Consider 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 20cm pipe just upstream of the reducer is 150 kPa. The fluid has a vapour pressure of 50 kPa and a specific weight of 5kN/m³. Neglecting frictional effects, the maximum discharge (in m³/sec) that can pass through the reducer without causing cavitations is
- A. 0.05
- B. 0.16
- C. 0.27
- D. 0.38
Answer: B. 0.16
Explanation: Bernoulli: P1/w + V1^2/2g = P2/w + V2^2/2g. w = 5 kN/m³. P1=150, P2=50 (limit). (150-50)/5 = (V2^2 - V1^2)/2g. 20 = (V2^2 - V1^2)/2g. A1V1 = A2V2. D1=2D2 => A1=4A2 => V2=4V1. 20 = (16V1^2 - V1^2)/2g = 15V1^2/2g. V1^2 = 400/15 * g / 10? No g=9.81? V1 = 5.11 m/s. Q = A1V1 = \pi/4 (0.2)^2 * 5.11 = 0.16 m³/s.