Answer to Question #113379 in Mechanical Engineering for Jayapal Reddy

Question #113379
A centrifugal water pump operates at 30 m3/hr and at 1440 RPM.The pump operating efficiency is 65% and motor efficiency is 89%.The discharge pressure gauge shows 3.4 kg/cm2.The suction is 3mtr below the pump centreline.If the speed of the pump is reduced by 25%, estimate pump flow, head and motor power.Assume motor and pump efficiency remains same at the reduced speed.
1
Expert's answer
2020-05-03T15:27:15-0400

We know that, The relation between pump efficiency and motor efficiency as

pump efficiency= 65 % and motor efficiency = 89 %, N=1440 rpm, "Q= 30 \\frac{m^3}{hr}"


"\\eta_p=\\frac{(p_2-p_1)Q}{P\\times\\eta_m}"


"0.65= \\frac{ (1000\\times 9.8 \\ 3) \\times 30}{P\\times 3600 \\times 0.89}"


P= 423.5 Pa and as per question , N"_2=" 1440 -"\\frac{25 \\times 1440}{100}=1080 rpm"

we know that


"\\frac{P_1}{P_2}= (\\frac{N_1}{N_2})^3"


P2= "423.5 \\times \\frac{(1080^3)}{1440^3}=178.66"


and head is proportional to speed square


"\\frac {H_2}{H_1}= (\\frac{N_2}{N_1})^2"


"H_2= 1.6875 m"


"\\frac{Q_2}{Q_1}=(\\frac{N_2}{N_1})"


Q_2= "30 \\times \\frac{1080}{1440}= 22.5 \\frac{m^3}{hr}"




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