HW4_solution - Problem 8.86 Given Flow through sudden...

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Problem 8.86 [2] Given: Flow through sudden expansion Find: Inlet speed; Volume flow rate Solution: Basic equations p 1 ρ α V 1 2 2 + g z 1 + p 2 ρ α V 2 2 2 + g z 2 + h lm = h lm K V 1 2 2 = Q V A = Δ p ρ H2O g Δ h = Assumptions: 1) Steady flow 2) Incompressible flow 3) α at 1 and 2 is approximately 1 4) Horizontal Hence the energy equation becomes p 1 ρ V 1 2 2 + p 2 ρ V 2 2 2 + K V 1 2 2 = From continuity V 2 V 1 A 1 A 2 = V 1 AR = Hence p 1 ρ V 1 2 2 + p 2 ρ V 1 2 AR 2 2 + K V 1 2 2 = Solving for V 1 V 1 2 p 2 p 1 ( ) ρ 1 AR 2 K ( ) = AR D 1 D 2 2 = 75 225 2 = 0.111 = so from Fig. 8.14 K 0.8 = Also p 2 p 1 ρ H2O g Δ h = 1000 kg m 3 9.81 × m s 2 5 1000 × m N s 2 kg m × = 49.1 Pa = Hence V 1 2 49.1 × N m 2
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