A 2 in nozzle is bolted to the flange of a 6 in pipe and dis

A 2 in. nozzle is bolted to the flange of a 6 in. pipe and discharges water into the atmosphere with a velocity of 90 ft/s. The pressure in the 6 in. pipe is 50 p.s.i. Determine the sum of the tensile forces in the bolts. Neglect the initial tensile forces that are in the bolts when the pipe is empty.

Solution

Nozzle opening area A = 3.14/4* 2² = 3.14 in²

Mass flow rate m = rho*A*V

= 1.94*(3.14 / 12²)*90.....where rho = water density = 1.94 slug/ft3

= 3.80725 slug/s

By mass continuity, A1*V1 = A2*V2

(pi/4 * 6²) * V1 = (pi/4 * 2²) * 90

V1 = 10 ft/s

Net force = net rate of momentum

Force on nozzle = (P1*A1 - P2*A2) + m*(V2 - V1)

F = 50*(pi/4 * 6²) - 0 + 3.80725*(90 - 10)

F = 1717.58 lbs