GATE 2024 CH – Question 60

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

A Venturi meter with a throat diameter $d = 2$ cm measures the flow rate in a pipe of diameter $D = 6$ cm, as shown in the figure. A U-tube manometer is connected to measure the pressure drop. Assume the discharge coefficient is independent of the Reynolds number and geometric ratios. If the volumetric flow rate through the pipe is doubled $Q_2 = 2Q_1$, the corresponding ratio of the manometer readings $\Delta h_2/\Delta h_1$, rounded off to the nearest integer, is _______

a Venturi meter in a horizontal pipe of diameter D = 6 cm, with a throat of diameter d = 2 cm, and a U-tube manometer between the pipe and the throat that reads $\Delta h$.

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Correct answer: 4

Explanation

For a Venturi meter, $Q = C_dA_t\sqrt{\frac{2\Delta p}{\rho(1 - \beta^4)}}$ and the pressure difference is proportional to the manometer reading, so $Q \propto \sqrt{\Delta h}$. Doubling $Q$ gives $\frac{\Delta h_2}{\Delta h_1} = 2^2 = 4$.