hw4 - S09 - Chemical Engineering 150A Spring Semester, 2009...

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Chemical Engineering 150A Spring Semester, 2009 Homework 4: Macroscopic Balances in Incompressible Fluids Problem 1 (a) Consider a rectangular duct as shown in the figure below. If the velocity profile (in terms of the coordinates as shown) is given by V = V M 1 ! x 2 B 2 " # $ $ % 1 ! y 2 C 2 " # $ $ % evaluate the surface average velocity V for this flow. (b) Experimental data for turbulent flow in a pipe of circular cross section with radius R suggests that the velocity varies with radial position approximately as follows: V ( r ) = 1.22 V 1 ! r R " # $ % 1 /7 Use this result to calculate α and β for turbulent flow. Problem 2 For steady flow of water through the device in the figure below, we are given inlet conditions D 1 =10 cm, Q 1 = 200 m 3 /hr, and p 1 = 170 kPa. Outlet conditions are D 2 = 8 cm, Q 2 = 100 m 3 /hr, p 2 = 205 kPa, D 3 = 5 cm, and p 3 = 240 kPa. Heat transfer, temperature, and gravity effects are negligible. Compute the rate of shaft work done in this device. Is it done on or by the fluid?
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This note was uploaded on 02/05/2010 for the course CHEM 150A taught by Professor Muller during the Spring '10 term at University of California, Berkeley.

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hw4 - S09 - Chemical Engineering 150A Spring Semester, 2009...

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