Lecture 3 - Open Channel Flow
Mashilo Nkgoeng
November 9, 2021
Contents
1 Introduction 1
1.1 Classification of Open Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Properties of Open Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Geometrical Properties for analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Discharge through OC by Chezy’s Formula 3
3 Values of Manning’s Roughness Coefficient for Straight Uniform Channels 4
4 Application of Bernoulli’s Equation in Open Channels 5
Abstract
An open channel is a flow system in which the top surface of the fluid is exposed to the atmosphere.
The term open channel refers to liquid flow that is not completely enclosed by solid boundaries (such as
in a river). Open-channel flow, a branch of hydraulics and fluid mechanics, is a type of liquid flow within
a conduit or in channel with a free surface, known as a channel. The other type of flow within a conduit
is pipe flow. These two types of flow are similar in many ways but differ in one important respect: the
free surface. Open-channel flow has a free surface, whereas pipe flow does not.
1 Introduction
Open channel flow (OCF) is simply defined as the flow of a liquid in a channel or conduit that is not com-
pletely filled. There is usually a surface that exists between the flowing fluid (water in most cases) and fluid
above it (air or atmosphere). Normally this fliuid is driven by its weight- gravitational force forces the the
fluid to flow downhill.
OCF’s are important in the world that we live in. Think about the drainage system and the flow of
water in rivers which is rather a bit complex because its not easy to mathematically model a river, well to
my knowledge but if it is a man-made dam then it is easier. Some of the examples of OCF’s that you may
remember are gutters of our houses, sewers, flow in canals, etc. OCF’s as we have said before invoves the
existence of a free surface.
1.1 Classification of Open Channel Flow
A channel in which the cross-sectional shape and size and also the bottom slope are constant is termed as
a prismatic channel. Most of the man made (artificial) channels are prismatic channels over long stretches.
The rectangle, trapezoid, triangle and circle are some of the commonly used shapes in made channels. All
natural channels generally have varying cross-sections and consequently are non-prismatic.
OCF is said to be uniform if the depth of flow does not vary along the channel, i.e. dy/dx = 0. When
the flow is non-uniform, it could either be rapidly varying flow (RVF) or gradually varying flow (GVF). So
according to Basal, OCF are classified as follows:
1
, 1. steady flow
2. unsteady flow
3. uniform flow
4. non-uniform flow
5. laminar flow
6. turbulent flow
7. sub-critical, critical and super-critical flow
Figure 1: Classification of Open Channel Flow
1. Steady flow - when depth of flow, velocity of flow, rate of flow at any point in the open channel flow
does not change wrt to time, the flow is considered steady, i.e.
∂V ∂Q ∂y
= 0, = 0, or =0
∂t ∂t ∂t
2. Unsteady flow - when the velocity of flow, depth of flow or rate of flow changes with respect to time.
∂V ∂Q ∂y
̸= 0, ̸= 0, or ̸= 0
∂t ∂t ∂t
3. Uniform flow - the length of the channel, the velocity of flow, the depth of flow, the slope of the channel
and the cross-section remain constant then the flow is considered to be uniform, i.e.
∂y ∂V
= 0, =0
∂S ∂S
A prismatic channel carrying a certain discharge with a constant velocity is an example of uniform
flow.
4. Non-uniform flow - if the above parameters do not remain constant, the flow is said to be non-
uniform,i.e.
∂y ∂V
̸= 0, ̸= 0
∂S ∂S
As mentioned before, non-uniform flow can be RVF or GVF. Check Figure 1 for an illustration. A
typical example of this kind of flow is the backwater water surface profile at the upstream of a dam.
2
Mashilo Nkgoeng
November 9, 2021
Contents
1 Introduction 1
1.1 Classification of Open Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Properties of Open Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Geometrical Properties for analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Discharge through OC by Chezy’s Formula 3
3 Values of Manning’s Roughness Coefficient for Straight Uniform Channels 4
4 Application of Bernoulli’s Equation in Open Channels 5
Abstract
An open channel is a flow system in which the top surface of the fluid is exposed to the atmosphere.
The term open channel refers to liquid flow that is not completely enclosed by solid boundaries (such as
in a river). Open-channel flow, a branch of hydraulics and fluid mechanics, is a type of liquid flow within
a conduit or in channel with a free surface, known as a channel. The other type of flow within a conduit
is pipe flow. These two types of flow are similar in many ways but differ in one important respect: the
free surface. Open-channel flow has a free surface, whereas pipe flow does not.
1 Introduction
Open channel flow (OCF) is simply defined as the flow of a liquid in a channel or conduit that is not com-
pletely filled. There is usually a surface that exists between the flowing fluid (water in most cases) and fluid
above it (air or atmosphere). Normally this fliuid is driven by its weight- gravitational force forces the the
fluid to flow downhill.
OCF’s are important in the world that we live in. Think about the drainage system and the flow of
water in rivers which is rather a bit complex because its not easy to mathematically model a river, well to
my knowledge but if it is a man-made dam then it is easier. Some of the examples of OCF’s that you may
remember are gutters of our houses, sewers, flow in canals, etc. OCF’s as we have said before invoves the
existence of a free surface.
1.1 Classification of Open Channel Flow
A channel in which the cross-sectional shape and size and also the bottom slope are constant is termed as
a prismatic channel. Most of the man made (artificial) channels are prismatic channels over long stretches.
The rectangle, trapezoid, triangle and circle are some of the commonly used shapes in made channels. All
natural channels generally have varying cross-sections and consequently are non-prismatic.
OCF is said to be uniform if the depth of flow does not vary along the channel, i.e. dy/dx = 0. When
the flow is non-uniform, it could either be rapidly varying flow (RVF) or gradually varying flow (GVF). So
according to Basal, OCF are classified as follows:
1
, 1. steady flow
2. unsteady flow
3. uniform flow
4. non-uniform flow
5. laminar flow
6. turbulent flow
7. sub-critical, critical and super-critical flow
Figure 1: Classification of Open Channel Flow
1. Steady flow - when depth of flow, velocity of flow, rate of flow at any point in the open channel flow
does not change wrt to time, the flow is considered steady, i.e.
∂V ∂Q ∂y
= 0, = 0, or =0
∂t ∂t ∂t
2. Unsteady flow - when the velocity of flow, depth of flow or rate of flow changes with respect to time.
∂V ∂Q ∂y
̸= 0, ̸= 0, or ̸= 0
∂t ∂t ∂t
3. Uniform flow - the length of the channel, the velocity of flow, the depth of flow, the slope of the channel
and the cross-section remain constant then the flow is considered to be uniform, i.e.
∂y ∂V
= 0, =0
∂S ∂S
A prismatic channel carrying a certain discharge with a constant velocity is an example of uniform
flow.
4. Non-uniform flow - if the above parameters do not remain constant, the flow is said to be non-
uniform,i.e.
∂y ∂V
̸= 0, ̸= 0
∂S ∂S
As mentioned before, non-uniform flow can be RVF or GVF. Check Figure 1 for an illustration. A
typical example of this kind of flow is the backwater water surface profile at the upstream of a dam.
2
