Question

In the following system, flow proceeds left to right from Point 1 to Point 2. Three different sized pipes are connected together. Flow enters at Point 1 at 0.7 cfs. Indicate the flow rate (cfs) and velocity (fps) in each section of pipe.

8 in dia 6 in dia 4 in dia 2. 750 ft 1200 ft

Answer 1

Function is dicontinuous at x = 1 and x = 2 because at x = 1 hole present and at x = 2 (g(2) = does not exist) hole present flow rates at each sector will be same and equal to 0.7 cfs Equation of continuous Q_in = Q_out section (1 - 1) Q_in = Q_out = 0.7 cfs Q = v_1 times A_2 = v_1 times pi/4 times (4/12)^2 = 0.7 v_1 = 9 times 0.7 times 4/pi = 8.02 ft/sec section 2-2 Q_in = Q_out = 0.7 cfs Q = v_2 times A_2 = v_2 times pi/4 times (8/12)^2 = 0.7 v_2 = 2.0ft/sec section 3-3 Q_in = Q_out = 0.7 cfs Q = A_3 times v_3 pi/4 times (6/12)^2 times v_3 = 0.7 v_3 = 3.57 ft/sec
Assumption is taken that fluid is incompressible .