Answer to Question #113379 in Mechanical Engineering for Jayapal Reddy

Question

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.

Answer 1

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