Hydraulic Engineering Eng. Osama Dawoud
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Hydraulic EngineeringHydraulic
Engineering
Eng. Osama Dawoud
Eng. Osama Dawoud
Lecture 14
Open Channel Flow
Open Channel
• Open channel hydraulics, a subject of great importance to civil engineers, deals with flows having a free surface in channels constructed for water supply, irrigation, drainage, and hydroelectric power generation; in sewers, culverts, and tunnels flowing partially full; and in natural streams and rivers.
Pipe system
Open Channel
Classification
• Steady Flow– Not time
dependent
• Unsteady Flow– Is time dependent
Typical situations Uniform flow
Gradually Varied Flow Rapidly Varied Flow
Open channel section types
Uniform Flow
SRCV h
Chezy equation
C is the Chezy C, a dimensional factor which characterizes the resistance to flow
P wetted
A wetted Radius hydraulic
slope bedS
Rh
Manning equation
2/13/21SR
nV h
tCoefficien M
P wetted
A wetted Radius hydraulic
anningn
slopebedS
Rh
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
Most Efficient Sections
During the design stages of an open channel, the channel cross-section, roughness and bottom slope are given.
The objective is to determine the flow velocity, depth and flow rate, given any one of them. The design of channels involves selecting the channel shape and bed slope to convey a given flow rate with a given flow depth. For a given discharge, slope and roughness, the designer aims to minimize the cross-sectional area A in order to reduce construction costs
Most Efficient Sections
The most ‘efficient’ cross-sectional shape is determined for uniform flow conditions. Consideringa given discharge Q, the velocity V is maximum for the minimum cross-section A. According to the Manning equation the hydraulic diameter is then maximum.
It can be shown that:1. the wetted perimeter is also minimum,2. the semi-circle section (semi-circle having its
centre in the surface) is the best hydraulic section
Most Efficient Sections
Because the hydraulic radius is equal to the water cross section area divided by the wetted parameter, Channel section with the least wetted parameter is the best hydraulic sectionRectangular section
DBA
BD2P
D
A 2DP
0 dD
dP
222 2 0 2 D
DB
D
A
D
A
dD
dP
D
B 2
2
B D
Trapezoidal section D)Dk(BA
212 kDBP
Dk D
A B
212 kD ) kD D
A(P
0 dD
dP
0 12 22
kkD
A
dD
dPk
D
Ak12
22
D
DkBk
D
DkD)(Bk
2 12
22
2
Dk2Bk1D 2
ork
k
Other criteria for economic Trapezoidal section
DOF
The best side slope for Trapezoidal section
3
1 k 60
0 dk
dP
k
Circular section
2sin8
4
22 ddA
drP 2
dD 95.0154 Maximum Flow using Manning
Maximum Flow using Chezy
dD 94.0151
dD 81.075.128
Maximum Velocity using Manning or Chezy
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
Variation of flow and velocity with depth in circular pipes
Circular 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
DkDBA
mV
QA
BD
DBD
kDBkD
78.1
667.6)2
36055.0(
667.65.1
10
6055.02
232
231
2
21
2
2
2
mP
kDDP
kDBP
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
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