Project ForgeConsider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from 20 cm to 10 cm. The pressure in the 20 cm pipe just upstream of the reducer is 150 kPa. The fluid has a vapour pressure of 50 kPa and a specific weight of 5 kN/m³. Neglecting frictional effects, the maximum discharge (in m³/s) that can pass through the reducer without causing cavitation is
- A0.05
- 0.16
- C0.27
- D0.38
Explanation
Continuity: A1V1=A2V2, with D2=D1/2 giving V2=4V1. Cavitation begins when P2 drops to vapour pressure (50 kPa). Bernoulli (ρ=γ/g=5000/9.81≈509.7 kg/m³): P1+ρV1²/2=P2+ρV2²/2 ⟹ 100000=254.84×(16-1)V1²=3822.6V1² ⟹ V1≈5.11 m/s. Q=A1V1=(π/4)(0.2)²(5.11)≈0.16 m³/s.
Source: GATE ME 2009 (2009)
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