GATE 2019 CE (CE1) – Question 32
A water duct contracts gradually from diameter 30 cm to 15 cm. A differential mercury manometer is arranged as shown and reads 8 cm deflection during flow. Mercury and water specific gravities are 13.6 and 1.0. With g = 9.81 m/s² and frictionless flow, find duct discharge (m³/s), to three decimal places.
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Correct answer: .078 to .085
Explanation
The piezometric head difference is $0.08(13.6-1)=1.008$ m water. Continuity gives $V_2=4V_1$. Frictionless Bernoulli gives $1.008=(16-1)V_1^2/(2\times9.81)$, hence $V_1=1.14825$ m/s. Discharge is $Q=V_1\pi(0.30)^2/4=$ **0.081 m³/s**. Subtract water’s specific gravity in the manometer conversion.