Consider a two meter long horizontal pipe with a 5cm^2 cross sectional area on t
ID: 2077627 • Letter: C
Question
Consider a two meter long horizontal pipe with a 5cm^2 cross sectional area on the left end at x = 0 and a 10 cm^2 cross sectional area on the right end at x = 2. Water flows leftward out of the pipe at x = 0 with flow velocity 0.3 m/sec at every point within the pipe intake area. At x = 2, the flow rate is leftward going 0.1 m/sec. Assume the water is a conserved quantity in the pipe. Assume the system to be in equilibrium and compute net volumetric flow of the source/sink, if the system to be in equilibrium. Specify if the flow is a source or a sink. Assume net volumetric rate of change for the system is 0.0001 m^3/sec. Compute the volumetric flow rate of the source/sink.Explanation / Answer
flow rate at the rigth end = v*A = 0.1 m/s *10cm2 = 100 cc/s
flow rate at the left end = 0.3 m/s * 5cm2 = 150 cc/s
both at left and right the water flow is towards left
water outflow at left is more than the inflow at the right end , hence the flow is a source.
net volumetric flow = 150 cc/s - 100 cc/s = 50 cc/s
2. input volumetric flow = 0.1* 10e-4 = 1.0e03 cu.m/s
net volumetric rate of change of the system = 0.0001 cu.m/s = 1.0e+3 cu.m/s
net volumetric flow rate = 1.0e+3 + 1.0e+3 = 2.0e+3 cu.m /s