Spring 08 HW 7

Spring 08 HW 7 - CEE 3304 Spring 2008 CEE 3304 Spring 2008...

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Unformatted text preview: CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#7 by: Amr A. El-Sayed 1 HW #7 Control Volume Approach, and Continuity Principle Problem 5.12 Given: Air flows in a square duct with velocity profile shown in the figure. Find: (a) Volume flow rate: Q (b) Mean velocity: V (c) Mass flow rate: ˙ m (if density is 1.2 kg/m3) Solution ∫ = A n dA v Q Where: Q Flowrate at section n v The velocity component normal to the control surface, b ay v n + = At y = 0, v n = 10, and at y = 0.5, v n = 0 Î 10 20 + − = y v n ∫ = A n dA v Q ∫ = 5 . 2 bdy v Q n ( ) ( ) ∫ − = 5 . . 1 20 10 2 dy y Q ( ) ∫ − = 5 . 20 10 2 dy y Q CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#7 by: Amr A. El-Sayed 2 y dy v(n) changes in y-direction only if v(n) changes in y & z directions y z dA = b dy y z b ( ) ∫ − = 5 . 20 10 2 dy y Q Î 5 . . 2 2 20 10 2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = y y Q ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × − × = 2 5 . 20 5 . 10 2 2 Q = 5.0 m 3 /s ………. (a) ( ) 2 3 . 1 . 1 . 5 m s m A Q V × = = = 5.0 m/s = × = × = s m m kg Q m 3 3 . 5 20 . 1 ρ & 6.0 kg/s CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#7 by: Amr A. El-Sayed 3 Problem 5.49 Given : A tank with one inflow and two outflows indicated by diagram with problem statement. Find : (a) Is the tank filling or emptying. (b) Rate at which the tank level is changing: dt dh dt V d Q Q out in = − ∑ ∑ dt V d Q Q Q = − − 3 2 1 V A Q × = ( ) ( ) ( ) dt V d V A V A V A = × − × − × 3 3 2 2 1 1 dt V d = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × . 7 12 6 4 1 . 4 12 3 4 1...
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Spring 08 HW 7 - CEE 3304 Spring 2008 CEE 3304 Spring 2008...

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