1 ن الرحيم الرحم بسمOpen Channel Flow) المفتوحة في القنواتلجريانا( -3 rd Class Dr. Sataa A. Al-Bayati(09-10) Introduction: What is the difference between the flow in open-channel & closed pipe? Open channel flow is flow of a liquid in a conduit in which upper surface of liquid (free surface) is in contact with atmosphere. Natural channels: rivers, & streams. Manmade channels: irrigation canals, sewer lines, storm drains, & street gutters. What are the important parameters to be calculated in open-channel? Fig.(1) Flow in an open-channel
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1
بسم الله الرحمن الرحيم
Open Channel Flow)3- )الجريان في القنوات المفتوحةrd
Class Dr. Sataa A. Al-Bayati(09-10)
Introduction:
What is the difference between the flow in open-channel & closed pipe?
Open channel flow is flow of a liquid in a conduit in which upper surface of
liquid (free surface) is in contact with atmosphere.
Natural channels: rivers, & streams.
Manmade channels: irrigation canals, sewer lines, storm drains, & street
gutters.
What are the important parameters to be calculated in open-channel?
Fig.(1) Flow in an open-channel
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Fig.(2) Uniform flow in an open-channel
Calculation of Q using Moody diagram:
The discharge can be calculated as follows,
oRSf
gAAVQ
8 ------- (1)
Where:
A = cross section area
ƒ = friction factor
R = hydraulic radius = A/P
P = wetted perimeter
So= channel slope
What is Moody Diagram Fig.(3)?
V2/2g
3
Fig.(3) Moody diagram: friction factors for commercial pipe (Featherstone,
R. E. & Nalluri, C., 1995)
4
Example (1):
Determine the discharge in a long rectangular concrete channel that is 5ft
wide, that has a slope of 0.002, & in which the water depth is 2ft. Use
K=5×10-3
ft, ν = 1.22 × 10-5
ft2/s.
Solution:
What are the relation between D & R?
Given: rectangular ch., b = 5ft, So = 0.002, y = 2ft, K = 5x10-3
ft, &
ν = 1.22×10-5
ft2/s.
Q =?
522
52
P
AR
= 1.11ft
as D = 4R
11.14
105
4
3
R
K s
= 1.13 x 10-3
Assume ƒ = 0.020
Eq. (1)
oRSf
gAAVQ
8
002.011.102.0
2.32852
= 53.5ft3/s
V = Q/A = 53.5 / 10
= 5.35ft/s
RVRe
4
51022.1
11.1435.5
eR
= 1.95 × 106
From Moody diagram, Fig. (3), ƒ = 0.02 OK
5
Stop & take Q = 53.5cfs.
Note: if ƒ is not equal repeat the calculation with the new ƒ.
*************
Calculation of Q using Manning Equation:
Manning Equation
What is Manning equation? Used for what?
2/13/249.1oSAR
nQ (EI) ----------- (2-a)
2/13/21oSAR
nQ (SI) ----------- (2-b)
Where:
n = Manning coefficient
Dividing the actual parameters of Eqs.(2) by the flowing full parameters we
get the following ( o or f = flowing full):
2/13/2
2/13/2
oo
o
o SnR
SnR
V
V
2/13/2
2/13/2
ooo
o
o SRnA
SnAR
Q
Q
From these two forms Fig.(4) is plotted.
Fig. (4) Flow characteristics of a circular section, Q/Qf vs. z=y/df.
V/Vf vs. z=y/df
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Fig. (4) Flow characteristics of a circular section
For quick solution Eqs.(2) is arranged in Fig. (5).
Fig. (5) Chart for flow of water in pipes flowing full, (Q, D, n, V, & S).
Need to know 3-parameters → find the other 2-parameters.
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Fig. (5) Chart for flow of water in pipes flowing full.
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Example (2):
Determine the discharge in a 3ft sewer pipe if the depth of flow is 1ft, &
pipe slope is 0.0019. Assume n = 0.012.
Solution:
Given: pipe ch., d = 3ft, y = 1ft, S = 0.0019, & n = 0.012.
Q =?
Use Fig. (5).
Draw a straight line through the points for n = 0.012 & S = 0.0019.
This line intersects match line.
Draw a line through intersection point & the 3ft diameter point.
Full discharge, Qf = 20mgd.
y/df = 1/3 = 0.333 → Fig. (4) → Q/Qf = 0.2
Q = 0.2Qf
= 0.2 × 20
= 4mgd.
*********************
Flow in Channel of Trapezoidal Cross Section)الجريان في القنوات شبه منحرف(
Fig. (6) Determining the normal depth.
A R2/3
/ b8/3
vs. y/b (trapezoidal)
A R2/3
/ do8/3
vs. y/do (circular)
Where:
b = bottom channel width,
do = pipe diameter.
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Fig. (6) Curves for the computation of normal depth, s=z (Chow 1959)
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Example (3):
Determine the normal depth for a trapezoidal channel with side slopes of 1
vertical to 2 horizontal, a bottom width of 8ft, discharge of 200cfs, channel