GATE 2022 CH – Question 52
A venturi meter (venturi coefficient, $C_v = 0.98$) is connected to a pipe of inner diameter 50 mm. Water (density 1000 kg m$^{-3}$) is flowing through the pipe. The pressure-drop measured across the venturi meter is 50 kPa. If the venturi throat diameter is 20 mm, the estimated flow rate of water is _______ $10^{-3}$ m$^3$ s$^{-1}$ (rounded off to two decimal places).
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Correct answer: 3.10 to 3.14
Explanation
The diameter ratio is $\beta = \frac{20}{50} = 0.4$, so $\beta^4 = 0.0256$. The throat area is $\frac{\pi}{4} \times 0.02^2 = 3.1416 \times 10^{-4}$ m². $Q = C_vA_t\sqrt{\frac{2\Delta P}{\rho(1 - \beta^4)}} = 0.98 \times 3.1416 \times 10^{-4} \times \sqrt{\frac{100000}{1000 \times 0.9744}} = 0.98 \times 3.1416 \times 10^{-4} \times 10.13 = 3.12 \times 10^{-3}$ m³/s.