Open Channel

The Islamic University of Gaza

Faculty of Engineering

Civil Engineering Department

Hydraulics - ECIV 3322

Chapter 6Chapter 6

2

Example 1

1.5m

3.0m

2

1

Open channel of width = 3m as shown, bed slope = 1:5000, d=1.5m find the flow rate using Manning equation, n=0.025.

sVAQ

V

P

AR

P

A

SRn

V

h

h

/m 84.49538.0

m/s 538.050001927.0

025.0

1

927.0708.9

9

9.708 35.132

m 95.1935.0

1

3

3

2

22

2

3

2

Example 2Open channel as shown, bed slope = 69:1584, find the flow rate using Chezy equation, C=35.

sVAQ

V

P

AR

P

A

SRCV

h

h

/m 84.11352.1627.0

m/s 7.01584

69.0917.035

917.018.177

52.162

m 177.18 04.552.28.166.38.115072.0

m 52.16215072.06.32

52.272.08.1652.2

2

04.552.2

3

2222

2

Example 3Circular open channel as shown d=1.68m, bed slope = 1:5000, find the Max. flow rate & the Max. velocity using Chezy equation, C=70.

sVAQ

V

mP

AR

dP

ddA

SRCV

h

h

/m 496.117.269.0

m/s 69.05000

1485.070

485.05.4

17.2

m 4.5 68.1180

154

m 17.21542sin8

68.1

180154

4

68.12sin

84

3

22222

154Max. flow rate

m/s 748.05000

157.070

57.03775.3

93.1

m 378.368.1180

75.128

m 93.175.1282sin8

68.1

18075.128

4

68.12sin

842

2222

V

mP

AR

dP

ddA

SRCV

h

h

75.128Max. Velocity

Trapezoidal open channel as shown Q=10m3/s, velocity =1.5m/s, for most economic section. find wetted parameter, and the bed slope n=0.014.

Example 4

mD

DDDA

DnDBA

mV

QA

BD

DBD

nDBnD

78.1

667.6)2

36055.0(

667.65.1

10

6055.02

232

231

2

21

2

2

2

mP

nDDP

nDBP

49.72

3178.12)78.1(6055.0

126055.0

12

2

2

2

To calculate bed Slope

6.1941:1

5.189.0014.0

1

89.049.7

667.6

m 49.7

m 667.6

1

3

2

2

3

2

S

SV

P

AR

P

A

SRn

V

h

h

Example 5

13

2

gA

TQ

1

81.93

14.2

3

124.233.1

23

2

3

2

cc

c

cc

c

DD

D

gDnDB

nDBQ

m 31.0cD

Determine the critical depth if the flow is 1.33m3/s. the channel width is 2.4m

Example 6

44

81.9

25

3

2

3

1

2

3

1

2

23

1

2

2

BBBgB

Qyc

0.006 2

D

0.016

125

2

P

AR

S R n

1V

32

c

32

BD

B

BD

BD

BD

cc

c

c

Rectangular channel , Q=25m3/s, bed slope =0.006, determine the channel width with critical flow using manning n=0.016

mB

B

B

B

BB

BB

BB

3

0.006 8

4

0.016

1

4

25

0.006 42

4

0.016

14

25

32

35

31

32

32

32

32

Example 7A 3-m wide rectangular channel carries 15 m3/s of water at a 0.7 m depth before entering a jump. Compute the downstrem water depth and the critical depth

72.27.081.9

14.7

/14.77.0

5

366.181.9

5

/s.mm 53

15

1

11

11

3

2

3

gd

VF

smd

qV

md

q

r

c

md

d

365.2

1)72.2(812

1

7.0

2

22

Example 8

dn = Depth can calculated from manning equation

d1=d

n

d2

calsupercriti is flow the142.108.181.9

63.4

/63.43

15

08.1

004.032

3

01.0

1

3

15

322

3

1

1

11

11

1

32

32

gd

VF

smd

V

mddD

D

D

D

DBDP

DBDA

SRnA

Q

r

n

h

d1=d

n

d2

a)

b)

md

d

7.1

1)42.1(812

1

08.1

2

22

c)

d1=d

n

d2

mgg

E

smd

V

032.02

94.27.1

2

63.408.1

/94.27.13

15

3

15

22

22

Example 9A trapezoidal channel with a bottom width of 5m, side slope of 1H: 1V, and a Manning n of 0.013 carries a discharge of 50m3/s at a slope of 0.0004. Compute by the direct step method the backwater profile created by a dam that backs up the water to a depth of 6 m immediately behind the dam. The upstream end of the profile is assumed at a depth equal to 1% greater than the normal depth.

17

3

2

3

5

3

22

3

5

2

1

3

22

3

5

3

5

3

2

2

1

2

13

2

3

22

1

3

2

2

1

3

2

225

15

1125

15

0004.0

013.0*50

12

*

11

1

n

nn

n

nn

n

n

y

yy

y

yy

nyb

ynyb

P

A

S

nQ

S

P

A

nSR

nA

Q

SRn

V

By trial and error, Yn = 2.87 m

determine normal depth, Yn

1

581.9

5250

12

3

2

3

2

3

2

3

2

cc

c

cc

c

YY

Y

gA

TQ

YbnYg

bnYQ

gA

TQ

determine critical depth, Yc

By trial and error, Yc = 1.90 mControl depth = 1.01*2.87 =2.90m

1 2 3 4 5 6 7 8 9 10 11 12

y A P R V E ΔE Sf Sfm So-Sfm Δx L

m m2 m m m/s m m *104 *104 *104 m m

2.9 22.91 13.2 1.735 2.182 3.165 3.710

0.057 3.545 0.455 1250 1250

3.0 24.0 13.49 1.779 2.080 3.222 3.380

0.080 3.190 0.810 987 2237

3.1 25.11 13.77 1.824 1.990 3.303 3.000

0.082 2.830 1.170 700 2937

3.2 26.24 14.05 1.868 1.900 3.384 2.660

0.260 2.268 1.732 1500 4437

3.5 29.75 14.90 1.997 1.680 3.644 1.875

0.455 1.505 2.495 1750 6187

4.0 36.0 16.31 2.207 1.390 4.099 1.135

1 2 3 4 5 6 7 8 9 10 11 12

y A P R V E ΔE Sf Sfm So-Sfm

Δx L

m m2 m m m/s m m *104 *104 *104 m m

4.0 36.0 16.31 2.207 1.390 4.099 1.135

0.472 0.925 3.075 1526 7713

4.5 42.75 17.73 2.411 1.170 4.570 0.715

0.481 0.592 3.408 1410 9123

5.0 50.0 19.14 2.612 1.000 5.051 0.469

0.487 0.394 3.606 1350 10473

5.5 57.75 20.56 2.808 0.865 5.538 0.318

0.491 0.271 3.729 1320 11793

6.0 66.0 21.97 3.005 0.758 6.029 0.223