraulic lift. cm cm N 947 m kg d = 4.0 cm kg kg Typesetting math: 100% You may want to review ( pages 415 – 419) . For help with math skills, you may want to review: Rearrangement of Equations Involving Multiplication and Division Part A What is the diameter of the piston the student is standing on? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Given that the height of the fluid on the two sides is the same in the figure, how is the pressure of the fluid on the two sides related? What is the definition of pressure? What is the area of the right cylinder? What is the force exerted by the elephant on the right cylinder? What is the additional pressure above atmospheric pressure in the fluid under the elephant? What is the additional pressure above atmospheric pressure under the student in the left cylinder? What is the force exerted by the student on the left cylinder? What is the area of the left cylinder? ANSWER: Correct Part B d = 0.50 m Typesetting math: 100% When a second student joins the first, the piston sinks 30 . What is the second student’s mass? Express your answer to two significant figures and include the appropriate units. You did not open hints for this part. ANSWER: Enhanced EOC: Problem 15.17 A 4.70 rock whose density is 4300 is suspended by a string such that half of the rock’s volume is under water. You may want to review ( pages 419 – 423) . For help with math skills, you may want to review: Conversion Factors Part A What is the tension in the string? Express your answer with the appropriate units. Hint 1. How to approach the problem What are the three forces acting on the rock? Draw a picture indicating the direction of the forces on the rock and an appropriate coordinate system indicating the positive direction. How is volume related to mass and density? What is the volume of the rock? What is the buoyant force on the rock given that half of the rock is underwater? What is the gravitational force on the rock? Given that the rock is suspended, what is the net force on the rock? Now, determine the tension in the string. cm m = kg kg/m3 Typesetting math: 100% ANSWER: Correct Problem 15.15 A block floats in water with its long axis vertical. The length of the block above water is 1.0 . Part A What is the block’s mass density? Express your answer with the appropriate units. ANSWER: Correct Crown of Gold? According to legend, the following challenge led Archimedes to the discovery of his famous principle: Hieron, king of Syracuse, was suspicious that a new crown that he had received from the royal goldsmith was not pure gold, as claimed. Archimedes was ordered to determine whether the crown was in fact made of pure gold, with the condition that only a nondestructive test would be allowed. Rather than answer the problem in the politically most expedient way (or perhaps extract a bribe from the goldsmith), Archimedes thought about the problem scientifically. The legend relates that when Archimedes stepped into his bath and caused it to overflow, he realized that he could answer the challenge by comparing the volume of water displaced by the crown with the volume of water displaced by an amount of pure gold equal in weight to the crown. If the crown was made of pure gold, the two volumes would be equal. If some other (less dense) metal had been substituted for some of the gold, then the crown would displace more water than the pure gold. A similar method of answering the challenge, based on the same physical principle, is to compute the ratio of the actual weight of the crown, , and the apparent weight of the crown when it is submerged in water, . See whether you can follow in Archimedes’ footsteps. The figure shows what is meant by weighing the crown while it is submerged in water. 40.7 N 2.0 cm × 2.0 cm × 8.0 cm cm 875 kg m3 Wactual Wapparent Typesetting math: 100% Part A Take the density of the crown to be . What is the ratio of the crown’s apparent weight (in water) to its actual weight ? Express your answer in terms of the density of the crown and the density of water . Hint 1. Find an expression for the actual weight of the crown Assume that the crown has volume . Find the actual weight of the crown. Express in terms of , (the magnitude of the acceleration due to gravity), and . ANSWER: Hint 2. Find an expression for the apparent weight of the crown Assume that the crown has volume , and take the density of water to be . Find the apparent weight of the crown submerged in water. Express your answer in terms of , (the magnitude of the acceleration due to gravity), , and . Hint 1. How to approach the problem c Wapparent Wactual c w V Wactual Wactual V g c Wactual = cV g V w Wapparent V g w c Typesetting math: 100% The apparent weight of the crown when it is submerged in water will be less than its actual weight (weight in air) due to the buoyant force, which opposes gravity. Hint 2. Find an algebraic expression for the buoyant force. Find the magnitude of the buoyant force on the crown when it is completely submerged in water. Express your answer in terms of , , and the gravitational acceleration . ANSWER: ANSWER: ANSWER: Correct Part B Imagine that the apparent weight of the crown in water is , and the actual weight is . Is the crown made of pure (100%) gold? The density of water is grams per cubic centimeter. The density of gold is grams per cubic centimeter. Hint 1. Find the ratio of weights for a crown of pure gold Given the expression you obtained for , what should the ratio of weights be if the crown is made of pure gold? Express your answer numerically, to two decimal places. Fbuoyant w V g Fbuoyant = wV g Wapparent = (c − w)gV = Wapparent Wactual 1 − w c Wapparent = 4.50 N Wactual = 5.00 N w = 1.00 g = 19.32 Wapparent Wactual Typesetting math: 100% ANSWER: ANSWER: Correct For the values given, , whereas for pure gold, . Thus, you can conclude that the the crown is not pure gold but contains some less-dense metal. The goldsmith made sure that the crown’s (true) weight was the same as that of the amount of gold he was allocated, but in so doing was forced to make the volume of the crown slightly larger than it would otherwise have been. Problem 15.23 A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. Liquid flows through the first segment at a speed of 2.0 . Part A What is the speed in the second segment? Express your answer with the appropriate units. ANSWER: Correct = 0.95 Wapparent Wactual Yes No = 4.50/5.00 = 0.90 Wapparent Wactual = 1 − = 0.95 Wapparent Wactual w g m/s 0.500 ms Typesetting math: 100% Part B What is the speed in the third segment? Express your answer with the appropriate units. ANSWER: Correct Part C What is the volume flow rate through the pipe? Express your answer with the appropriate units. ANSWER: Correct Understanding Bernoulli’s Equation Bernoulli’s equation is a simple relation that can give useful insight into the balance among fluid pressure, flow speed, and elevation. It applies exclusively to ideal fluids with steady flow, that is, fluids with a constant density and no internal friction forces, whose flow patterns do not change with time. Despite its limitations, however, Bernoulli’s equation is an essential tool in understanding the behavior of fluids in many practical applications, from plumbing systems to the flight of airplanes. For a fluid element of density that flows along a streamline, Bernoulli’s equation states that , where is the pressure, is the flow speed, is the height, is the acceleration due to gravity, and subscripts 1 and 2 refer to any two points along the streamline. The physical interpretation of Bernoulli’s equation becomes clearer if we rearrange the terms of the equation as follows: . 8.00 ms 1.57×10−4 m3 s p1 +gh1 + = +g + 1 2 v21 p2 h2 1 2 v22 p v h g p1 − p2 = g(h2 −h1)+ ( − ) 1 2 v22 v21 Typesetting math: 100% The term on the left-hand side represents the total work done on a unit volume of fluid by the pressure forces of the surrounding fluid to move that volume of fluid from point 1 to point 2. The two terms on the right-hand side represent, respectively, the change in potential energy, , and the change in kinetic energy, , of the unit volume during its flow from point 1 to point 2. In other words, Bernoulli’s equation states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the change in potential and kinetic energy per unit volume that occurs during the flow. This is nothing more than the statement of conservation of mechanical energy for an ideal fluid flowing along a streamline. Part A Consider the portion of a flow tube shown in the figure. Point 1 and point 2 are at the same height. An ideal fluid enters the flow tube at point 1 and moves steadily toward point 2. If the cross section of the flow tube at point 1 is greater than that at point 2, what can you say about the pressure at point 2? Hint 1. How to approach the problem Apply Bernoulli’s equation to point 1 and to point 2. Since the points are both at the same height, their elevations cancel out in the equation and you are left with a relation between pressure and flow speeds. Even though the problem does not give direct information on the flow speed along the flow tube, it does tell you that the cross section of the flow tube decreases as the fluid flows toward point 2. Apply the continuity equation to points 1 and 2 and determine whether the flow speed at point 2 is greater than or smaller than the flow speed at point 1. With that information and Bernoulli’s equation, you will be able to determine the pressure at point 2 with respect to the pressure at point 1. Hint 2. Apply Bernoulli’s equation Apply Bernoulli’s equation to point 1 and to point 2 to complete the expression below. Here and are the pressure and flow speed, respectively, and subscripts 1 and 2 refer to point 1 and point 2. Also, use for elevation with the appropriate subscript, and use for the density of the fluid. Express your answer in terms of some or all of the variables , , , , , , and . Hint 1. Flow along a horizontal streamline p1 − p2 g(h2 − h1) 1 ( − ) 2 v22 v21 p v h p1 v1 h1 p2 v2 h2 Typesetting math: 100% Along a horizontal streamline, the change in potential energy of the flowing fluid is zero. In other words, when applying Bernoulli’s equation to any two points of the streamline, and they cancel out. ANSWER: Hint 3. Determine with respect to By applying the continuity equation, determine which of the following is true. Hint 1. The continuity equation The continuity equation expresses conservation of mass for incompressible fluids flowing in a tube. It says that the amount of fluid flowing through a cross section of the tube in a time interval must be the same for all cross sections, or . Therefore, the flow speed must increase when the cross section of the flow tube decreases, and vice versa. ANSWER: ANSWER: h1 = h2 p1 + = 1 2 v21 p2 + v2 2 2 v2 v1 $V A $t $V = = $t A1v1 A2v2 v2 > v1 v2 = v1 v2 < v1 Typesetting math: 100% Correct Thus, by combining the continuity equation and Bernoulli's equation, one can characterize the flow of an ideal fluid.When the cross section of the flow tube decreases, the flow speed increases, and therefore the pressure decreases. In other words, if , then and . Part B As you found out in the previous part, Bernoulli's equation tells us that a fluid element that flows through a flow tube with decreasing cross section moves toward a region of lower pressure. Physically, the pressure drop experienced by the fluid element between points 1 and 2 acts on the fluid element as a net force that causes the fluid to __________. Hint 1. Effects from conservation of mass Recall that, if the cross section of the flow tube varies, the flow speed must change to conserve mass. This means that there is a nonzero net force acting on the fluid that causes the fluid to increase or decrease speed depending on whether the fluid is flowing through a portion of the tube with a smaller or larger cross section. ANSWER: Correct Part C Now assume that point 2 is at height with respect to point 1, as shown in the figure. The ends of the flow tube have the same areas as the ends of the horizontal flow tube shown in Part A. Since the cross section of the flow tube is decreasing, Bernoulli's equation tells us that a fluid element flowing toward point 2 from point 1 moves toward a region of lower pressure. In this case, what is the pressure drop The pressure at point 2 is lower than the pressure at point 1. equal to the pressure at point 1. higher than the pressure at point 1. A2 < A1 v2 > v1 p2 < p1 A v decrease in speed increase in speed remain in equilibrium h Typesetting math: 100% experienced by the fluid element? Hint 1. How to approach the problem Apply Bernoulli's equation to point 1 and to point 2, as you did in Part A. Note that this time you must take into account the difference in elevation between points 1 and 2. Do you need to add this additional term to the other term representing the pressure drop between the two ends of the flow tube or do you subtract it? ANSWER: Correct Part D From a physical point of view, how do you explain the fact that the pressure drop at the ends of the elevated flow tube from Part C is larger than the pressure drop occurring in the similar but purely horizontal flow from Part A? The pressure drop is smaller than the pressure drop occurring in a purely horizontal flow. equal to the pressure drop occurring in a purely horizontal flow. larger than the pressure drop occurring in a purely horizontal flow. Typesetting math: 100% Hint 1. Physical meaning of the pressure drop in a tube As explained in the introduction, the difference in pressure between the ends of a flow tube represents the total work done on a unit volume of fluid by the pressure forces of the surrounding fluid to move that volume of fluid from one end to the other end of the flow tube. ANSWER: Correct In the case of purely horizontal flow, the difference in pressure between the two ends of the flow tube had to balance only the increase in kinetic energy resulting from the acceleration of the fluid. In an elevated flow tube, the difference in pressure must also balance the increase in potential energy of the fluid; therefore a higher pressure is needed for the flow to occur. Venturi Meter with Two Tubes A pair of vertical, open-ended glass tubes inserted into a horizontal pipe are often used together to measure flow velocity in the pipe, a configuration called a Venturi meter. Consider such an arrangement with a horizontal pipe carrying fluid of density . The fluid rises to heights and in the two open-ended tubes (see figure). The cross-sectional area of the pipe is at the position of tube 1, and at the position of tube 2. p1 − p2 A greater amount of work is needed to balance the increase in potential energy from the elevation change. decrease in potential energy from the elevation change. larger increase in kinetic energy. larger decrease in kinetic energy. h1 h2 A1 A2 Typesetting math: 100% Part A Find , the gauge pressure at the bottom of tube 1. (Gauge pressure is the pressure in excess of outside atmospheric pressure.) Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. Hint 1. How to approach the problem Use Bernoulli's law to compute the difference in pressure between the top and bottom of tube 1. The pressure at the top of the tube is defined to be atmospheric pressure. Note: Inside the tube, since the fluid is not flowing, the terms involving velocity in Bernoulli's equation can be ignored. Thus, Bernoulli's equation reduces to the formula for pressure as a function of depth in a fluid of uniform density. Hint 2. Simplified Bernoulli's equation For a fluid of uniform density that is not flowing, the pressure at a depth below the surface is given by , where is the pressure at the surface and is the magnitude of the acceleration due to gravity. ANSWER: Correct The fluid is pushed up tube 1 by the pressure of the fluid at the base of the tube, and not by its kinetic energy, since there is no streamline around the sharp edge of the tube. Thus energy is not conserved (there is turbulence at the edge of the tube) at the entrance of the tube. Since Bernoulli's law is essentially a statement of energy conservation, it must be applied separately to the fluid in the tube and the fluid flowing in the main pipe. However, the pressure in the fluid is the same just inside and just outside the tube. Part B Find , the speed of the fluid in the left end of the main pipe. Express your answer in terms of , , , and either and or , which is equal to . p1 g p h p = p0 + gh p0 g p1 = gh1 v1 h1 h2 g A1 A2 A1 A2 Typesetting math: 100% Hint 1. How to approach the problem Energy is conserved along the streamlines in the main flow. This means that Bernoulli's law can be applied to obtain a relationship between the fluid pressure and velocity at the bottom of tube 1, and the fluid pressure and velocity at the bottom of tube 2. Hint 2. Find in terms of What is , the pressure at the bottom of tube 2? Express your answer in terms of , , and any other given quantities. Hint 1. Recall Part A Obtain the solution for this part in the same way that you found an expression for in terms of in Part A of this problem. ANSWER: Hint 3. Find in terms of given quantities Find , the fluid pressure at the bottom of tube 2. Express your answer in terms of , , , , and . Hint 1. Find the pressure at the bottom of tube 2 Find , the fluid pressure at the bottom of tube 2. Express your answer in terms of , , and . ANSWER: p2 h2 p2 h2 g p1 h1 p2 = gh2 p2 p2 p1 v1 A1 A2 p2 p1 v1 v2 p2 = p1 + ( − ) 1 2 v1 2 v2 2 Typesetting math: 100% Hint 2. Find in terms of The fluid is incompressible, so you can use the continuity equation to relate the fluid velocities and in terms of the geometry of the pipe. Find , the fluid velocity at the bottom of tube 2, in terms of . Your answer may include and , the cross-sectional areas of the pipe. ANSWER: ANSWER: ANSWER: Correct Note that this result depends on the difference between the heights of the fluid in the tubes, a quantity that is more easily measured than the heights themselves. Problem 15.39 The container shown in the figure is filled with oil. It is open to the atmosphere on the left. v2 v1 v1 v2 v2 v1 A1 A2 v2 = A1 A2 v1 p2 = p1 + ( )(1 − ) 1 2 v1 2 ( ) A1 A2 2 v1 = 2g h1−h2 ( ) −1 A1 A2 2 −−−−−−−−−−−−−− Typesetting math: 100% Part A What is the pressure at point A? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B What is the pressure difference between points A and B? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct PA = 106 kPa PB − PA = 4.4 kPa Typesetting math: 100% Part C What is the pressure difference between points A and C? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 15.48 You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads 32.4 . If you then lower the statue into a tub of water, so that it is completely submerged, the scale reads 17 . Part A What is the density? Express your answer with the appropriate units. ANSWER: Correct Problem 15.60 Water flows from the pipe shown in the figure with a speed of 2.0 . PC − PA = 4.4 kPa N N statue = 2100 kg m3 m/s Typesetting math: 100% Part A What is the water pressure as it exits into the air? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the height of the standing column of water? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again P = 1.0×105 Pa h h = Typesetting math: 100% Score Summary: Your score on this assignment is 83.9%. You received 78.84 out of a possible total of 94 points. Typesetting math: 100%

info@checkyourstudy.com

## Chapter 07 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 7 Reading Quiz Question 17 Part A A lake is currently at high pool, with the same amount of water flowing into the lake as is flowing over the spillway. Which of the following temporary changes would increase the resident time of water in this lake? ANSWER: Chapter 7 Reading Quiz Question 16 Part A A large reservoir behind a dam is rapidly rising, as rain and melting snow add more water than is being released out of the dam’s spillway. In this situation, _____. ANSWER: Chapter 7 Reading Quiz Question 1 Part A Which one of the following statements is correct? ANSWER: Double the rate of water flow into the lake and double the rate of water flow out of the lake, while keeping the lake at the same level. Keep the inflow into the lake the same, but release twice as much water from the lake, resulting in a lowering of the lake level. Decrease the inflow into the lake by half, and decrease the outflow of the lake by half. None of the choices would increase the resident time in the lake. the net flux is positive and the capital of water within the reservoir is decreasing the net flux is positive and the capital of water within the reservoir is increasing the net flux is negative and the capital of water within the reservoir is increasing the net flux is negative and the capital of water within the reservoir is decreasing Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 18 Part A A raging river cascades down a granite mountain and eventually reaches the ocean. At the mouth of the river is a beautiful sandy beach composed of fine grains of granite particles from the river. The entire process of producing this sand is a result of _____. ANSWER: Chapter 7 Reading Quiz Question 4 Part A The physical and chemical properties of soils are primarily determined by _____. ANSWER: Chapter 7 Reading Quiz Question 19 Part A Several inches of rain fall over a field of tall corn, soaking into the soil and draining into ditches. Within an hour, there is no standing water and the humidity over the field rises quickly. At a nearby shopping mall, the rainwater fell onto blacktop and drained to sewer pipes, which carried the water directly into a stream. Which of the following occurred in The cycling time of an element or molecule in an ecosystem is equal to the sum of all the flux times. The cycling time is how long it takes an element or molecule to pass through a biogeochemical cycle. The cycling time of water moving through an ecosystem is typically shorter than the resident time in any pool in this system. The amount of time that water spends in an ocean is the cycling time. mineral evaporation erosion, weathering, transport, and then deposition erosion, dissolution, and precipitation organisms consuming and eroding granite the properties of rock from which the soils develop the amount of precipitation that the soil experiences the range of temperatures that the soil experiences the types of animals that live and move through the soils Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 8 5/21/2014 8:01 PM the cornfield but not in the parking lot? ANSWER: Chapter 7 Reading Quiz Question 6 Part A Most of the water on Earth is found in _____. ANSWER: Chapter 7 Reading Quiz Question 5 Part A Which one of the following primarily results from the effects of solar energy? ANSWER: Chapter 7 Reading Quiz Question 20 Part A A rural Minnesota farmer grows a variety of vegetables to feed her family. In addition, she cuts down some of her dead trees for firewood to heat her home in the winter. This farmer is adding to the flux of the carbon cycle in her region by _____. precipitation evaporation runoff transpiration the polar ice caps lakes and streams aquifers the oceans evaporation of water from a lake the formation of ice on the top of a pond movement of ocean tides the movement of water over a waterfall Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 8 5/21/2014 8:01 PM ANSWER: Chapter 7 Reading Quiz Question 8 Part A In a terrestrial ecosystem, most carbon is stored in the biomass of _____. ANSWER: Chapter 7 Reading Quiz Question 7 Part A In which of the following countries would we expect that the terrestrial ecosystems have the highest net primary production and biomass? ANSWER: Chapter 7 Reading Quiz Question 22 Part A Some farmers in the Midwest of the United States rotate their crops from year to year, switching from soybeans to corn on the same fields. What is one of the advantages of doing this? encouraging photosynthesis as she raises crops burning carbon-based fuels by consuming vegetables grown on her farm All of the choices are correct. the animals living there air the top layers of soil containing dead organisms living plants China Australia Brazil United States Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 8 5/21/2014 8:01 PM ANSWER: Chapter 7 Reading Quiz Question 10 Part A Most nitrogen enters the biosphere through the process of _____ ANSWER: Chapter 7 Reading Quiz Question 9 Part A Where do we expect to find the least amount of nitrogen? ANSWER: Chapter 7 Reading Quiz Question 12 Part A Along the west coast of the United States, upwellings bring deep ocean waters to the surface, carrying with them _____, which greatly increases NPP. ANSWER: The corn crop benefits from reactive nitrogen added to the soil by the soybean crop. Both crops require the same fertilizing supplies, so farmers save by buying fertilizer in bulk. Soybeans add large amounts of carbon dioxide to the soil, which helps the corn crop. Corn adds large amounts of phosphorus to the soil, which helps the soybean crop. nitrogen fixation in which bacteria convert N2 to NH3 cellular respiration, in which animals convert N2 to NH4 fermentation in which bacteria convert N2 to HNO3 photosynthesis, in which plants convert N2 to NO2 in Earth’s crust in plants in animals in the atmosphere Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 11 Part A Which one of the following statements about the carbon, phosphorus, and nitrogen cycles is true? ANSWER: Chapter 7 Reading Quiz Question 24 Part A A large coal-burning power plant is about 50 miles upwind from a lake that used to be popular for fishing. But now, just five years after the plant was constructed, the fish populations are decreasing dramatically. Which one of the following impacts of this coal-burning power plant is most likely hurting the fish populations in this downwind lake? ANSWER: Chapter 7 Reading Quiz Question 14 Part A Which one of the following statements about sulfur is correct? ANSWER: oxygen phosphate carbon sulfur Phosphorus is virtually absent in the atmosphere. The major source of carbon used by plants is the soil. Bacteria drive the phosphorus cycle. The major source of nitrogen used by plants is the air. insufficient sunlight reaching the lake low oxygen levels from burning fossil fuels eutrophication of the lake acidification of the lake Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 8 5/21/2014 8:01 PM Chapter 7 Reading Quiz Question 13 Part A Nitrogen and sulfur are important to all organisms because they are important constituents of _____. ANSWER: Chapter 7 Reading Quiz Question 25 Part A In Iowa, a small, deep lake in the summer becomes stratified with warmer, less-dense water at the surface and colder, denser water near the bottom. As fall air temperatures decrease, the surface water cools and then drops toward the bottom, mixing the lake levels together. As a result of this mixing, _____. ANSWER: Chapter 7 Reading Quiz Question 15 Part A A fire spreads across hundreds of acres of prairie, burning most of the plant parts above the ground. Compared to before the fire, right after this fire the pool of nutrients in the prairie plants _____. The main pool of sulfur is in the atmosphere where the flux is high and the residence time is long. The main pool of sulfur is in rocks. The flux of sulfur through the atmosphere is high and the residence is short. The main pool of sulfur is in the atmosphere where the flux is low and the residence time is long. The main pool of sulfur is in rocks. The flux of sulfur through the atmosphere is low and the residence is short. nucleic acids glucose phosphates some amino acids nitrogen and phosphorus are added to the lake nitrogen and phosphorus decrease near the surface of the lake nitrogen and phosphorus increase near the surface of the lake None of the choices is correct. Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 8 5/21/2014 8:01 PM ANSWER: Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 21 points. and the soil decreases increases and the pool of nutrients in the soil decreases and the soil increases decreases and the pool of nutrients in the soil increases Chapter 07 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 8 5/21/2014 8:01 PM

info@checkyourstudy.com

## An electron in a vacuum is first accelerated by a voltage of 61500 V and then enters a region in which there is a uniform magnetic field of 0.627 T at right angles to the direction of the electron’s motion. The mass of the electron is 9.11 × 10−31 kg and its charge is 1.60218 × 10−19 C. What is the magnitude of the force on the electron due to the magnetic field?

- 1
- 2