Water at 68(deg)F flows through a 180(deg) horizontal bend in a piping system at a steady rate of 6 ft^3/s. What is the force required to hold this bend in place if the inlet pressure is 175 psi and exit pressure is 162 psi?
Work:
Flow is steady, incompressible, and one-dimensional
Q = flow rate = 6 ft^3/s
p1 = pressure at inlet = 175 psi
A1 = area at inlet = 0.75 ft^2
p2 = pressure at exit = 162 psi
A2 = area at exit = 0.60 ft^2
Sum of forces = (V*ro*Q)2 - (V*ro*Q)1
V1 = Q/A1 = 6 ft^3/s/0.75 ft^2 = 8 ft/s
V2 = Q/A2 = 6 ft^3/s/0.60 ft^2 = 10 ft/s
F1 = (8 ft/2)*(1.94 lbf*s^2/ft^4)*(6 ft^3/s)
F1 = 93.12 lbf
F2 = 116.4 lbf
Solution
F2 = 116.4 lbf