A pump is to be designed by scaling an existing pump. The existing pump operates

Question

A pump is to be designed by scaling an existing pump. The existing pump operates at 1160 rpm, and pumps 400 gal/min of water, with a pressure rise equal to 193,053 pa. The impellar diameter is .301 m. The pump efficiency is 80 %. A geometrically similar pump is to be designed to pump 3.028 m3/min of water at a rotational speed of 1075 rpm. Calculate the required impellar diameter for the new pump, the expected pressure rise, and the required pumping power (hp) at design point. Assume that dynamic similarity is maintained, and Reynolds number effects can be neglected. Assume that the fluid is at 20 deg C, 101325 pa (rho = 1000 kg/m3 , mu = 1.002(10-3) Ns/m2 , nu = 1.004(10-6) m2/s) . The following conversion factors may be useful: 40.1 psia, 23.4 hp

Explanation / Answer

For similarity, the model pump must operate at the same flow coefficient so that

            Þ Qm = Qp

            Qm = (1)(1/5)3(4.1) = 0.0328 m3

We also have ha,m =ha,p

            ha,m = (1)(1)2(1/5)2(200) = 8.0 m

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