Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2015
Medium
Water (ρ=1000 kg/m³) flows through a venturimeter with inlet diameter 80 mm and throat diameter 40 mm. The inlet and throat gauge pressures are measured to be 400 kPa and 130 kPa respectively. Assuming the venturimeter to be horizontal and neglecting friction, the inlet velocity (in m/s) is __________.
6 m/s(± 0.1 accepted)
Explanation
Area ratio A1/A2 = (80/40)² = 4, so by continuity V2=4V1. Bernoulli (horizontal): ΔP = P1−P2 = (1/2)ρ(V2²−V1²) = (1/2)ρ(16V1²−V1²) = 7.5ρV1². 270,000 = 7.5×1000×V1² ⟹ V1² = 36 ⟹ V1 = 6 m/s.
Source: GATE ME 2015 (Session 1) (2015)
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