# open-channel-flow

```SAI RAJESWARI INSTITUTE OF TECHNOLOGY
Lingapuram (V), Proddatur, Y S R District – 516 362, A.P
Department of civil Engineering
Classification of flows,
Types of channels
Objectives
Understand how flow in open channels
differs from flow in pipes
Learn the different flow regimes in open
channels and their characteristics
Predict if hydraulic jumps are to occur
during flow, and calculate the fraction of
energy dissipated during hydraulic jumps
Learn how flow rates in open channels
are measured using sluice gates and
weirs
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Classification of Open-Channel Flows
Open-channel flows are
characterized by the
presence of a liquid-gas
interface called the free
surface.
Natural flows: rivers,
creeks, floods, etc.
fresh-water aqueducts,
irrigation, sewers,
drainage ditches, etc.
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Classification of Open-Channel Flows
In an open channel,
Velocity is zero on bottom and sides of
channel due to no-slip condition
Velocity is maximum at the midplane of the
free surface
In most cases, velocity also varies in the
streamwise direction
Therefore, the flow is 3D
Nevertheless, 1D approximation is made with
good success for many practical problems.
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Classification of Open-Channel Flows
Flow in open channels is
also classified as being
uniform or nonuniform,
depending upon the
depth y.
Uniform flow (UF)
encountered in long
straight sections where
is balanced by elevation
drop.
Depth in UF is called
normal depth yn
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Classification of Open-Channel Flows
Obstructions cause the flow depth to vary.
Rapidly varied flow (RVF) occurs over a short distance
near the obstacle.
Gradually varied flow (GVF) occurs over larger distances
and usually connects UF and RVF.
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Classification of Open-Channel Flows
The wetted perimeter
does not include the
free surface.
Examples of Rh for
common geometries
shown in Figure at the
left.
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Froude Number and Wave Speed
OC flow is also
classified by the
Froude number
Resembles
classification of
compressible flow
with respect to Mach
number
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Specific Energy
For a channel with constant
width b,
Plot of Es vs. y for constant V
and b
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Specific Energy
This plot is very useful
Easy to see breakdown of Es into pressure (y)
Es   as y  0
Es  y for large y
Es reaches a minimum called the critical point.
There is a minimum Es required to support the
given flow rate.
Noting that Vc = sqrt(gyc)
For a given Es &gt; Es,min, there are two different
depths, or alternating depths, which can occur
for a fixed value of Es
A small change in Es near the critical point
causes a large difference between alternate
depths and may cause violent fluctuations in flow
level. Operation near this point should be
avoided.
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Uniform Flow in Channels
Uniform depth occurs
when the flow depth (and
thus the average flow
velocity) remains
constant
Common in long straight
runs
Flow depth is called
normal depth yn
Average flow velocity is
called uniform-flow
velocity V0
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Uniform Flow in Channels
Uniform depth is maintained as long as the slope,
cross-section, and surface roughness of the channel
remain unchanged.
During uniform flow, the terminal velocity reached, and
the head loss equals the elevation drop
We can the solve for velocity (or flow rate)
Where C is the Chezy coefficient. f is the friction
factor determined from the Moody chart or the
Colebrook equation
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Best Hydraulic Cross Sections
Same analysis can be
performed for a trapezoidal
channel
Similarly, taking the derivative
of p with respect to q, shows
that the optimum angle is
For this angle, the best flow
depth is
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
In GVF, y and V vary slowly,
and the free surface is stable
In contrast to uniform flow, Sf 
S0. Now, flow depth reflects
the dynamic balance between
gravity, shear force, and
inertial effects
To derive how how the depth
varies with x, consider the total
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Take the derivative of H
Slope dH/dx of the energy line is equal to negative of the
friction slope
Bed slope has been defined
Inserting both S0 and Sf gives
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Introducing continuity equation, which can be written as
Differentiating with respect to x gives
Substitute dV/dx back into equation from previous slide,
and using definition of the Froude number gives a
relationship for the rate of change of depth
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
This result is important. It
permits classification of liquid
surface profiles as a function of
Fr, S0, Sf, and initial conditions.
Bed slope S0 is classified as
Steep : yn &lt; yc
Critical : yn = yc
Mild : yn &gt; yc
Horizontal : S0 = 0
Initial depth is given a number
1 : y &gt; yn
2 : yn &lt; y &lt; yc
3 : y &lt; yc
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
12 distinct
configurations for
surface profiles in
GVF.
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Typical OC system
involves several
sections of different
slopes, with
transitions
Overall surface profile
individual profiles
described on previous
slides
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Rapidly Varied Flow and Hydraulic
Jump
Flow is called rapidly
varied flow (RVF) if the
flow depth has a large
change over a short
distance
Sluice gates
Weirs
Waterfalls
Abrupt changes in cross
section
Often characterized by
significant 3D and
transient effects
Backflows
Separations
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Rapidly Varied Flow and Hydraulic
Jump
Consider the CV
surrounding the
hydraulic jump
Assumptions
1. V is constant at sections
(1) and (2), and 1 and 2
1
2. P = gy
3. w is negligible relative to
the losses that occur
during the hydraulic jump
4. Channel is wide and
horizontal
5. No external body forces
other than gravity
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Rapidly Varied Flow and Hydraulic
Jump
Solving the quadratic equation and keeping only the
positive root leads to the depth ratio
Energy equation for this section can be written as
Head loss associated with hydraulic jump
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
Rapidly Varied Flow and Hydraulic
Jump
Experimental
studies
indicate that
hydraulic
jumps can be
classified into
5 categories,
depending
upon the
upstream Fr
ME33 : Fluid Flow
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Chapter 13: Open Channel Flow
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