# 978-0134292380 Chapter 4 Part 2

Document Type

Test Prep

Book Title

Fundamentals of Hydraulic Engineering Systems 5th Edition

Authors

A. Osman H. Akan, Ned H. C. Hwang, Robert J. Houghtalen

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36

9. Determine the flow in each pipe in the figure below if all of the pipes are made of the same

material with e = 0.05 mm and water temperature at 20°C (ν = 1.00 x 10-6). Try an initial

energy level at the junction of 82 m, and go through one complete iteration of the solution

including a comment on your second trial energy level at the junction.

Ans. Assume a total energy elevation at the junction of HJ = 82 m. Then balance energy

between all reservoirs and the junction. (Use Darcy-Weisbach eq’n for friction loss.)

10. Determine the flow into or out of each reservoir in the figure if the connecting pipes all have

a Hazen-Williams coefficient of 120. (Hint: Try a junction energy elevation of 81.8 m.)

81.8

WS2 =

80

m

Trial until ∑Qs

WS3 =

70

m

Balance

Pipe Lengths

Pipe Diameters

L1 =

3000

m

D1 =

0.80

m

L2 =

4000

m

D2 =

1.20

m

L3 =

5000

m

D3 =

0.60

m

Pipe#

CHW

hf

S*

Rh**

V***

Q

(m)

(m)

(m/sec)

(m3/sec)

1

18.2

0.00607

0.20

1.18

2

1.8

0.00045

0.30

0.74

0.84

3

11.8

0.00236

0.15

1.18

0.33

* S = hf/L (friction slope or EGL slope in this case)

If HJ < WSβ; ∑Q =

1.69

** Rh = D/4 (Equation 3.26)

*** V = 0.849CRh0.63S0.54 (Equation 3.27)

If HJ > WSβ; ∑Q =

0.01

11. A small branching pipe system distributes water to three holding tanks. Pipe 1 contains a

valve that is partly closed that limits the flow rate to 1.0 cfs with a valve head loss of 3.60

feet. Estimate the length of Pipe 2 given the following water surface (WS) elevation and pipe

data (lengths, diameters, and Hazen-Williams coefficients):

WS1 = 4020 ft L1 = 1000 ft D1 = 1.0 ft C1 = 80

WS2 = 4018 ft L2 = ? D2 = 10 in. C2 = 100

WS3 = 4000 ft L3 = 5000 ft D3 = 1.0 ft C3 = 120

The total energy elevation at the junction (HJ) is 4015 ft.

38

12. The total discharge from A to B in the figure below is 50.0 cfs (ft3/sec). Pipe 1 is 4000 ft long

with a diameter of 1.5 ft, and pipe 2 is 3000 ft long with a diameter of 2 ft. Using Hardy-

Cross principles, determine the head loss between A and B and the flow rate in each pipe.

Assume f1 = 0.019, f2 = 0.018, ν = 1.08 x 10-5 ft2/sec, and ignore minor losses.

J

Pipe 2

Pipe 1

WS3

WS2

WS1

Reservoir

Reservoir 2

Reservoir 3

HJ

Pipe 3

1

2

B

A

39

13. The total discharge from A to B in the figure below is 12 liters/sec. Pipe 1 is 25 m long with a

diameter of 4 cm, and pipe 2 is 30 m long with a diameter of 5 cm. Using the method of

equivalent pipes, determine the head loss between A and B and the flow rate in each pipe.

Assume f1 = 0.033, f2 = 0.0γ0, ν = 1.00 x 10-6 m2/sec, ignore bend losses, and for the

equivalent pipe, let DE = 0.06 m and fE = 0.029.

14. Fill in the blanks for the partially completed pipe network solution table given below.

Loop

Pipe

Q

(m3/sec)

K

(sec2/m5)

hf

(m)

hf/Q

(sec/m2)

New Q

(m3/sec)

C

8

?

?

31.7

?

9

0.025

4880

122.0

?

10

(0.095)

775

?

?

?

4

0.153

131

3.07

20.1

?

1

2

B

A

40

15. From the pipe network data below, determine the flow in pipes CE and DE, and the pressure

head HE. Also determine the pressure (in psi) at E if the ground elevation is 650 ft.

Pipe

Flow

(ft3/sec)

Length

(ft)

Diameter

(in.)

K

(sec2/ft5)

AB

15.35

1000

12

0.424

BC

5.76

1500

8

1.510

BD

9.55

1200

12

1.100

DC

2.29

1500

6

9.530

CE

?

2000

12

1.540

DE

?

1000

8

0.949

16. Pipe flows are estimated in the pipe network below based on mass balance principles. These

flow rates are given in the table with the direction specified (e.g., AB indicates flow from A

to B). Proceed through one iteration of the Hardy Cross algorithm for each loop. Also, if the

total head at A is 50 feet, determine the pressure (psi) at E (elev = 0) using your results.

A

E

QE = ?

HE = ?

B

D

C

HA = 1000 ft

0.4 cfs

1.8 cfs

A

B

C

D

E

0.8 cfs

0.6 cfs

1

2

41

17. In the pipe network shown below, all of the pipes have a Darcy-Weisbach friction factor of

0.02. Pipe AB is has a length of 5000 ft and a diameter of 3 ft. Each of the pipes BC, BD,

CE, and DE have a length of 1000 ft and a diameter of 2 ft. Pipe DC is 1410 ft long and has a

diameter of 2 ft. The final solution obtained for this network indicates that the flows in pipes

BC, CE, and DE are respectively 20 cfs, 10 cfs, and 10 cfs as shown in the figure. Also, the

energy head at D is 100 feet. Determine the water surface elevation in Reservoir A, the

energy loss in pipe DC, and the energy loss in DC if the diameter were increased to 3 feet.

42

18. A 2,400-ft-long, 2-ft-diameter pipeline conveys water from a hill-top reservoir to an

industrial site. The pipe is made of ductile iron, has an outside diameter of 2.25 feet, and has

expansion joints. If the flow rate is 30 cfs, determine the maximum water hammer pressure

(in psi) that is likely to occur if the downstream flow valve is closed in 0.95 seconds. Also

determine the water hammer reduction (in psi) if a diverter is added that reduces the flow rate

from 30 cfs to 10 cfs almost instantly upon valve closure.

43

19. A pipeline conveys water from a reservoir to a point 100 m below its water surface and

discharges into the air. The commercial steel pipe is 30 cm in diameter, 420 m long, has a

wall thickness of 1 cm, and is free to move longitudinally. A rotary valve is installed at the

downstream end. Calculate the maximum water hammer pressure that can be expected on the

valve if it closes in a 0.5-sec period. Also, determine the total (maximum) pressure the

pipeline will be exposed to during the water hammer phenomenon.

20. A pipeline is being designed to withstand a total maximum pressure of 2.13 x 106 N/m2. The

20-cm pipeline is ductile iron and conveys water at 40 liters/sec. Determine the required

thickness of the pipe wall if the operational head on the pipeline is 40 m and it is also subject

to water hammer if the flow control valve on the downstream end is closed suddenly.

Assume that the longitudinal stresses will be negligible when the pipe is installed.

44

21. A 425-m-long, commercial steel pipe with a 0.90 m diameter carries irrigation water between

a reservoir and a distribution junction. The maximum flow is 2.81 m3/sec. A simple surge

tank is installed just upstream from the control valve to protect the pipeline from water

hammer damage. Determine the minimum diameter of the surge tank if the allowable water

surface rise is 5 m over the supply reservoir water level. Ignore minor losses.

Ans. Neglecting minor losses, determine the head loss and the pipeline friction factor.

hL = hf = f(L/D)(V2/2g); where V = Q/A = (2.81 m3/sec)/[(π/4)(0.90m)2] = 4.42 m/sec;

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