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Unformatted text preview: ES330 Assignment 4 Solutions Chapter 5 Due Date: Thursday September 23, 2010 I Problem 1 The flow between two parallel plates, where one plate is fixed and the other moves with a speed U is characterized by a linear velocity profile u = Uz/h as shown. Develop an expression for the mass flow rate per unit width. Solution To find the mass flow rate, we use the following equation: m = Z CV ( ~ V R n ) dA (1) Lets assume the width of the channel (into the page in the figure) is W . We can also assume that , h , and U are constants and can be taken outside the integral. Therefore, substituting u into the above equation for ~ V R n we get: m = Z W Z h U h z dz dx = U h Z W Z h z dz dx (2) Solving the integral, we get: m = U h Z W " z 2 2 # h dx = U 2 h h 2 [ x ] W = 1 2 UhW (3) However, since the problem asks for mass flow rate per unit width: m/W = 1 2 Uh 1 II Problem 2 Water is being pumped into a pool whose radius is 3 m while water is discharged through a 5- cm- diameter orifice in the pool at constant average velocity of 5 m/s . If the water level in the pool rises at a rate of 5 cm/min , determine the rate at which water is supplied to the pool, in m 3 /s . Solution In order to find the rate at which water is being poured into the pool, we must use the following equation: m in- m out = dm CV dt (4) The mass flow rate for water entering or exiting can be expressed as: m = V avg A (5) Also, The rate of accumulation of mass in the pool can be expressed as: dm CV dt = d dt = A h (6) In the above equation, is the volume of the pool and...
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This note was uploaded on 09/30/2010 for the course FLUIDS ES 340 taught by Professor Bohl during the Fall '10 term at Clarkson University .
- Fall '10