hw5 - a control volume whose surface is the interior...

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The University of Michigan Department of Mechanical Engineering ME 320 - Section 1 Homework #5 - Due February 16, 2011 Problem 1: Problems 3.72 , 3.108 and 3.111 of the text. Problem 2: Consider the reservoir system shown in the ±gure. The reservoir is initially ±lled to a height H with water of density ρ . At time t = 0, a valve is opened and the water begins to drain through the disks at the bottom. Neglecting viscous e²ects and assuming a large reservoir (so that the velocities in the reservoir are negligible), obtain a di²erential equation governing the ³ow rate Q ( t ) for t 0 in this system. Problem 3: A sanding operation injects 10 5 particles/sec into the air in a room as shown in the ±gure. The amount of dust in the room is kept at a constant level by a ventilating fan that draws clean air into the room at section (1) and expels dusty air at section (2). Consider
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Unformatted text preview: a control volume whose surface is the interior surface of the room (excluding the sander) and a system consisting of the material within the control volume at time t = 0. (a) If N is the number of particles, discuss the physical meaning and evaluate the terms DN sys /Dt and N cv /t . (b) Use the Reynolds transport theorem to determine the concentration of particles (particles/ m 3 ) in the exhaust air for steady state conditions. (c) Consider this problem for the case that the ventilating fan fails to work so that V 1 = V 2 = 0. Evaluate and discuss the meaning of the terms DN sys /Dt and N cv /t for this case. Problem 4: Problems 5.13 , 5.16 and 5.25 of the text. Problem 5: Problems 5.26 , 5.30 and 5.31 of the text....
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