1. Chapter 1. Flow in Open Channel
Learning Outcomes:
Differentiate between open channel flow and pipe flow
Define and explain on the types of flow
Identify the state of flow and flow regimes
Define open channel geometries

2. Chapter 1. Flow in Open Channel
Stormwater Management and Road Tunnel (SMART), Kuala Lumpur, Malaysia
Tahan river rapids
Why do we need to learn open channel flow?
Siberian meandering river

3. Figure. Sketch of open channel geometry
Open channel flow is flow of a liquid in a conduit with a free surface subjected to atmospheric pressure.
Free surface
Flow
Datum  x y u A B T
Figure. Sketch of open channel geometry
Definition
Examples: flow of water in rivers, canals, partially full sewers and drains and flow of water over land.

4. Practical applications are the determination of:
flow depth in rivers, canals and other conveyance conduits,
changes in flow depth due to channel controls e.g. weirs, spillways, and gates,
changes in river stage during floods,
surface runoff from rainfall over land,
optimal channel design, and
others

5. 1.1 Flow Parameters and Geometric Elements
a. Depth of flow y is the vertical measure of water depth.
Normal depth d is measured normal to the channel bottom.
d = y cos 
For most applications, d  y when   10%. cos 0.1 =
Free surface
Flow Q
Datum  x y d
So = bottom slope
Sw = water surface slope
b. Flow or discharge Q is the volume of fluid passing a cross-section perpendicular to the direction of flow per unit time.
Mean velocity V is the discharge divided by the cross-sectional area

6. A = cross sectional area covered by flowing water
1.1 Geometric Elements
c. Wetted perimeter P is the length of channel perimeter that is wetted or covered by flowing water.
T = top width y P
A = cross sectional area covered by flowing water A
B = bottom width

7. 1.1 Geometric Elements
d. Hydraulic radius R is the ratio of the flow area A to wetted perimeter P.
e. Hydraulic depth D is the average depth of irregular cross section. B T A P y

8. Table. Open channel geometries
Channel shape
Area A
Top width T
Wetted perimeter P y B T
Rectangular By B
B + 2y y z T
Triangular 1
zy2
2zy y z T
Trapezoidal 1 B
By + zy2
B + 2zy y T
Circle  D
 in radian
 in angle
 in radian

9. 1.2 Types of Open Channel  Prismatic and non-prismatic channels
Prismatic channel is the channel which cross-sectional shape, size and bottom slope are constant. Most of the man-made (artificial) channels are prismatic channels over long stretches. Examples of man-made channels are irrigation canal, flume, drainage ditches, roadside gutters, drop, chute, culvert and tunnel.
All natural channels generally have varying cross-sections and therefore are non-prismatic. Examples of natural channels are tiny hillside rivulets, through brooks, streams, rivers and tidal estuaries.
 Rigid and mobile boundary channels
Rigid channels are channels with boundaries that is not deformable. Channel geometry and roughness are constant over time. Typical examples are lined canals, sewers and non-erodible unlined canals.
Mobile boundary channels are channels with boundaries that undergo deformation due to the continuous process of erosion and deposition due to the flow. Examples are unlined man-made channels and natural rivers.

10. Terusan Wan Muhammad Saman, Kedah
Canals - is usually a long and mild-sloped channel built in the ground, which may be unlined or lined with stoned masonry, concrete, cement, wood or bituminous material.
Terusan Wan Muhammad Saman, Kedah
Griboyedov Canal, St. Petersburg, Russia

11. Flumes - is a channel of wood, metal, concrete, or masonry, usually supported on or above the surface of the ground to carry water across a depression.
This flume diverts water from White River, Washington to generate electricity
Bull Run Hydroelectric Project diversion flume
Open-channel flume in laboratory

12. Chute - is a channel having steep slopes.
Natural chute (falls) on the left and man-made logging chute on the right on the Coulonge River, Quebec, Canada
The spillway of Leasburg Diversion Dam is a vertical hard basin drop structure designed to dissipate energy
Drop - is similar to a chute, but the change in elevation is within a short distance.

13. Stormwater sewer - is a drain or drain system designed to drain excess rain from paved streets, parkinglots, sidewalks and roofs.
Storm drain receiving urban runoff
Storm sewer

14. 1.3 Types / Classification of Open Channel Flows
Open channel flow conditions can be characterised with respect to space (uniform or non-uniform flows) and time (steady or unsteady flows).
Space - how do the flow conditions change along the reach of an open channel system.
a. Uniform flow - depth of flow is the same at every section of the flow dy/dx = 0
b. Non-uniform flow - depth of flow varies along the flow dy/dx  0
Time - how do the flow conditions change over time at a specific section in an open channel system.
c. Steady flow - depth of flow does not change/ constant during the time interval under consideration dy/dt = 0
d. Unsteady flow - depth of flow changes with time dy/dt  0

15. 1.3 Types / Classification of Open Channel Flows
a. Uniform flow y
Constant water depth
b. Non-uniform flow y1 y2
Depth changes along the channel
c. Steady flow y
Time = t1
Time = t2 y1
Time = t1
Time = t2
d. Unsteady flow y t3 t2 t1 y t3 t2 t1

16. Gradually-varied flow Rapidly-varied flow
Open channel flow
Steady flow
Unsteady flow
Uniform flow
Non-uniform flow
Gradually-varied flow
Rapidly-varied flow
Various types of open-channel flow

17. The flow is rapidly varied if the depth changes abruptly over a comparatively short distance. Examples of rapidly varied flow (RVF) are hydraulic jump, hydraulic drop, flow over weir and flow under a sluice gate.
The flow is gradually varied if the depth changes slowly over a comparatively long distance. Examples of gradually varied flow (GVF) are flow over a mild slope and the backing up of flow (backwater).
RVF
GVF
RVF
GVF
RVF
GVF
RVF
Sluice
Hydraulic jump
Flow over weir
Hydraulic drop
Contraction below the sluice

18. 1.4 State of Flow
The state or behaviour of open-channel flow is governed basically by the viscosity and gravity effects relative to the inertial forces of the flow.
Effect of viscosity - depending on the effect of viscosity relative to inertial forces, the flow may be in laminar, turbulent, or transitional state.
- Reynolds number represents the effect of viscosity relative to inertia,
where V is the velocity, R is the hydraulic radius of a conduit and  is the kinematic viscosity (for water at 20C,  =  106 m2/s, dynamic viscosity  =  103 Ns/m2 and density  = kg/m3).
Re < 500 , the flow is laminar
500 < Re < 12500, the flow is transitional
Re > , the flow is turbulent

19. Re < 500 , the flow is laminar
500 < Re < 12500, the flow is transitional
Re > , the flow is turbulent
The flow is laminar if the viscous forces are dominant relative to inertia. Viscosity will determine the flow behaviour. In laminar flow, water particles move in definite smooth paths.
The flow is turbulent if the inertial forces are dominant than the viscous force. In turbulent flow, water particles move in irregular paths which are not smooth.

20. 1.4 State of Flow
Effect of gravity - depending on the effect of gravity forces relative to inertial forces, the flow may be subcritical, critical and supercritical.
- Froude number represents the ratio of inertial forces to gravity forces,
where V is the velocity, D is the hydraulic depth of a conduit and g is the gravity acceleration (g = 9.81 m/s2).
Fr < 1 , the flow is in subcritical state
Fr = 1 , the flow is in critical state
Fr > 1 , the flow is in supercritical state

21. 1.5 Regimes of Flow
A combined effect of viscosity and gravity may produce any one of the following four regimes of flow in an open channel:
a. subcritical - laminar , when Fr < 1 and Re < 500
b. supercritical - laminar , when Fr > 1 and Re < 500
c. supercritical - turbulent , when Fr > 1 and Re > 12500
d. subcritical - turbulent , when Fr < 1 and Re > 12500