Case 50: Water – Fourteen Pipe Network - With PRV
Reference: Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Rowland W. Jeppson, Example problem 2 page 88 - 89
Pipe Flow Expert File: Case_50_Water_Fourteen_Pipe_Network_withPRV.pfe
Problem Description:
Water is supplied from a reservoir to a fourteen pipe network. The network contains a pump.
Out flows from the network occur at eight node points.
The network contains a pressure reducing valve.
The downstream pressure at the node leaving the PRV is greater than the PRV setting, therefore the PRV acts a check valve.
Find the new flow rate and head loss for each pipe.
Find the Hydraulic Grade Line values upstream and downstream of the PRV.
Fluid Data: Water at 68° F (assumed).
Result Comparison:
|
Pipe |
Published Flow (ft³/s) |
Pipe Flow Expert (ft³/s) |
|
Pipe |
Published Head Loss (ft) |
Pipe Flow Expert Head Loss (ft) |
|
P 1 |
0.50 |
0.5000 |
|
P 1 |
2.44 |
2.42 |
|
P 2 |
0.37 |
0.3704 |
|
P 2 |
0.63 |
0.63 |
|
P 3 |
2.16 |
2.1636 |
|
P 3 |
19.27 |
19.26 |
|
P 4 |
3.16 |
3.1636 |
|
P 4 |
6.40 |
6.40 |
|
P 5 |
0.00 |
0.0000 |
|
P 5 |
0.00 |
0.00 |
|
P 6 |
1.00 |
1.0000 |
|
P 6 |
6.40 |
6.37 |
|
P 7 |
0.25 |
0.2464 |
|
P 7 |
1.01 |
1.00 |
|
P 8 |
0.25 |
0.2536 |
|
P 8 |
1.06 |
1.05 |
|
P 9 |
0.05 |
0.0464 |
|
P 9 |
0.06 |
0.06 |
|
P 10 |
1.00 |
1.0000 |
|
P 10 |
2.56 |
2.55 |
|
P 11 |
0.79 |
0.7932 |
|
P 11 |
2.73 |
2.71 |
|
P 12 |
0.71 |
0.7068 |
|
P 12 |
2.22 |
2.17 |
|
P 13 |
0.13 |
0.1296 |
|
P 13 |
0.09 |
0.09 |
|
P 14 |
1.84 |
1.8364 |
|
P 14 |
2.21 |
2.20 |
|
P 15 |
n/a |
closed |
|
P 15 |
n/a |
closed |
|
Node |
Published Press. (ft hd) |
Pipe Flow Expert (psig) |
|
Node |
Published HGL. (ft) |
Pipe Flow Expert HGL (ft) |
|
N4 |
Not stated |
50.8793 |
|
N1 |
417.60 |
417.60 |
|
N8 |
Not stated |
61.9071 |
|
N2 |
393.08 |
393.04 |
Commentary:
The published flow rates, pipe head losses and HGL data compare well with the calculated results.
In the Pipe Flow Expert model, pipe P5 has been split into two pipes of equal length, so that the PRV can be positioned halfway along the original pipe length as shown in the reference text.
Since the pressure at node N8 downstream of the PRV is higher than the PRV pressure setting, the PRV will close and act as a check value preventing back flow in the pipe. Pipe Flow Expert reports that this is the case.
Pipe P15 has then been closed in the Pipe Flow Expert model to represent this situation.
The reference text list the length of pipe P1 as 1000 ft. This is most likely a printing error.
The flow rate of 0.50 ft³/s with a head loss of 2.44 ft (as stated in the reference text) can only be applicable to a pipe 500 ft long.