Project ForgeFluid Mechanics
Flow Through Pipes
GATE 2018
Hard
A venturi meter measures water flow in a 178mm ID pipe with 102mm throat. Differential pressure=154.3 kN/m². Cd=0.98, ρ=1000 kg/m³. The volumetric flow rate (m³/s) is
0.149 m^3/s(± 0.005 accepted)
Explanation
β=102/178=0.573, β⁴=0.1078, 1−β⁴=0.8922. A2=π/4×0.102²=0.008171m². Q=Cd·A2·√(2ΔP/(ρ(1−β⁴)))=0.98×0.008171×√(308600/892.2)=0.98×0.008171×18.6=0.149 m³/s.
Source: GATE CH 2018 (2018)
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