Chapter 10 Fluid

7/30/2019 Chapter 10 Fluid

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CHAPTER 10. OPEN CHANNEL FLOWCHAPTER 10. OPEN CHANNEL FLOW

EXAMPLE 1EXAMPLE 1

Example 1. Water flows in a rectangular channel at a depth of 4.0

ft and a flow rate of Q = 200 cfs. Determine the minimum

channel width if the flow is to be subcritical.

sftVandfeetwidthbbftb

sft

A

QV /

50

)4)((

/200 3

sft

b

yg

VFr

)4)(/2.32(

/50

2

ftbor

sft

b

yg

VFr

FrSet

41.4

1)4)(/2.32(

/50

1

2


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EXAMPLE 2EXAMPLE 2

Example 2. Water flows at a rate of 1,000 cubic feet per second in

a horizontal channel 30 feet wide with a 2-ft depth. Determine

the depth if the channel contracts to a width of 25 ft. Explain.


EXAMPLE 2EXAMPLE 2


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EXAMPLE 2EXAMPLE 2


EXAMPLE 3EXAMPLE 3

Example 3. Plot the specific energy diagram for a wide channel

carrying q = 50 cfs per foot (50 ft2/s). determine (a) the critical

depth, (b) the minimum specific energy, (c) the alternate depth

corresponding to a depth of 2.5 ft, and (d) the possible flow

velocities ifE= 10 ft.

ysft

sfty

yg

qyE

)/2.32(2

)/50(

2 22

22

2

2

(a) ftsft

sft

g

qyNOTE

yyE

c 27.4/2.32

)/50(

.

3/1

2

223/1

2

2


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EXAMPLE 2EXAMPLE 2

=

E=6.4ft


EXAMPLE 3EXAMPLE 3






ftftyEb c 41.6)27.4(2/32/3) min

ftyandftyftyy

y

fty

yEthenftyifc

91.1;12.8;5.2;8.38

71.8

71.85.2

8.385.2

8.38,5.2)

2

22


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EXAMPLE 2EXAMPLE 2

y= .

E=8.71 ft

y=2.5 ft


EXAMPLE 3EXAMPLE 3






8.381010)

2ythenftEFord

;/3.2222.2

/50;/22.5

57.9

/50/

81.1;24.2;57.9

22

sftft

sftsft

ft

sftyqV

yroots


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EXAMPLE 2EXAMPLE 2

y=9.57 ft

y=2.24 ft


EXAMPLE 4EXAMPLE 4

Example 3. A weedy irrigation canal of trapezoidal cross section

is to carry a flow of20 m3/s when built on a slope of0.56 m per

km. The side slope ratio (Z) is 1.0 and the bottom width is 8

meters. Determine the width of the waterline at the free surface.

1

Z


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EXAMPLE 4EXAMPLE 4

Quess d,m Area, m2 Per, m Rh, m Q,calc Top, m

1.00 9.00 10.83 0.83 6.28 10.00

1.10 10.01 11.11 0.90 7.37 10.20

1.20 11.04 11.39 0.97 8.53 10.40

1.30 12.09 11.68 1.04 9.76 10.60

1.40 13.16 11.96 1.10 11.06 10.80

1.50 14.25 12.24 1.16 12.44 11.00

1.60 15.36 12.53 1.23 13.88 11.20

. . . . . .

1.80 17.64 13.09 1.35 16.98 11.60

1.90 18.81 13.37 1.41 18.63 11.802.002.00 20.0020.00 13.6613.66 1.461.46 20.3420.34 12.0012.00

2.10 21.21 13.94 1.52 22.13 12.20

2.20 22.44 14.22 1.58 23.99 12.40


EXAMPLE 4EXAMPLE 4


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EXAMPLE 10.3 TEXT (Modified)EXAMPLE 10.3 TEXT (Modified)

Example 3. Water flows in a channel of trapezoidal cross section.

The bottom drops 1.4 ft per 1000 ft of length. The canal is lined

with new finished concrete. LET Z =2!!!!

FIND: (a) the flow rate and (b)The Froude Number for this flow.



Example 3. Water flows in a channel of trapezoidal cross section.

The bottom drops 1.4 ft per 1000 ft of length. The canal is lined

with new finished concrete. LET Z =2!!!!

FIND: (a) the flow rate and (b)The Froude Number for this flow.

S0 = 0.0014 ft/ft

b = 12.0 ft

d = 5.0 ft


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b =12 ft, d = 5 ft, Z=2

A = bd + zd2

P = b + 2d (Z2+1)1/2

Rh = A/PQ = 1.49 (A) (Rh)2/3 S0

1/2

n

Fr = V/(gy)1/2 = V/(gdh)

1/2

with dh = AREA/TOPWIDTH


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0.012 Finish Concrete

0.015 Brickwork

0.016 Asphalt

0.025 Rubble

0.035 Pasture

0.050 Li ht brush

0.075 Heavy Brush0.150 Trees


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Area, ft2 Per, f t Rh, f t Q, c fs Top, f t n Material

110.0 34.361 3.201 1110 32.0 0.012 Finish Conc

110.0 34.361 3.201 888 32.0 0.015 Brickwork

110.0 34.361 3.201 833 32.0 0.016 Asphalt

110.0 34.361 3.201 533 32.0 0.025 Rubble

110.0 34.361 3.201 381 32.0 0.035 Pasture

. . . . .

110.0 34.361 3.201 178 32.0 0.075 Heavy Brush

110.0 34.361 3.201 89 32.0 0.15 Trees



Finish Concrete

Brickwork

Asphal t

Rubble

Pasture

Light brush eavy rus Trees


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Material Velocity, f t/s Fr

. .

Brickwork 8.07 0.77

Asphalt 7.57 0.72

Rubble 4.84 0.46

Pasture 3.46 0.33

g rus . .

Heavy Brush 1.61 0.15

Trees 0.81 0.08



b =12 ft, Z=2

= 400 cfs

S0 =0.0014 ft/ft

WEEDY n = 0.030

FIND depth of flow

A = bd + zd2 P = b + 2d (Z2+1)1/2

Rh = A/P Q = 1.49 (A) (Rh)2/3 S0

1/2

n


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Quess d,ft Area, ft2 Per, ft Rh, ft Q,calc Top, ft Vel, ft/s Fr

4.00 80.00 29.89 2.68 286.6 28.0 3.58 0.37

4.10 82.82 30.34 2.73 300.6 28.4 3.63 0.37

4.20 85.68 30.78 2.78 315.1 28.8 3.68 0.38

4.30 88.58 31.23 2.84 329.8 29.2 3.72 0.38

4.40 91.52 31.68 2.89 345.0 29.6 3.77 0.38

4.50 94.50 32.12 2.94 360.5 30.0 3.82 0.38

4.60 97.52 32.57 2.99 376.5 30.4 3.86 0.38

. . . . . . . .

4.75 102.13 33.24 3.07 401.1 31.0 3.93 0.38

4.80 103.68 33.47 3.10 409.5 31.2 3.95 0.384.90 106.82 33.91 3.15 426.5 31.6 3.99 0.38

5.00 110.00 34.36 3.20 444.0 32.0 4.04 0.38

5.10 113.22 34.81 3.25 461.9 32.4 4.08 0.38




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EXAMPLE 10.6 TEXTEXAMPLE 10.6 TEXT

Water flows along a drainage canal having the properties shown in

the figure below. The bottom slope S0 = 0.002 ft/ft. Estimate the

flow rate when the depth is 1.4 feet.

Q = Q1 + Q2 + Q3 Qi = 1.49 (Ai) (Rhi)2/3 S0

1/2

ni



S0= 0.002

i A i ,ft2 Pi , ft Rhi, ft n i Qi, ft3/s

1 1.8 3.6 0.500 0.020 3.78

2 2.8 3.6 0.778 0.015 10.52

. . . . .

16.82

TOTAL 6.4 10.8 0.5926 0.0179


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Chapter 10 Fluid

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