GATE 2023 CH – Question 51
A pump draws water (density = 1000 kg m$^{-3}$) at a steady rate of 10 kg s$^{-1}$. The pressures at the suction and discharge sides of the pump are −20 kPa (gauge) and 350 kPa (gauge), respectively. The pipe diameters at the suction and discharge side are 70 mm and 50 mm, respectively. The suction and discharge lines are at the same elevation, and the pump operates at an efficiency of 80%. Neglecting frictional losses in the system, the power (in kW) required to drive the pump is ______ (rounded off to two decimal places).
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Correct answer: 4.72 to 4.76
Explanation
The volume flow is $Q = 0.01$ m³/s. The velocities are $v_s = \frac{0.01}{\frac{\pi}{4} \times 0.07^2} = 2.598$ m/s and $v_d = \frac{0.01}{\frac{\pi}{4} \times 0.05^2} = 5.093$ m/s. The work per kg given to the fluid is $\frac{\Delta P}{\rho} + \frac{v_d^2 - v_s^2}{2} = \frac{370000}{1000} + \frac{25.94 - 6.75}{2} = 370 + 9.60 = 379.6$ J/kg. For 10 kg/s this is 3796 W, and the shaft power at 80% efficiency is $\frac{3796}{0.8} = 4745$ W $= 4.74$ kW.