INTRODUCTION :
Flow in open channels is defined as the flow
of a liquid with a free surface.
A free surface is a surface having constant
pressure such as atmospheric pressure.
Thus a liquid flowing at atmospheric
pressure through a passage is known as flow
in open channels.
In most of cases, the liquid is taken as water.
Hence flow of water through a passage
under atmospheric pressure is called flow in
open channels.
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CLASSIFICATION OF FLOW IN CHANNELS :
The flow in open channel is classified into the following types:
1. Steady flow and unsteady flow,
2. Uniform flow and non-uniform flow,
3. Laminar flow and turbulent flow, and
4. Sub-critical, critical and super critical flow.
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Steady Flow and Unsteady Flow.
If the flow characteristics such as depth of flow, velocity of flow, rate of flow at any
point in open channel flow do not change with respect to time, the flow is said to be
steady flow.
Mathematically, steady flow is expressed as
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Uniform Flow and Non-uniform Flow :
If for a given length of the channel,
the velocity of flow, depth of flow,
slope of the channel and cross-section
remain constant, the flow is said to be
uniform.
Mathematically, uniform and non-
uniform flow are written as:
Non-uniform flow in open channels is
also called varied flow, which is
classified in the following two types as:
(i) Rapidly Varied Flow (R.V.F.)
(ii) Gradually Varied Flow (G.V.F
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Laminar Flow and Turbulent Flow :
The flow in open channel is said to be laminar if the Reynold number (R) is less than 500 or 600.
Reynold number in case of open channels is defined as:
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Sub-critical, Critical and Super Critical Flow : where
The flow in open channel is said to be sub- V is Mean velocity of flow
critical if the Froude number (F) is less D = Hydraulic depth of channel and is equal to
the ratio of wetted area to the top width of
than 1.0.
channel
The Froude number is defined D = A/T
Here, T= Top width of channel.
Sub-critical flow is also called tranquil or
streaming flow.
For sub-critical flow, F, < 1.0.
Flow is called critical if F = 1.0
If F > 1.0, the flow is called super critical or
shooting or rapid or torrential.
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DISCHARGE THROUGH OPEN CHANNEL BY CHEZY'S FORMULA :
Discharge (Q) = A x V = A x C√mi
Here
A = Area of flow of water.
P = wetted perimeter of flow
i = slope of the bed,
V = Mean velocity of flow of water
m = A/P
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1. Find the velocity of flow and rate of flow of water through a rectangular channel of 6 m wide and 3 m
deep, when it is running full. The channel is having bed slope as 1 in 2000. Take Chezy's constant C = 55
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EMPIRICAL FORMULAE FOR THE VALUE OF CHEZY'S CONSTANT :
V = C√mi, is known Chezy's formula after the name of a French Engineer, Antoine Chezy
who developed this formula in 1975.
In this equation C is known as Chezy's constant, which is not a dimensionless co-
efficient.
The dimension of C is [L½ T-¹]
Hence the value of C depends upon the system of units.
The following are the empirical formulae, after the name of their inventors, used to
determine the value of C:
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MOST ECONOMICAL SECTION OF CHANNELS :
A section of a channel is said to be most economical when the cost of construction of the
channel is minimum.
But the cost of construction of a channel depends upon the excavation and the lining.
To keep the cost down or minimum, the wetted perimeter, for a given discharge, should
be minimum.
Most economical section is also called the best section or most efficient section.
The discharge, passing through a most economical section of channel for a given cross-
sectional area (A), slope of the bed (i) and a resistance co-efficient, is maximum.
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The conditions to be most economical for the following shapes of the channels will be
considered:
1. Rectangular Channel,
2. Trapezoidal Channel, and
3. Circular Channel
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Most Economical Rectangular Channel :
1. A = 2d²
2. b = 2d
3. m = d/2
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2. A rectangular channel of width, 4 m is having a bed slope of 1 in 1500. Find the
maximum discharge through the channel. Take value of C = 50
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Most Economical Trapezoidal Channel :
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Best Side Slope for Most Economical
Trapezoidal Section :
Area of trapezoidal section, A = (b + nd) x d
where
b = width of trapezoidal channel,
d = depth of flow, and
n = slope of the side of the channel
1. n = 1/√3
2. θ = 60°
3. b = 2d/√3
4. P = 6d/√3 = 3 x b
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Most Economical Circular Section :
In case of circular channels, for most economical section, two separate conditions are
obtained.
They are:
1. Condition for maximum velocity
2. Condition for maximum discharge.
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1. Condition for Maximum Velocity for Circular Section :
Fig. shows a circular channel through which water is flowing.
d = of water
2θ = angle subtended at the centre by water surface
R = of channel
i = slope of the bed,
Results :
1. θ = 128°45'
2. depth of flow = 0.81 x D
Here D = diameter of circular section
3. m = 0.31 x D
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2. Condition for Maximum Discharge for Circular Section :
Results :
1. θ = 154°
2. depth of flow = 0.95 x D
Here D = diameter of circular section
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