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Exam3_solution_SP11_Annotated

Exam3_solution_SP11_Annotated - (a 2 pts Re D =...

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<Problem 1> (a) Re D = 4 ˙ m π D μ = 4 0.5 kg / s ( ) π 0.005 m ( ) 8.6 × 10 4 N s / m 2 ( ) = 148,051 > 2,300 = Re D , critcal Turbulent Flow Re D > Re D , critcal = 2,300 ( ) (b) ˙ E in ˙ E out + ˙ E gen = ˙ E store ˙ E gen = ˙ E store = 0 ˙ E in = ˙ m c p T m + q " P dx ; P = π D ˙ E out = ˙ m c p T m + dT m ( ) ˙ E in ˙ E out = ˙ m c p T m + q " P dx ˙ m c p T m + dT m ( ) = 0 !" $ % $ % & !$ % !' ( ') ! * ! !"
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˙ m c p dT m = q " P dx = q " max sin π x 2 L π D dx dT m 0 x = q " max π D ˙ m c p sin π x 2 L dx 0 x T m x ( ) T in = q " max π D ˙ m c p ⋅ − 2 L π cos π x 2 L 0 x = 2 q " max L D ˙ m c p 1 cos π x 2 L T m x ( ) = T in + 2 q " max L D ˙ m c p 1 cos π x 2 L (c) q "( x ) = h T s x ( ) T m x ( ) [ ] T s x ( ) = T m x ( ) + q "( x ) h T s x ( ) = T in + 2 q " max L D ˙ m c p 1 cos π x 2 L
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