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HW_29_Soln

HW_29_Soln - ME 309 Fall 2008 Section 2 Homework 29 Due...

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ME 309 Fall 2008 Section 2 Homework # 29 Due Friday 7 November 2008 Problem 29-1 . A centrifugal pump is used to pump water from a reservoir. The centerline of the pump is 2.2 m below the water level in the reservoir. The pipe is PVC with and ID of 24 mm and negligible average roughness. The pipe length from the submerged inlet to the pump inlet is 2.8 m . There are two minor losses in the piping system from the pipe inlet to the pump inlet: a sharp-edged inlet with K = 0.6 and a flanged elbow with K = 0.3. The pump’s NPSHR is provided by the manufacturer as NPSHR = 2.2 +0.0013 Q 2 with Q in m 3/ s and NPSHR in m . Estimate the maximum volume flow rate that may be pumped without cavitation when the reservoir is at a temperature of 300 K .. Given : Pump 2.2 m below reservoir Smooth PVC Pipe D = 0.24 m L = 2.8 m Inlet K = 0.6, elbow K = 0.3 NPSHR = 2.2 +0.0013 Q 2 Find : Max flow rate without cavitation Assumptions : Steady, incompressible Properties : rho 997, mu 8.91e-4, p v = 3169 Pa p atm = 101325 Pa Solution : Mechanical energy equation: ( ) [ ] tot gh z z g u u p p W Q ρ ρ + - + - + - = - 1 2 2 1 2 2 1 2 2 1 & & No heat and no work up to pump. u 1 = 0, p 1 = 101325, z 2 – z 1 = -2 m Stagnation pressure at pump inlet: [ ] tot gh z z g p u p ρ ρ - - - = + 1 2 1 2 2 2 2 1 [ ] tot v v h z z g p p g p g u g p NPSHA - - - - = - + = 1 2 1 2 2 2 2 2 ρ ρ ρ Know everything but h_tot—evaluate: + = s K D L f g u h D tot ' 2 2 2 Minor losses: 9 . 0 3 . 0 6 . 0 = + = K

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Use Colebrook equation for friction factor: D 2 10 0.9 0.25 , 5.74 log 3.7 D f D Re ε = + Smooth pipe—use with eps = 0 Need Reynolds number to compute friction factor Solve for a sequence of flow rates and compare with NPSHR equation: Set u 2 = 2 and increment by two: See Table below: Table of NPSHR vs NPSHA Problem 29-1 NSPH L 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 ID 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 K_elb 0.3 0.3 0.3 0.3
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HW_29_Soln - ME 309 Fall 2008 Section 2 Homework 29 Due...

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