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1. Open Channel Flow
ERT 349 SOIL AND WATER
ENGINEERING
Siti Kamariah Md Sa’at
PPK Bioproses, UniMAP

2. Topic Learning Outcomes
At the end of this topic, student should be able
to:
1.Design the open channel in uniform and non-
uniform flow
2.Design the most efficient section channel
3.Calculate the flow in open channel

3. Introduction
“Occur when free water surface in the channel is
at atmosphere pressure”
Example of open channel:
 Rivers and streams
 Drainage
 Ditches
 Irrigation canal

4. Application
Interest to hydraulic engineers
 location of free surface
 velocity distribution
 discharge - stage (depth) relationships
 optimal channel design

5. Types of channels
1. Man made
• Channel designed and made by human
• Examples: earth or concrete lined drainage and
irrigation
• Prismatic channel (no change in geometry with
distance)
2. Natural
• Examples: River and streams
• Changes with spatial and temporal (non prismatic
channel)

6. FLOW IN OPEN CHANNEL
STEADY FLOW UNSTEADY FLOW
UNIFORM FLOW NON-UNIFORM FLOW
RAPIDLY VARIED FLOW
GRADUALLY VARIED FLOW
TEMPORAL (Time)
SPATIAL (Space)

7. Types of flow
Based on temporal (Time, t) and Spatial
(Space,x)
Time Criteria
 Steady flow (dy/dt = 0). Water depth at one point
same all the time. (Flow constant with time)
 Unsteady flow (dy/dt ≠ 0). Water depth changes all
the time. (Flow variation with time)
Space criteria
 Uniform flow (dy/dx = 0). Water depth same along
the whole length of flow.
 Non-uniform flow (dy/dx ≠ 0). Water depth changes
either rapidly or gradually flow

8. Steady and Non-Steady Flow
Unsteady
Steady
Flow Rate
Time

9. Uniform and Non-Uniform Flow
V1 V2
A1 A2
V1
A1 V2
A2
Uniform Flow Non-Uniform Flow
V1 = V2
A1 = A2

10. States of flow
Flow vary with following forces:
 Viscous
 Inertia
 Gravity
Defines by Reynolds number (Re) and Froude
numbers (Fr)

11. To determine:
 Laminar flow : Re < 500 (viscous > inertia)
 Transitional flow : 500 < Re < 1300
 Turbulent flow : Re > 1300 (inertia >
viscous)
Reynolds Number

12. Froude Number
The Froude Number, Fr describes the following
states of flow:
Fr < 1 : flow is subcritical
Fr = 1 : flow is critical ( inertia < gravity)
Fr > 1 : flow is supercritical ( inertia > gravity)

13. A flow is called critical if the flow velocity is equal
to the velocity of a gravity wave having small
amplitude.
The flow is called subcritical flow, if the flow
velocity is less than the critical velocity
The flow is called supercritical flow if the flow
velocity is greater than the critical velocity.
Froude Number

14. Critical Flow
Characteristics
 Unstable surface
 Series of standing waves
 Difficult to measure depth
Occurrence
 Broad crested weir (and other weirs)
 Channel Controls (rapid changes in cross-section)
 Over falls
 Changes in channel slope from mild to steep
Used for flow measurements
 Unique relationship between depth and discharge
0
1
2
3
4
0 1 2 3 4
E
y

15. Parameters of Open Channels
Wetted Perimeter (P) :The Length of contact
between Liquid and sides and base of Channel
Hydraulic Mean Depth or Hydraulic Radius
(R): If cross sectional area is A, then R = A/P.
Depth of flow section (d) : depth of flow
normal to the direction of flow.

16. Parameters of Open Channels
Top width (T) : the width of channel section
at the free surface.
Hydraulic depth (D) : D = A/T
Base slope (So) : So = tan θ

17. Parameters of Open Channels
Freeboard: Vertical distance between the highest
water level anticipated in the design and the top
of the retaining banks. It is a safety factor to
prevent the overtopping of structures.
Side Slope (Z): The ratio of the horizontal to
vertical distance of the sides of the channel.

18. Table 1: Maximum Canal Side Slopes (Z)
Sand, Soft Clay 3: 1 (Horizontal: Vertical)
Sandy Clay, Silt Loam, Sandy
Loam
2:1
Fine Clay, Clay Loam 1.5:1
Heavy Clay 1:1
Stiff Clay with Concrete Lining 0.5 to 1:1
Lined Canals 1.5:1

19. M.Hanif Chaudry, Open Channel Flow 2nd Edition, Springer, 2008

20. Continuity Equation
Inflow – Outflow = Change in Storage
Inflow
1 2
A
A
3
Section AA
Change in Storage
Outflow
3a
3b

21. General Flow Equation
Q = vA
Flow rate
(m3
/s)
Avg. velocity
of flow at a
cross-section
(m/s)
Area of the
cross-section
(m2
)
Equation 1

22. Uniform flow in Open
Uniform flow in Open
Channel
Channel

23. Uniform flow in Open Channel
i
Sw
So
yo
Flow
Energy lines
Water Surface
For uniform flow (in prismatic channel), i = Sw = So
y = normal depth for uniform flow only

24. Resistance Equation
1. Chezy Equation
 By Antoine Chezy (France), 1768
2. Manning Equation
 By Robert Manning (Irish), 1889

25. Chezy Equation
Introduced by the French engineer Antoine
Chezy in 1768 while designing a canal for the
water-supply system of Paris
 Because i = So, so
Ri
C
v 
o
RS
C
v 
o
RS
AC
Q 

26. Chezy Equation
 where C = Chezy coefficient
= L1/2
/T (Unit m1/2
/s)
s
m
150
<
C
<
s
m
60
where 60 is for rough and 150 is for smooth

27. Manning Equation
 Most popular in for open channels around the world
(English system)
1/2
o
2/3
h S
R
1
n
V 
1/2
o
2/3
h S
R
49
.
1
n
V 
VA
Q 
2
/
1
3
/
2
1
o
h S
AR
n
Q  very sensitive to n
Dimensions of n? T /L1/3
Bottom slope
C = R1/6
/ n
n = Manning roughness
coefficient
= T/L1/3
(Unit s/m1/3
)
SI Unit

28. Lined Canals n
Cement plaster 0.011
Untreated gunite 0.016
Wood, planed 0.012
Wood, unplaned 0.013
Concrete, trowled 0.012
Concrete, wood forms, unfinished 0.015
Rubble in cement 0.020
Asphalt, smooth 0.013
Asphalt, rough 0.016
Natural Channels
Gravel beds, straight 0.025
Gravel beds plus large boulders 0.040
Earth, straight, with some grass 0.026
Earth, winding, no vegetation 0.030
Earth , winding with vegetation 0.050
n = f (surface
roughness, channel
irregularity, stage...)
Manning roughness coefficient, n

29. Example 1:
Trapezoidal channel:
 Bottom width = 3.0 m
 Side slope = 1: 1.5
 Base slope = 0.0016
 Manning coefficient = 0.013
Determine Q if yo = 2.6m.

30. M.Hanif Chaudry, Open Channel Flow 2nd Edition, Springer, 2008

31. Determination of yo
 If Q, So and n given or known and you need to
estimate yo, direct calculation cannot give you
answer. So there are another method can be
use:
1. Try and error
2. Graphical
3. Curves chart

32. Example 2:
 A rectangular channel with n = 0.017 with width
6 meter, base slope 0.0016 and to carry
10 m3
/s flowrate.
Determine yo with:
1. Try and error
2. Graphical
3. Curves chart