Case 43: Water - Eight Pipe Network with Pressure Regulating Valve (PRV)
Reference: Hydraulics of Pipeline Systems, 2000, CRC Press LLC, Bruce E. Larock, Rowland W. Jeppson, Gary Z. Watters, Page 67, Example figure 4.6
Pipe Flow Expert File: Case_43_Water_Eight_Pipe_Network_With_Pressure_Regulating_Valve(PRV).pfe
Problem Description:
A network of 8 interconnected pipes delivers water from two reservoirs to outlet demands at two pipework junctions.
The network includes a pump.
The pressure at a node where two pipes join is controlled by a pressure regulating valve set to 8.6527 psig. The elevation of the PRV node is 35 ft.
Calculate the flow rate in each individual pipe and the pump head added to the system.
Fluid Data: Water at 20° C (assumed).
Result Comparison:
|
Data Item |
Published data |
Pipe Flow Expert |
|
P1 Flow rate (ft³/s) |
1.11 |
1.1092 |
|
P2 Flow rate (ft³/s) |
1.07 |
1.0697 |
|
P3 Flow rate (ft³/s) |
0.07 |
0.0697 |
|
P4 Flow rate (ft³/s) |
0.89 |
0.8908 |
|
P5 Flow rate (ft³/s) |
0.96 |
0.9677 |
|
P6 Flow rate (ft³/s) |
0.04 |
0.0323 |
|
P7 Flow rate (ft³/s) |
0.01 |
0.0072 |
|
P8 Flow rate (ft³/s) |
0.04 (same as P6) |
0.0323 |
|
Pump - head added |
59.1 ft fluid |
59.078 ft fluid |
|
HGL at PRV Node N7 |
55.00 ft |
55.000 ft |
|
Pressure at Node N2 (psi) |
31.1 (Node 1 in text) |
31.1023 |
|
Pressure at Node N3 (psi) |
20.2 (Node 2 in text) |
20.1536 |
|
Pressure at Node N4 (psi) |
20.1 (Node 3 in text) |
20.1091 |
|
Pressure at Node N6 (psi) |
15.2 (Node 4 in text) |
15.1358 |
Commentary:
The published data and the calculated results compare well.
Pipe Flow Expert correctly identified that pipe 3 was drawn with the wrong flow direction in the design schematic, this pipe was reversed and the flow was reported as positive value.
The reference text notes that the flow direction of pipe 3 has been reversed from the input data.