Types of flow in open channel, Most Economical channel section

1. FLOW IN OPEN CHANNELS
QUEST CAMPUS
LARKANA
DEPARTMENT OF
CIVIL ENGINEERING

2. Introduction
◦ When the surface of flow is open to atmosphere, in other terms
when there is only atmospheric pressure on the surface, the flow
is named as open channel flow.
◦ The governing force for the open channel flow is the gravitational
force component along the channel slope apart from inertia and
viscous forces.
◦ Water flow in rivers and streams are obvious examples of open
channel flow in natural channels.
◦ Other occurrences of open channel flow are flow in irrigation
canals, sewer systems that flow partially full, storm drains, and
street gutters.
◦ The flow in a pipe takes place due to difference of pressure
(pressure gradient), whereas in open channel it is due to the
slope of the channel bed (i.e.; due to gravity).

5. Classification of Open
Channel Flows
◦ Artificial Channel: Artificial open channels are built for
some specific purpose, such as irrigation, water supply,
water power development etc. Such channels are regular
in shape and alignment. Surface roughness is also
uniform.
◦ Natural channels: The irregular sections of varying
shapes are the natural channels. Ex. Rivers, streams and
drains etc.

6. Classification of Open
Channel Flows
Depending upon the shape, a channel is either prismatic
or non-prismatic.
A channel is said to be prismatic when the cross section is
uniform and the bed slope is constant.
Ex. Rectangular, trapezoidal, circular, parabolic.
A channel is said to be non-prismatic when its cross
section and for slope change.
Ex: River, Streams & Estuary.

7. FLOW CLASSIFICATION
◦Steady & unsteady flow.
◦Uniform and Non uniform flow
◦Laminar flow and turbulent flow
◦Sub critical , Critical and supercritical flow.

8. a) Steady and Unsteady
Open Channel Flow
A flow in a channel will said to be steady If the flow
Characteristics like depth, discharge and mean velocity at any
point within cross-section of an open channel is not changing
with time, then the flow is steady flow, otherwise it is called as
unsteady flow.
Away from the down stream of any obstruction in a channel like
regulator, barrage etc flow is considered steady flow.
Flood flows in rivers and rapidly varying surges in canals are
some examples of unsteady flows.
Unsteady flows are considerably more difficult to analyze than
steady flows..

9. b) Uniform and Non-Uniform
Open Channel Flow:
◦ If the flow depth along the channel is not changing at
every cross-section for a taken time, then the flow is
uniform flow. If the flow depth changes at every cross-
section along the flow direction for a taken time, then it is
non-uniform flow.
◦ Non-uniform flow is also called varied flow which can be
further classified as: Gradually varied flow (GVF and
Rapidly varied flow (RVF)
◦ A prismatic channel carrying a certain discharge with a
constant velocity is an example of uniform flow.

11. Gradually varied and rapidly varied flow
◦ In real-life projects, however, channel cross sections and bottom
slopes are not constant with distance in natural channels and these
are varied in constructed channels to suit the existing topographical
conditions for economic reasons.
◦ In addition, hydraulic structures are provided for flow control. These
changes in the channel geometry produce nonuniform flows while
changing from one uniform-flow condition to another.
◦ such flows are called gradually varied flows if the rate of variation of
depth with respect to distance is small, and rapidly varied flows if the
rate of variation is large.
◦ For nonuniform open-channel flow, the cross sectional area, depth,
and velocity vary along the channel. The flow is classified as
gradually varied flow when the change of the fluid depth along the
channel dy/dx is much less than one.

12. Gradually varied and
rapidly varied flow
◦ In other words, the flow depth changes gradually over a long distance
in gradually varied flows and in a short distance in rapidly varied
flows. Since the analysis of gradually varied flows is usually done for
long channels, the friction losses due to boundary shear have to be
included.
◦ These losses, however, may be neglected in the analysis of rapidly
varied flows because the distances involved are short. In addition, the
pressure distribution in gradually varied flow may be assumed
hydrostatic because the streamlines are more or less straight and
parallel.

13. Gradually varied and rapidly varied flow
◦ However, this is not the case in rapidly varied flows where
significant acceleration normal to flow direction may be produced by
sharp curvatures in the streamlines
◦ If the water depth in a flow varies at every cross-section along the
channel but does not vary with time at each cross-section, it is steady
varied flow other wise unsteady varied flow.

15. Identify GVF, RVF and uniform flow in different sections

16. 16
Spatially-varied flow
Varied flow classified as GVF and RVF assumes that no
flow is externally added to or taken out of the canal
system. The volume of water in a known time interval is
conserved in the channel system. In steady-varied flow the
discharge is constant at all sections.
However, if some flow is added to or abstracted from the
system the resulting varied flow is known as a spatially
varied flow (SVF).

17. Laminar & Turbulent flow
◦ For laminar flow to occur, the cross section must be extremely small,
the velocity very small, or the kinematic viscosity extremely high.
◦ Pipe flow has a lower critical Reynolds number of 2000, and this same
value may be applied to an open channel when the diameter D is
replaced by R, R is the hydraulic radius, defined as the cross-sectional
flow area of the channel divided by the wetted perimeter.
◦ In the range of Reynolds number, based on R in place of D, R = VR/v
< 500 flow is laminar, 500 < R < 2000 flow is transitional and may be
either laminar or turbulent, and R > 2000 flow is generally turbulent.
◦ Most open-channel flows are turbulent, usually with water as the
liquid.

19. Sub critical, super critical
and critical Flow
◦ When flow occurs at low velocities so that a small
disturbance can travel upstream and thus change upstream
conditions, it is said to be sub critical or tranquil flow
(the Froude number F < 1).
◦ Conditions upstream are affected by downstream
conditions, and the flow is controlled by the downstream
conditions.

20. Sub critical, super critical
and critical Flow
◦ When flow occurs at such high velocities that a small
disturbance, such as an elementary wave is swept downstream,
the flow is described as shooting or rapid or super critical flow
(F > 1).
◦ Small changes in downstream conditions do not effect any
change in upstream conditions; hence, the flow is controlled by
upstream conditions.
◦ When flow is such that its velocity is just equal to the velocity
of an elementary wave, the flow is said to be critical (F = 1).

21. Velocity DistributionVelocity Distribution
◦ The velocity at a solid boundary must be zero, and in open-
channel flow it generally increases with distance from the
boundaries.
◦ The maximum velocity does not occur at the free surface but is
usually below the free surface a distance of 0.05 to 0.25 of the
depth.
◦ The average velocity along a vertical line is sometimes
determined by measuring the velocity at 0.6 of the depth, but a
more reliable method is to take the average of the velocities at
0.2 and 0.8 of the depth, according to measurements of the U.S.
Geological Survey.

23. Geometric properties of open channels
◦ Depth of flow (y): It is the vertical distance between the
lowest points of the channel sections from the free liquid
surface. It is expressed in meters it is also called hydraulic
depth.
◦ Top width (T): It is the width of the channel at the free
surface as measured perpendicular to the direction of flow at
any given section. It is expressed in meters.
◦ Wetted perimeter (P): It is the total length of the channel
boundary in contact with the flowing liquid at any section. It
is expressed in meters.
◦ Hydraulics radius or Hydraulic mean depth (R): It is the ratio
of area of cross section (A) to the wetted perimeter (P). t is
expressed in meters.
◦ R= A/P

24. Hydraulic mean depth

25. Geometric properties of open channels
◦ Hydraulic Slope (S/i): Hydraulic slope of the total energy
line is defined as the ratio of drop in total energy line (hf)
to the channel length (L). It is also called hydraulic
gradient.
◦ S or i =hf/L
◦ Freeboard: Vertical distance between the highest water
level anticipated in the design and the top of the retaining
banks. It is a safety factor to prevent the overtopping of
structures.

27. Most Economical Channel
Section

28. 28
Most common shapes of prismatic channels

29. 29
◦ Most economical section is called the best hydraulic
section or most efficient section as the discharge,
passing through a given cross-sectional area A, slope
of the bed S0 and a resistance coefficient, is
maximum.
◦ Hence the discharge Q will be maximum when the
wetted perimeter P is minimum.

30. 30
Economical Rectangular Channel
D,BA ×= BD2P +=
D
A
2DP +=
0
dD
dP
=
222
202
D
DB
D
A
D
A
dD
dP
==⇒=





−=
D
B
2 =⇒ 2
B
D =
P should be minimum for a given area;
D
D
DD
DD
DB
DB
P
A
Rh
4
2
22
2
2
2
=
+
×
=
+
×
==
So, the rectangular channel will be most economical when eitherthe
depth of the flow is half the width, or
the hydraulic radius is half the depth of flow.
2
D
Rh =

31. 31
Economical Trapezoidal Channel
D)Dn(BA +=
2
12 nDBP ++=
Dn
D
A
B −=
2
12 nD)Dn
D
A
(P ++−=
0
dD
dP
= ⇒=++−−= 012 2
2
nn
D
A
dD
dP
n
D
A
n12 2
2
+=+
D
DnB
n
D
DnD)(B
n
2
12 2
2 +
=+
+
=+ 2
Dn2B
n1D 2 +
=+
or
P B B n D B n D= + + = +2 2( )
R
A
P
B n D D
B n D
h = =
+
+
( )
( )2
R
D
h =
2

32. Economical Trapezoidal
Channel
◦ Therefore for a trapezoidal channel to be most economical
“ half the top width must be equal to one of the sloping
sides of the channel” and hydraulic mean radius is half of
the flow depth.

33. Economical Circular
Channel
◦ Most economical circular section is one whose
◦ Depth of flow is 0.94 to 0.95 of its dia

34. Economical Triangular
Channel
◦ a triangular channel section will be most economical or
most efficient when each of its sloping sides makes an
angle of 45 with the vertical.
◦ The hydraulic radius R of the channel section can be
expressed as