1. Unit 4: Uniform flow Open channel flow
Dr A D Katdare
Associate Professor and (I/C) Head of department,
Department of Civil Engineering
Sanjay Ghodawat University, Kolhapur
2. Introduction to open channel flow
Open channel flow is a flow which has a
free surface and flows due to gravity.
In open channels, the flow is driven by
the slope of the channel rather than
the pressure
Top surface is under atmospheric
pressure
SGU/Civil/ADK/FM 2
Natural open channel flow
Manmade open channel flow
Does pipe running half full is pipe flow or open channel flow ?
3. Flow through pipes Vs open channel flow
SGU/Civil/ADK/FM 3
Open channel flow Pipe flow
Defines as a passage in which liquid flows
with its upper surface exposed to atmosphere.
A pipe is closed conduit which is used for
carrying fluids.
The flow is under gravity. Flow is under pipe pressure.
Flow conditions are greatly affected by slope
of channel.
Flow conditions s are greatly affected by pipe
pressure.
Hydraulic gradient line coincides with water
surface.
Hydraulic gradient line does not coincide with
water surface.
The maximum velocity occurs at a small
distance below water surface.
Maximum velocity occurs at pipe centre.
The shape of velocity profile is dependent on
channel roughness.
Velocity distribution is symmetrical about pipe
axis.
4. Classification of open channel
SGU/Civil/ADK/FM 4
1. Artificial or natural channel
2. Prismatic or non-prismatic channels
3. Rigid or mobile boundary channels
5. Types of flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow
4. Sub-critical, Critical and Super-critical Flow
SGU/Civil/ADK/FM 5
6. Types of flows
Steady and unsteady flow
Uniform and non-uniform flow
Gradually varied flow
Rapidly varied flow
Spatially varied flow
Subcritical, critical and super critical flow
SGU/Civil/ADK/FM 6
7. Laminar and Turbulent Flow
Both laminar and turbulent flow can occur in open channels depending on the Reynolds
number (Re).
Reynolds number in open channel is given by,
= Where,
ρ= density of fluid (for water ρ = 1000 kg/m3)
µ = dynamic viscosity
R = Hydraulic Mean Depth = Area / Wetted Perimeter
SGU/Civil/ADK/FM 7
Note the difference in Reynolds number for open channel flow and flow through pipe.
If Re ≤ 500, flow is laminar
If Re ≥ 2000, flow is turbulent
If 500 < Re < 2000, flow is translation
8. Subcritical, critical and super critical flow
Froud number is defined as,
SGU/Civil/ADK/FM 8
=
If Fr = 1, critical flow
If Fr <1, sub-critical flow or tranquil flow
If Fr > 1, super critical flow or rapid or shooting
flow
Subcritical laminar, Fr <1, Re ≤ 500
Supercritical laminar, Fr > 1, Re ≤ 500
Subcritical turbulent, Fr >1, Re ≥ 2000
Supercritical turbulent, Fr >1, Re ≥ 2000
10. Geometric elements
The geometric elements are the physical properties of a channel section which can be defined
by the flow depth and other dimensions of the channel section.
The depth of flow is ‘y’ is vertical distance of lowest point of a channel from free surface
‘T’ is top width of the free surface
‘A’ is wetted area or c/s area in direction normal to flow
‘P’ is wetter perimeter
Hydraulic radius ‘R’ is ratio of wetter area to wetted perimeter.
Section factor for critical flow computations is ‘Z’,
SGU/Civil/ADK/FM 10
=
=
12. Velocity Distribution in open channel flow
Velocity is always vary across channel because of friction along the boundary
The maximum velocity usually found just below the surface
SGU/Civil/ADK/FM 12
13. Discharge through open channel
Discharge though open channel is calculated by
•The Chezy’s equation
•The Ganguillet-Kutter formula
•The Bazin formula
• The Manning’s formula
SGU/Civil/ADK/FM 13
14. Chezy’s equation
It is used to determine velocity in open channel flow for uniform flow.
SGU/Civil/ADK/FM 14
15. Chezy’s equation
The main features of the uniform flow in in channel is as follows:
The depth of flow, wetted area, velocity of flow and discharge are constant at every section
along the channel reach.
The total energy line and water surface and the channel bottom are parallel to each other.
Newton’s second law of motion is to be applied for fluid in motion.
SGU/Civil/ADK/FM 15
16. Chezy’s equation
Forces acting on element are:
1. The force of hydrostatic pressure f1 and f2 on two ends of free body. As the depth is same, f1
and f2 are same and cancel each other.
2. The component of weight of water in a direction of flow, which is γ sin
3. The resistance to flow is exerted by wetted surface of the channel. It is given by, , τ0 is
average shear stress along boundary
SGU/Civil/ADK/FM 16
17. Chezy’s equation
For equilibrium of element, γ sin - = 0
SGU/Civil/ADK/FM 17
But it is known that, = Therefore, equating two equations,
= sin OR =
8
! =
8
!
The above equation can be written as,
= " ! This equation is known as Chezy’s equation and C is known as Chezy’s constant.
Or = sin
(Sin θ = s = Slope)
18. Chezy’s constant
C is known as Chezy’s constant
SGU/Civil/ADK/FM 18
# =
8
French scientist Antonnie Chezy derived this formula in 1775.
It varies inversely with fsquare root of f 9Darcy Weisbach friction
factor)
C has dimension of [L1/2T-1]
19. Formulae for Chezy’s C
• The Ganguillet-Kutter formula
SGU/Civil/ADK/FM 19
• The Bazin formula
20. Manning’s formula
In 1889, Irish scientist engineer Robert Manning presented a formula according to which the
mean velocity of flow in c channel is expressed in terms of coefficient of roughness n, called
Manning’s n, hydraulic radius R and bottom slope S.
It is given as,
SGU/Civil/ADK/FM 20
=
1
&
! /( )/
If we compare manning’s n and Chezy’s C, we get,
" =
1
&
)/*
