Question

Consider water flowing through a converging channel as shown and discharging freely to the atmosphere at the exit. What is the gage pressure at the inlet? Assume the flow to be incompressible, and neglect any frictional effects. D, = 150 mm D2 = 75 mm V1 = 1.2 m/s P2 = Patm %3D (A) 10.2 kPa (B) 10.8 kPa (C) 11.3 kPa (D) 12.7 kPa

Answer 1

Since flow is incompressible hence A1 v1= A2 v2

=> v2= (A1/A2) v1

=> v2= (D1/D2)² v1 = 4 X 1.2 = 4.8 m/s

applying bernoulli's theorem between point 1 and 2

p1 + 0.5 X 1000 X v1² = p2 + 0.5 X 1000 X v2² (since flow height is same at both points thus h1=h2 and they cancel out)

p1-p_atm = 500 X (4.8² - 1.2² ) (since it is given p2= p_atm)

gauge pressure = 10800 Pa = 10.8Kpa

Answer. b) 10.8 Kpa