Reference:  Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Rowland W. Jeppson, Example problem 8 page 99-101


Pipe Flow Expert File: Case_49_Water_Fifty_One_Pipe_Network.pfe


Problem Description: 

Water is supplied from two reservoirs to a fifty one pipe network. 

The pipes are connected at thirty two node points. 

The network contains one pump.

Out flows from the network occur at 27 of the node points.


Find the flow rate and head loss for each pipe.


A screenshot of a computer??Description automatically generated


Fluid Data: Water at 68° F (assumed).


Result Comparison: 


● = Pipe Flow Expert reversed pipe direction and reported flow as positive


Pipe

Published

Flow (ft³/s)

Pipe Flow Expert (ft³/s)


Pipe

Published 

Head Loss (ft)

Pipe Flow Expert 

Head  Loss (ft)

P 1 

20.40

20.3982


P 1 

5.58

5.55

P 2 

20.50

20.4878


P 2 

11.31

11.31

P 3 

10.50

10.4794


P 3 

3.03

3.02

P 4 

4.92

4.9235


P 4 

0.70

0.70

P 5

-4.16

● 4.1712


P 5 

26.58

26.60

P 6

2.76

2.7661


P 6 

0.23

0.23

P 7

4.29

4.2943


P 7

18.77

18.78

P 8

4.69

4.6960


P 8

11.19

11.20

P 9

4.83

4.8387


P 9

17.81

17.83

P 10

14.18

14.1935


P 10

12.15

12.16

P 11

2.76

2.7728


P 11

3.96

3.97

P 12

-4.35

● 4.3548


P 12

19.28

19.31

P 13

-6.35

● 6.3548


P 13

2.50

2.49

P 14

1.76

1.7618


P 14

3.28

3.28

P 15

-1.47

● 1.4805


P 15

1.74

1.76

P 16

-6.11

● 6.1276


P 16

1.06

1.06

P 17

-3.02

● 3.0552


P 17

0.22

0.22

P 18

1.60

1.6011


P 18

4.11

4.09

P 19

0.40

0.3989


P 19

0.10

0.10

P 20

-1.06

● 1.0530


P 20

0.93

0.91

P 21

2.56

2.5530


P 21

0.43

0.42

P 22

4.56

4.5530


P 22

0.91

0.90

P 23

-4.31

● 4.3198


P 23

14.23

14.25

P 24

2.62

2.6175


P 24

10.67

10.65

P 25

1.39

1.3825


P 25

1.04

1.03

P 26

3.24

3.3460


P 26

8.61

8.62

P 27

3.24

3.2477


P 27

16.27

16.26

P 28

3.19

3.1980


P 28

7.89

7.89

P 29

2.63

2.6314


P 29

5.39

5.38

P 30

7.23

7.2285


P 30

65.76

65.75

P 31

-2.73

●   2.7402


P 31

0.97

0.97

P 32

-8.32

●   8.3311


P 32

8.50

8.49

P 33

-10.82

● 10.8288


P 33

1.61

1.61

P 34

-12.82

● 12.8288


P 34

5.63

5.62

P 35

3.02

3.0210


P 35

7.07

7.05

P 36

0.98

0.9790


P 36

0.80

0.79

P 37

17.83

17.8498


P 37

8.62

8.61

P 38

-0.73

● 0.7313


P 38

0.06

0.06

P 39

-8.37

● 8.3808


P 39

6.45

6.44

P 40

12.10

12.1121


P 40

3.02

3.01

P 41

4.57

4.5666


P 41

1.58

1.57

P 42

12.33

12.3341


P 42

13.82

13.81

P 43

12.85

12.8599


P 43

10.01

10.00

P 44

8.34

8.3445


P 44

5.12

5.11

P 45

30.45

30.4630


P 45

18.60

18.60

P 46

27.18

27.1941


P 46

9.90

9.90

P 47

57.63

57.6570


P 47

7.77

7.74

P 48

20.11

20.1184


P 48

8.19

8.18

P 49

-2.61

● 2.6119


P 49

7.08

7.07

P 50

-5.16

● 5.1677


P 50

27.05

27.07

P 51

10.55

10.5690


P 51

3.07

3.07



Commentary:  


The published data and the calculated results compare very well.


The reference text indicates that the flow direction in a pipe is opposite to the direction shown on the schematic diagram by reporting the flow as negative value.

Pipe Flow Expert reversed the flow direction of the pipes indicated with ‘●’ automatically, and reported the flow rates in these pipes as a positive value.


The reference text indicates that the out flow from node N14 is 4.00 ft³/s, and that the out flow from node N21 is 3.00 ft³/s. These outflows appear to have been interchanged, probably due to be a printing error.

Using the published flow rate results, the sum of flows in the pipes entering and leaving node N14 indicate a flow rate of 3.00 ft³/s leaves this node, the sum of flows in the pipes entering and leaving node N21 indicate a flow rate of 4.00 ft³/s leaves this node.


The Pipe Flow Expert system is based on these ‘corrected’ outflow values.


The close correlation of the calculation results indicates that the reference text calculations were based on these ‘corrected’ outflow values stated above.


There are no published values for pressures and HGL values at the node points.

The reference text only lists the elevations for the fluid surface of the 3 reservoirs.

As all the other nodes are completely surrounded by pipes which do not connect to atmosphere a change in elevation of these nodes would not affect the flow rate through the pipes in the system.