GATE 2022 CH – Question 51

Fluid Mechanics and Mechanical Operations · Flow through pipes, friction factors, flow meters and pumps · 2 marks · Numerical answer

Two reservoirs located at the same altitude are connected by a straight horizontal pipe of length 120 m and inner diameter 0.5 m, as shown in the figure. A pump transfers the liquid of density 800 kg m$^{-3}$ at a flow rate of 1 m$^3$ s$^{-1}$ from Reservoir-1 to Reservoir-2. The liquid levels in Reservoir-1 and Reservoir-2 are 2 m and 10 m, respectively. Assume that the reservoirs' cross-section areas are large enough to neglect the liquid velocity at the top of the reservoirs. All minor losses can be ignored. The acceleration due to gravity is 9.8 m s$^{-2}$. If the friction factor for the pipe-flow is 0.01, the required power of the pump is _________ kW (rounded off to one decimal place).

two reservoirs side by side with a horizontal pipe of length 120 m at the bottom and a pump in it. The liquid level in Reservoir-1 is 2 m and in Reservoir-2 is 10 m.

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Correct answer: 87.16 to 88.04

Explanation

The velocity in the pipe is $v = \frac{1}{\frac{\pi}{4} \times 0.5^2} = 5.093$ m/s. The friction head is $h_f = f\frac{L}{D}\frac{v^2}{2g} = 0.01 \times \frac{120}{0.5} \times \frac{25.94}{19.6} = 3.176$ m. The energy balance between the two free surfaces gives the pump head $H = (10 - 2) + 3.176 = 11.176$ m. The power is $\rho gQH = 800 \times 9.8 \times 1 \times 11.176 = 87.6$ kW.