Reference:  Analysis of Flow in Pipe Networks, 1976, Publisher Ann Arbor Science, Rowland W. Jeppson, Example problem 9 page 102 -105


Pipe Flow Expert File: Case_45_Water_Sixty_Five_Pipe_Network.pfe


Problem Description: 

Water is supplied from five reservoirs to a sixty five pipe network. 

The pipes are connected at twenty nine node points. 

The network contains 5 pumps.

Out flows from the network occur at each node point.


Find the flow rate and head loss for each pipe.

Find the pressure and Hydraulic Grade Line at each node point.


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 

11.6100

11.6682


P 1 

82.15

82.73

P 2 

3.1800

3.1979


P 2 

14.20

14.36

P 3 

2.1800

2.1979


P 3 

9.23

9.38

P 4 

1.5000

1.5106


P 4 

23.43

23.74

P 5 

2.2200

2.2298


P 5 

26.31

26.55

P 6

-1.1900

● 1.1830


P 6 

2.87

2.81

P 7

0.3000

0.3440


P 7

0.18

0.22

P 8

-0.6800

● 0.6815


P 8

3.60

3.63

P 9

0.4900

0.5229


P 9

0.73

0.83

P 10

-1.4300

● 1.4369


P 10

3.42

3.41

P 11

2.6300

2.5927


P 11

7.68

7.42

P 12

2.0600

2.0429


P 12

11.10

10.83

P 13

10.0000

10.0120


P 13

25.67

27.15

P 14

0.9300

0.9905


P 14

1.89

2.13

P 15

1.4900

1.5157


P 15

5.33

5.45

P 16

1.8900

1.8702


P 16

11.07

10.83

P 17

1.5400

1.4571


P 17

3.78

3.36

P 18

1.4700

1.4476


P 18

3.44

3.32

P 19

2.7500

2.6487


P 19

7.22

6.69

P 20

2.7100

2.6216


P 20

7.04

6.55

P 21

-0.2600

● 0.2351


P 21

0.18

0.13

P 22

-1.4500

● 1.3865


P 22

4.21

3.82

P 23

-1.7700

● 1.6927


P 23

4.03

3.69

P 24

-1.7100

● 1.6544


P 24

5.74

5.38

P 25

0.5800

0.5758


P 25

1.71

1.70

P 26

2.0900

2.0713


P 26

19.84

19.48

P 27  

-2.1000

2.0786


P 27

18.13

17.78

P 28

0.0700

● 0.0217


P 28

0.02

0.00

P 29

1.1800

1.1619


P 29

3.26

3.16

P 30

2.7300

2.7058


P 30

21.37

20.94

P 31

1.1400

1.1335


P 31

20.22

20.04

P 32

-0.9200

● 0.8899


P 32

1.88

1.73

P 33

4.7200

4.7300


P 33

28.18

28.28

P 34

3.5100

3.4863


P 34

28.34

27.86

P 35

0.7100

0.7080


P 35

8.01

7.82

P 36

-1.9500

● 1.9296


P 36

22.30

21.80

P 37

-2.7200

● 2.6943


P 37

14.28

13.98

P 38

0.8800

0.8636


P 38

0.85

0.81

P 39

-0.4300

● 0.3942


P 39

0.13

0.11

P 40

-3.7200

● 3.6901


P 40

21.31

20.88

P 41

1.0500

1.0306


P 41

2.40

2.29

P 42

-1.0000

● 0.9865


P 42

4.25

4.09

P 43

-0.8600

● 0.8423


P 43

1.63

1.56

P 44

-0.5000

● 0.5015


P 44

1.72

1.68

P 45

-0.4000

● 0.3940


P 45

0.90

0.85

P 46

1.4500

1.4230


P 46

4.75

4.55

P 47

1.4300

1.4012


P 47

4.87

4.68

P 48

0.3500

0.3338


P 48

0.79

0.72

P 49

2.5500

2.5327


P 49

17.59

17.33

P 50

1.4500

1.4441


P 50

4.21

4.13

P 51

4.2500

4.2280


P 51

13.38

13.20

P 52

9.0300

9.0853


P 52

26.61

26.86

P 53

1.2400

1.2794


P 53

3.32

3.49

P 54

-3.0200

● 3.0118


P 54

24.63

24.36

P 55

3.2700

3.2912


P 55

18.65

18.83

P 56

-1.2100

● 1.1874


P 56

1.55

1.49

P 57

-0.2200

● 0.2029


P 57

0.08

0.07

P 58

-1.2200

● 1.1933


P 58

3.78

3.62

P 59

0.9200

0.9094


P 59

1.17

1.13

P 60

-0.8000

● 0.7839


P 60

1.15

1.10

P 61

1.8000

1.7839


P 61

4.23

4.16

P 62

6.2500

6.2915


P 62

12.87

13.00

P 63

-5.1400

● 5.0346


P 63

19.47

18.62

P 64

2.8000

2.7568


P 64

16.80

16.61

P 65

7.0000

6.7275


P 65

23.88

26.56


Node (text ref)

Published 

Press. (lb/in²)

Pipe Flow 

Expert (lb/in²)


Node (text ref)

Published 

HGL. (ft)

Pipe Flow 

Expert HGL (ft)

N1 (n/a)

  n/a

  n/a


N1 (n/a)

Fluid Surface

300.0000

N2 (1)

104.1

103.2907


N2 (1)

390.2

388.7300

N3 (2)

97.9

97.0770


N3 (2)

376.0

374.3700

N4 (3)

89.6

88.6939


N4 (3)

366.7

365.0000

N5 (4)

92.7

91.8056


N5 (4)

363.9

362.1900

N6 (5)

87.3

86.4336


N6 (5)

366.6

364.7700

N7 (6)

88.0

87.1218


N7 (6)

363.3

361.3600

N8 (7)

84.2

83.1561


N8 (7)

374.2

372.2000

N9 (n/a)

n/a

  n/a


N9 (n/a)

Fluid Surface

350.0000

N10 (8)

79.0

77.9059


N10 (8)

372.3

370.0700

N11 (11)

77.5

76.4725


N11 (11)

368.9

366.7500

N12 (12

75.0

74.1433


N12 (12

363.2

361.3700

N13 (9)

76.3

75.0384


N13 (9)

376.1

373.4300

N14 (10)

81.9

80.8566


N14 (10)

369.1

366.8800

N15 (20)

80.1

79.2045


N15 (20)

364.9

363.0600

N16 (13)

71.5

70.7767


N16 (13)

345.0

343.5800

N17 (14)

78.8

78.0611


N17 (14)

341.8

340.4200

N18 (15)

91.9

91.0567


N18 (15)

362.0

360.4600

N19 (16)

79.6

79.0029


N19 (16)

333.8

332.6000

N20 (25)

77.8

77.2810


N20 (25)

319.5

318.6200

N21 (17)

87.1

86.3629


N21 (17)

340.9

339.6100

N22 (24)

82.7

81.9878


N22 (24)

340.8

339.5000

N23 (18)

83.4

83.0292


N23 (18)

343.3

341.9000

N24 (23)

82.7

82.6617


N24 (23)

342.4

341.0500

N25(19)

77.2

76.3452


N25(19)

348.1

346.4600

N26 (22)

81.2

80.36452


N26 (22)

347.3

345.7300

N27 (21)

78.65

77.8199


N27 (21)

351.2

349.8600

N28 (n/a)

n/a

  n/a


N28 (n/a)


280.0000

N29 (26)

80.7

80.0996


N29 (26)

316.1

315.1300

N30 (27)

92.0

91.2857


N30 (27)

342.3

340.9900

N31 (28)

93.6

92.8505


N31 (28)

346.1

344.6000

N32 (29)

96.3

95.4911


N32 (29)

347.3

345.7100

N33 (n/a)

n/a

  n/a


N33 (n/a)

Fluid Surface

150.0000

N34 (n/a)

n/a

  n/a


N34 (n/a)

Fluid Surface

300.0000

N35 (n/a)

n/a

  n/a


N35 (n/a)

Fluid Surface

400.0000


Commentary:  

The published data and the calculated results compare well.


The reference text uses a linear approximation to calculate head losses, and only performs six iterations to find an approximate result. 

Pipe Flow Expert uses the more accurate Darcy-Weisbach equation and converges to within a pressure balance tolerance of 0.000145 psi.


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


The reference text indicates that the flow in pipe P27 is negative, and this appears to be a printing error, since the flow direction of this pipe is drawn correctly. 

However the flow direction of pipe P28 is drawn opposite to the actual flow direction and should be reported as a negative value in the text, but this is listed as a positive value.

We believe that the reference text reports the flow direction of these two pipes incorrectly.


The schematic diagram lists pipe P63 as 10” diameter.

These flow and pressure loss values cannot be reconciled with a 10” diameter pipe.

We have assumed that the text calculations were based on 12” diameter for this pipe.

The published results for pipe P63 are: Flow 5.14 ft³/s with a pressure loss of 19.47 ft hd.

Pipe Flow Expert reports: Flow 5.0346 ft³/s with a pressure loss of 18.62 ft hd for a 12” diameter pipe.


If the system is solved using a 10” diameter for pipe P63 the flow is 3.941 ft³/s with a pressure loss of 29.59 ft hd.

The correlation for flows and pressure losses in many other pipes is also lost.

Hence the reference text was not solved with a 10” diameter for pipe P63.