Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2011
Medium
The velocity of air (density = 1.2 kg/m³) through a constant-area duct is measured using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg/m³) in the two columns of the manometer is 10 mm. Taking g=9.8 m/s², the velocity of air in m/s is
- A6.4
- B9.0
- 12.8
- D25.6
Explanation
Manometer pressure difference: Δp=ρwater·g·Δh=1000×9.8×0.010=98 Pa. This equals the dynamic pressure of the air: Δp=½ρair V². V=√(2Δp/ρair)=√(2×98/1.2)=√163.33≈12.78 m/s.
Source: GATE ME 2011 (2011)
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