Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2020
Hard
Air discharges steadily through a converging nozzle, with inlet velocity V1, pressure p1, and area A1=0.2 m², and outlet at atmospheric pressure, velocity V2=50 m/s, and area A2=0.02 m². Air density is constant at 1.23 kg/m³. Assuming steady, incompressible, inviscid flow, the pressure difference (p1−p_atm) is __________ kPa (round off to 2 decimal places).
1.52 kPa(± 0.03 accepted)
Explanation
Continuity: V1A1=V2A2 → V1=50×0.02/0.2=5 m/s. Bernoulli (same elevation, p2=p_atm): p1−p_atm = ½ρ(V2²−V1²) = 0.5×1.23×(2500−25) = 0.5×1.23×2475 ≈ 1522.1 Pa ≈ 1.52 kPa.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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