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Problem 6.16

# Problem 6.16 - Problem 6.16[Difficulty 3 Given Flow in a...

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Problem 6.16 [Difficulty: 3] Given: Flow in a pipe with variable area Find: Expression for pressure gradient and pressure; Plot them; exit pressure Solution: Assumptions: 1) Incompressible flow 2) Flow profile remains unchanged so centerline velocity can represent average velocity Basic equations QV A = Given data ρ 1.75 slug ft 3 = p i 35 psi = A i 15 in 2 = A e 2.5 in 2 = L1 0 f t = u i 5 ft s = For this 1D flow Qu i A i = uA = AA i A i A e () L x = so ux () u i A i A = u i A i A i A i A e L x = a x u x u v y u + = u i A i A i A i A e L x x u i A i A i A i A e L x = A i 2 L 2 u i 2 A e A i A i L A e x + A i x 3 = For the pressure x p ρ a x ρ g x = ρ A i 2 L 2 u i 2 A e A i A i L A e x + A i x 3 = and dp x p dx = pp i 0 x x x p d = 0 x x ρ A i 2 L 2 u i 2 A e A i A i L A e x + A i x 3 d = This is a tricky integral, so instead consider the following: x p ρ a x = ρ u x u = 1 2

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Problem 6.16 - Problem 6.16[Difficulty 3 Given Flow in a...

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