GATE 2020 MT – Question 56
A venturimeter has areas 100 mm² at A and 50 mm² at B and air flow $10^{-3}$ m³/s. Find manometer height H in mm, nearest integer. Assume incompressible frictionless flow; air density 1 kg/m³, water density 1000 kg/m³, g = 9.8 m/s².
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Correct answer: 14 to 16
Explanation
Continuity gives $v_A=10^{-3}/10^{-4}=10$ m/s and $v_B=20$ m/s. Bernoulli gives $p_A-p_B=\rho_a(v_B^2-v_A^2)/2=150$ Pa. The air-over-water manometer gives $\Delta p=(\rho_w-\rho_a)gH$, so $H=150/[(1000-1)9.8]=0.01532$ m = 15.32 mm. Rounded H is 15 mm.