GATE 2024 PI – Question 48
A pump draws pond water. A 5.05 cm hose connects at its outlet 1.02 m below surface level. Just after the pump, gauge pressure is 50 kPa and mass flow is 8 kg/s. Water exits a nozzle at ground level. Assume steady laminar flow and negligible losses, density 1000 kg/m³ and g = 9.81 m/s². If exit static pressure just reaches atmospheric, find exit diameter (two decimal cm).
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Correct answer: 3.20 to 3.25
Explanation
Volume flow is Q = 0.008 m³/s. Hose speed is $v_1=4Q/(\pi D_1^2)\approx3.994$ m/s. Bernoulli between pump outlet and exit gives $v_2^2=v_1^2+2p_1/\rho-2g(1.02)\approx95.94$, so v₂ ≈ 9.795 m/s. From $D_2=\sqrt{4Q/(\pi v_2)}$, diameter is **about 3.23 cm**. The calculation uses the stated negligible-loss model; the laminar characterization is not needed for this Bernoulli result.