Reference:  Hydraulics of Pipeline Systems, 2000, CRC Press LLC, Bruce E. Larock, Rowland W. Jeppson, Gary Z. Watters, Page 115, Example problem 4.14


Pipe Flow Expert File: Case_11_Water_Eight_Pipe_Network_With_Turbine.pfe


Problem Description: 

Water is pumped from a single source around a network of 8 interconnected pipes. A booster pump is used get the water over hills which are at a higher elevation than the source. 

A turbine is placed in the system to recovery the extra head after the water has been moved over the hill crest. The network has one closed loops and one open loop.


1. Calculate the flow rate & head loss in each pipe.


2. Calculate the pressure and the hydraulic grade line at each node point.


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Fluid Data: Water at 20° C (assumed).


Result Comparison: 


Data Item

Published data

Pipe Flow Expert


Data Item

Published data

Pipe Flow Expert

Q1 Flow rate (m³/s)

0.330

0.3309


Head Loss (m)

  8.78

  8.800

Q2 Flow rate (m³/s)

0.217

0.2180


Head Loss (m)

23.02

23.128

Q3 Flow rate (m³/s

0.177

0.1780


Head Loss (m)

15.39

15.472

Q4 Flow rate (m³/s

0.033

0.0330


Head Loss (m)

76.55

76.346

Q5 Flow rate (m³/s

0.027

0.0270


Head Loss (m)

  6.93

  6.920

Q6 Flow rate (m³/s

0.147

0.1480


Head Loss (m)

15.87

15.984

Q7 Flow rate (m³/s

0.095

0.0959


Head Loss (m)

27.83

28.166

Q8 Flow rate (m³/s)

0.010

0.0100


Head Loss (m)

  5.89

  5.865


Data Item

Published data

Pipe Flow Expert


Data Item

Published data

Pipe Flow Expert

N1 Pressure  (kPa)

416.02

416.851


HGL (m)

117.45

117.592

N2 Pressure  (kPa)

  90.10

  90.810


HGL (m)

109.19

109.279

N3 Pressure  (kPa)

  37.30

  37.216


HGL (m)

  93.80

  93.803

N4 Pressure  (kPa)

303.00

305.807


HGL (m)

  40.9

  41.246

N5 Pressure  (kPa)

272.90

275.665


HGL (m)

  47.83

  48.166

N6 Pressure  (kPa)

294.30

297.342


HGL (m)

  35.83

  35.381


Commentary:

The published data and the calculated results compare well.

The reference contains a printing error on the network diagram:

The outflow from node 4 is shown as 0.025 m³/s the calculation input table shows a value of 0.050 m³/s.

The outflow from node 5 is shown as 0.050 m³/s the calculation input table shows a value of 0.025 m³/s.

The Pipe Flow Expert results are based on outflows from node 4 and node 5 as shown in the calculation input table.