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

2. Topic Learning Outcomes
At the end of this topic, student should be able to:
Design the open channel in uniform and non-uniform flow
Design the most efficient section channel
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 Man made Natural Channel designed and made by human
Examples: earth or concrete lined drainage and irrigation
Prismatic channel (no change in geometry with distance)
Natural
Examples: River and streams
Changes with spatial and temporal (non prismatic channel)

6. 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
Flow Rate
Steady
Unsteady
Time
Steady and Non-Steady Flow

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

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

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

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. Froude Number
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.

14. Critical Flow Characteristics Occurrence Used for flow measurements
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

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

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

20. Continuity Equation Inflow 1 2 A 3 Change in Storage Outflow 3a 3b
Section AA
Change in Storage
Outflow 3a 3b
The continuity equation simply says that inflow minus outflow is equal to change in storage.
Inflow – Outflow = Change in Storage

21. Q = vA General Flow Equation Equation 1 Area of the cross-section (m2)
Flow rate (m3/s)
Avg. velocity of flow at a cross-section (m/s)
Area of the cross-section
(m2)
The general flow equation we are all familiar with says that the flow rate, Q, is equal to the avg. velocity of the flow at a cross-section multiplied by the area of the cross-section.
We are talking about the avg. flow rate of the cross-section here. In reality the flow velocity along a boundary such as the channel wall will be zero. Figure 4.2 in the book shows typical flow profiles for different channel cross sections.

22. Uniform flow in Open Channel

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

24. Resistance Equation Chezy Equation Manning Equation
By Antoine Chezy (France), 1768
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

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

27. Manning Equation Most popular in for open channels around the world
C = R1/6 / n
SI Unit
n = Manning roughness coefficient
= T/L1/3 (Unit s/m1/3)
T /L1/3
Dimensions of n?
(English system)
Bottom slope
very sensitive to n

28. Manning roughness coefficient, n
n = f (surface roughness, channel irregularity, stage...)

29. Example 1: Trapezoidal channel: Determine Q if yo = 2.6m.
Bottom width = 3.0 m
Side slope = 1: 1.5
Base slope =
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:
Try and error
Graphical
Curves chart

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