1) Water at 10°C flows from a large reservoir to a smaller one through a 5- cmdiameter cast iron piping system, as shown in Fig. 8-48. Determine the elevation z1 for a flow rate of 6 L/s. Sharp-edged entrance, KL 0. 5 Standard elbow, flanged, KL-0.3 D-5 cm G ate valve, fully open K-0.2 9m Control volume boundary 80m -Exit, KL = 1.06

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EXPERT ANSWER

Given: Diameter of pipe, D=5 cm=0.05 m

Flowrate of water, Q=6 L/s=0.006 m3/s

Total length of pipe, L=Horizontal length+Vertical length= 80m+9m=89 m

Elevation at point 2, z2 =4 m

Loss coefficient for sharp edged entrance, KL, entrance=0.5

Loss coefficient for standard flanged elbow, KL, elbow =0.3

Loss coefficient for gate valve (fully open), KL, valve =0.2

Loss coefficient for exit, KL, exit =1.06

Assumptions:

  1. Steady state and incompressible flow.
  2. There are no pumps or turbines included in the system. Thus loss due to turbine or pump is neglected.
  3. The elevations remain constant.

Both the points is open to atmosphere, thus the pressure is P1=P2=Patm. The velocity of fluid at point 1 and 2, V1=V2=0.

The energy equation for the control volume system is