Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2018
Hard
Air flows at the rate of 1.5 m³/s through a horizontal pipe with a gradually reducing cross-section, from a diameter of 400 mm to 200 mm. Take the air density as 1.2 kg/m³ and assume inviscid incompressible flow. The change in pressure (p2−p1) (in kPa) between sections 1 and 2 is
- −1.28
- B2.56
- C−2.13
- D1.28
Explanation
A1=(π/4)(0.4)²≈0.12566 m², A2=(π/4)(0.2)²≈0.031416 m². V1=Q/A1≈11.94 m/s, V2=Q/A2≈47.75 m/s. By Bernoulli (horizontal): p2−p1 = ½ρ(V1²−V2²) = 0.5×1.2×(142.5−2279.6) ≈ 0.6×(−2137.1) ≈ −1282 Pa ≈ −1.28 kPa (pressure drops as the flow accelerates through the contraction).
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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