WRE 301: Open Channel Hydraulics

4.00 Credit, 4 hrs/week

Lectured by:
Sara Ferdousi
Assistant Professor
Dept. of WRE, BUET
 Syllabus
❑ Basic Concepts of Open Channel Flow
❑ Introduction
❑ Kinds of open Channel
❑ Channel Geometry
❑ Types of open channel
❑ Effects of viscosity and gravity
❑ Velocity distribution
❑ Velocity distribution coefficients
❑ Pressure distribution
❑ Specific Energy and Critical Flow
❑ Definitions
❑ Characteristics of specific energy curve
❑ Calculating critical depth for different channel cross sections
❑ Numerical methods for calculating critical depth
❑ Section factor and hydraulic exponent for critical flow
❑ Transition
❑ Flow measuring devices
 Syllabus
❑ Hydraulic Jump
❑ Hydraulic Jump and its classification
❑ Principle of momentum and specific force
❑ Sequent depth of hydraulic jump
❑ Characteristics of Hydraulic Jump
❑ Submerged jump
❑ Stilling basin

❑ Design of Channels
❑ Design of rigid boundary channel using best hydraulic section
❑ Design of mobile boundary channel by tractive force method
❑ Design of alluvium channel by Lacey’s approach

❑ Hydraulics of Bridges and culvert

 Books

❑ Open Channel Hydraulics by Ven Te Chow

❑ Flow through Open Channels by K G Ranga Raju
❑ Open Channel Flow by M Hanif Chaudhury
❑ Open Channel flow by Subramanya
 Introduction
❑ Open Channel Flow is a flow of fluid (basically
water)in a conduit with a free surface
❑ A free surface is a surface on which pressure is
equal to local atmospheric pressure
❑Open Channel flow is also known as free surface
flow
 Introduction
❑ Flows in rivers, canals are some examples of
natural OCF
❑ Flows in Irrigation, sewer system, aquaduct are
examples of artificial OCF
 Introduction
❑ OCF occurs under the action of gravity and at
atmospheric pressure
❑ Basically all open channels have a bottom slope
and flow occurs from upstream to downstream
along the slope
❑The component of gravity or weight of water
along the flow direction acts a driving force
❑For OCF to occur the total energy at upstream
must be greater than the total energy at down
stream section
Total head of a section
 Kinds of Open Channel

❑Natural and Artificial Channel

❑Prismatic and Non-Prismatic Channel
❑Rigid and Fixed Boundary Channel
❑Small and large slope Channel
 Kinds of Open Channel
❑ Natural and Artificial Channel:

➢ Natural Open Channels include all channels that naturally exist

in the earth.

➢ Example: River, tidal estuaries

➢ These channels are very irregular in shape

➢ Artificial channels are channels developed by men

➢ Laboratory flumes, irrigation canals, chutes, spillways,

➢ These channels are designed with regular geometric shape

 Kinds of Open Channel
❑ Prismatic and Non-Prismatic Channel

➢ A channel with constant X section and constant

bottom slope is called prismatic channel

➢ Otherwise it is non-prismatic channel

➢ All natural channels are generally non-prismatic

 Kinds of Open Channel
❑ Rigid and Mobile Boundary Channel

➢ A channel with immovable bed and sides are known as

rigid boundary channel

➢ Lined canals, sewers and non-erodible unlined canals are

examples of rigid boundary channels

➢ If the channel boundary is composed of loose sedimentary

particles moving under the action of flowing water the
channel is called mobile boundary channel

➢ An alluvial channel is a mobile boundary channel

 Kinds of Open Channel
❑ Small and large slope Channel

➢An open channel having a bottom slope greater

than 1 in 10 is called a large slope channel
otherwise it is a channel of small slope

➢The slopes of ordinary channels whether natural

or artificial are far less than 1 in 10
Kinds of Open Channel
Kinds of Open Channel
Kinds of Open Channel
Kinds of Open Channel
 Channel Geometry

❑A channel built with constant cross section

and constant bottom slope is called a
PRISMATIC CHANNEL
❑ Rectangle, trapezoid, triangle, parabola and
circle are the most used prismatic channels for
OCF
Channel Geometry
Geometric elements of Parabolic
Channel section
Geometric elements of Parabolic
Channel section
 Wide Channel
❑ when the width of a rectangular channel is very large
compared to the depth of the channel ( b>>h, B>10h)
then the sides of the channel has no influence on the
velocity distribution of the central region of the channel.
Such a channel is known as Wide channel.

❑ For a wide channel the hydraulic radius is

 State of Flow( Effect of Viscosity)

❑ The effect of viscous forces relative to inertia forces on

open channel flow is expressed by Reynolds number
(Re).
❑ The Reynolds number may be written as

❑ Here, µ= dynamic viscosity

ν=kinematic viscosity (µ/ρ)= 10-6 m2/s
 State of Flow( Effect of Viscosity)
❑ In OCF the characteristic length commonly used is the
hydraulic radius

❑ For most OCF including rivers and canals flows are turbulent.
❑ The Re are very high for most rivers of the order106
❑ The viscous forces are very weak relative to inertia forces. Therefore the Reynolds number
does not play significant role in determining state of low in OCF
 Velocity Distribution
❑ In open channels the velocity is not uniformly distributed
because of the presence of free surface and friction over
the channel bed and banks
❑ The velocity is zero at the solid boundary and gradually
increases with distance from the boundary
❑ The velocity distribution in a channel section also
depends upon,
➢ The channel geometry
➢ Roughness
➢ Presence of bends
 Velocity Distribution
❑ In a broad, rapid and shallow stream or in a smooth
channel the maximum velocity may often be found at the
free surface.
 Velocity Distribution
❑ The roughness of the channel will cause the curvature of
the vertical velocity distribution curve to increase.
 Velocity Distribution(maximum velocity)

❑ the measured maximum velocity usually occurs below

the free surface at a distance 0.05 to 0.25 of the depth of
flow(h)
❑ umax=10% to 30% higher than uxsectional mean
 Velocity Distribution(maximum velocity)

❑ The reason for this maximum velocity to be below the

surface is due to secondary currents and is a function of
aspect ratio ( ratio of depth to width)
❑ For a deep narrow channel, the location of maximum
velocity point will be much lower than the water surface
than for a wider channel of the same depth.
 Velocity Distribution

❑ In turbulent flow the variation of velocity along the

vertical can be approximated by logarithmic or power law
❑ The average of the velocities at 0.2 and 0.8 of the depth
of flow or at 0.6 of the depth of flow below the water
surface is approximately the average velocity of the
vertical section.
 Velocity Measurement

❑ the velocity of a flow can be measured with a current

meter
❑ It is standard practice by the US geological survey to
determine the average velocity in a vertical section by
measuring velocities at 0.2 and 0.8 depth of flow below
the free surface when the depth of flow is more than 0.61
m (2ft) .
❑ If depth of flow less than 0.61 m then 0.6 of the depth
from free surface the measurement is taken to determine
the average velocity
Velocity Distribution
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(area velocity method)
 Velocity Distribution
(Isovels)
❑ The lines with equal velocity at a cross section are
called isovels
Velocity Distribution
(Isovels)
 ❑ Flow in straight prismatic channels
are 3 dimensional
❑ Flow properties like velocity,
discharge vary in the
Velocity longitudinal(x), lateral(y) and
vertical(z) direction.
Distribution
❑ The variations of flow parameters in
Coefficients lateral and vertical directions are
usually small compared to those
longitudinal direction
❑ Consequently a majority of open
channel flow problems are analyzed
by considering that the flow is 1D
 ❑ Owing to nonuniform velocity
distribution in a channel section the
kinetic energy and momentum of
Velocity flow computed from the X–sectional
mean velocity are generally less
Distribution than their actual values
Coefficients ❑ To get the actual kinetic energy of
flow the KE computed from the
mean velocity of flow is multiplied
by a coefficient known as the
kinetic energy coefficient (α) or
Coriolis coefficient.
 ❑ Similarly to get the actual
momentum , the momentum
Velocity computed using the mean velocity
is multiplied by a coefficient known
Distribution as the momentum coefficient (β)
or Boussinesq coefficient.
Coefficients ❑ The energy and momentum
coefficients α and β together are
known as the velocity distribution
coefficients.
 Velocity Distribution Coefficients

❑ In 1D method of flow analysis, the discharge and mean velocity

in a channel are computed by taking a small elementary area ΔA.
❑ Let u be the velocity over an elementary area ΔA of the channel
X-section.
❑ Then, discharge Q passing through the area is given by

❑ The mean velocity of flow U for the entire section

 Velocity Distribution Coefficients

❑ The kinetic energy of flow passing ΔA per unit time is equal to,

❑ Here, ρ is the density of water

❑ The total KE of flow passing the channel section per unit time is

❑ The kinetic energy based on mean velocity U and corrected for

non-uniform distribution is
 Velocity Distribution Coefficients

❑ Equating the two quantities and rearranging we get,

 Velocity Distribution Coefficients

❑ The momentum of flow passing through ΔA area is

ρu ΔA x u=ρu² ΔA

❑ The total momentum of flow passing the channel section

per unit time
 Velocity Distribution Coefficients

❑ The total momentum based on mean velocity U and

corrected for non-uniform distribution of velocity is

❑ Equating both we get,

 Velocity Distribution Coefficients
❑ The energy and momentum coefficients are always
positive and never less than unity.
❑ For uniform velocity distribution in a channel section
the values are equal to unity
❑ In all other cases, α>β>1
❑ The further the velocity departs from uniform
distribution the greater the coefficients become
❑ The effect of turbulence is to make flow more uniform
over the channel section. Therefore the values of α,β
are higher for laminar flow than turbulent flow.
 Velocity Distribution Coefficients

❑ Experimental evidence suggest that when channels are

straight prismatic, and the flow is turbulent and uniform
or gradually varied the two velocity coefficients do not
exceed 1.10 and 1.04 respectively
❑ For channels with complex cross section , upstream of
weirs, in the vicinity of obstructions or when the flow is
concentrated in one part of the section values of α,β may
even be greater than 2.00 and 1.35 respectively
❑ Although their numerical values vary over a wide range
their ratio (α-1)/(β-1) vary only slightly from 2.8 to 3.0
Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients

The ratio of the velocity distribution coefficients

Velocity Distribution Coefficients
Velocity Distribution Coefficients
Velocity Distribution Coefficients
 Pressure Distribution

❑ The pressure distribution in a channel section depend on

flow condition
 Pressure Distribution

❑ The pressure at any point on the X-section of a channel

is measured by the height of water column
❑ Let us consider,

a water column of height=h

X-sectional area =ΔA

Pressure intensity at the bottom of the water

column=P
 Pressure Distribution

❑ Then,
F=Force due to pressure at the bottom of the column
=pressure x area
=P ( ΔA)

W=weight of water column acting vertically downward

=ρgh (ΔA)

Since the vertical component of resultant force acting on water is zero

F=W
P ( ΔA)=ρgh (ΔA)
P = ρgh
P=γh
 Pressure Distribution

❑ The pressure at any point is directly proportional to the

depth of the point below the free surface

❑ This is known as the hydrostatic distribution of pressure

and h is known as the hydrostatic pressure head

❑ Hydrostatic law of pressure distribution:

The pressure at any point in a fluid is directly proportional to the
depth of that point below water surface and varies linearly
 Pressure
Distribution
❑ Hydrostatic pressure
distribution holds true for
the following

➢ Streamlines are parallel in

a horizontal or small slope
channel
➢ Uniform flow or gradually
varied flow
➢ Curvature of streamlines
are very small
Pressure Distribution in Curvilinear flow

❑ When the curvature of streamlines are substantial then

flow is known as curvilinear flow

❑ The effect of curvature is to produce appreciable

accelerations

❑ In such cases acceleration normal to flow is not

negligible so pressure distribution is not hydrostatic

❑ Curvature can be either convex or concave

Pressure Distribution in Curvilinear flow
Pressure Distribution in Curvilinear flow
Pressure Distribution in Curvilinear flow
Pressure Distribution in Curvilinear flow
Pressure Distribution in Curvilinear flow
Effect of slope on Pressure Distribution
 Effect of slope on Pressure Distribution

❑ The pressure distribution departs from hydrostatic if the

slope of the channel is large
❑ Consider a water column of height h and x-sectional
area ΔA
❑ Now,
Weight of water column=unit weight X volume
Effect of slope on Pressure Distribution
Effect of slope on Pressure Distribution
Effect of slope on Pressure Distribution