open channel hydraulics

1. Chapter 1
OPEN CAHNNEL FLOW

2. Introduction
Open channel: is a conduit for flow, which has a
free surface, i.e. a boundary, exposed to the
atmosphere.
Hence, open channel flow is a flow in which the
flowing fluid is subjected to atmospheric
pressure.

3. Examples of Open Channel Flow
The natural drainage of water through the
numerous creek and river systems.
The flow of rainwater in the gutters of our
houses.
The flow in canals, drainage ditches, sewers,
and gutters along roads.
The flow of small rivulets, and sheets of water
across field or parking lots.
The flow in the chutes of water rides. 5

6. Open Channel Flow Vs Pipe flow
Open channel flow Pipe flow
Has free surface subjected
to atmospheric pressure
Is confined in closed
conduit, exerts no direct
atmospheric pressure but
hydraulic pressure.
the motion is usually
caused by gravity effects
Flow is due to pressure
difference
HGL coincides with the
free flow surface
HGL is indicated by a
piezometer.
X-section of flow is not
fixed
Fixed/stationary
The analysis is
complicated
Relatively easier.

7. Open Channel Flow Vs Pipe flow

8. It is much more difficult to solve problems of flow in
open channels than in pressure pipes. Because:
In open channels the position of the free surface is
likely to change with respect to time and space,
Depth of flow (y), discharge (Q), and bottom slope
(S) and slope of the free surface are interdependent.
Physical condition of open channels vary more
widely than that of pipes.
Cross section of open channel is widely variable and
even might not be ridged,

9. Classification of flows
Open channels flow can be classified into many types
and described in various ways.
A) Classification according to the change in flow depth
with respect to time and space:
1) Steady flow and Unsteady flow (time as a criteria)
Steady flow: the depth of flow does not change.
In steady flow the flow variables (velocity, pressure,
density, flow path etc) do not vary with time at the
spatial point in the flow.
Unsteady Flow: the depth of flow changes with time.
Example: flood, surges and waves

11. Classification of flows
2) Uniform and Non uniform flow (space as a
criteria)
Uniform flow: the depth of flow is the same at every section
of the channel
Uniform flow can be steady or unsteady depending on
whether or not the depth changes with time
Non-uniform (Varied flow): the depth of flow change along
the length of the channel
Non-uniform can be gradually varied flow (GVF) or rapidly
varied flow (RVF)
Gradually varied flow: when the depth of flow changes
gradually

12. Classification of flows
Rapidly varied flow (RVF): when the depth of flow
changes abruptly over a comparatively a short distance
Example: hydraulic jump and hydraulic drop

13. Classification Based on Dimensionless
Number
 Reynolds Number
 Froude Number
These numbers help us to understand the different
type of fluid flow, fluid properties and the
mechanism by which entrained particles move.

14. 1) Reynolds Number
V is the average velocity of the fluid.
R = ρVR / μ R is the hydraulic radius of the channel.
e h h
Laminar flow: Re < 500.
Transitional flow: 500-12500
Turbulent flow: Re > 12,500.
Most open-channel flows involve water (which has a
fairly small viscosity) and have relatively large
characteristic lengths, it is uncommon to have laminar
open-channel flows.
10

15. Reynolds classified the flow type according to the motion of the fluid.
Laminar Flow: every fluid molecule
followed a straight path that was
parallel to the boundaries of the tube.
Turbulent Flow: every fluid molecule
followed very complex path that led to
a mixing of the dye.
Transitional Flow: every fluid
molecule followed wavy but parallel
path that was not parallel to the
boundaries of the tube.
15

16. • The flow is laminar if the viscous forces are so
strong relative to the inertial forces that viscosity plays
a significant part in determining flow behavior. In
laminar flow, the water particles appear to move in
definite smooth paths, or streamlines, and
infinitesimally thin layers of fluid seem to slide over
adjacent layers.
• The flow is turbulent if the viscous forces are weak
relative to the inertial forces. In turbulent flow the
water particles move in irregular paths, which are
neither smooth nor fixed but which in the aggregate
still represent the forward motion of the entire stream.
• Between the laminar and turbulent status there is a
mixed, or transitional state.
• An open channel flow is laminar if the Reynolds
number Re is small and turbulent if Re is large.

17. 2) Froude Number
The Froude number is a dimensionless number
proportional to the square root of the ratio of the
inertial forces over the weight of fluid:
Fr = fluid inertial forces .
gravitational forces in flow

18. Fr = V / gl
Critical Flow: Froude number Fr =1.
Subcritical Flow: Froude number Fr <1.
Super critical Flow: Froude number Fr >1.
11
• It compares the tendency of a moving fluid
(and a particle borne by that fluid) to continue
moving with the gravitational forces that act to
stop that motion

19. • When Fr2 is equal to unity:
V2=gd, and the flow is said to be critical state.
• If Fr2 is less than unity, or V < gd, the flow is sub
critical. In this state the role played by gravity force is
more pronounced; so the flow has low velocity and is
often described as tranquil and streaming.
• If Fr2 is greater than unity, or V > gd, the flow is
supercritical. In this state the inertia forces become
dominant; so the flow has high velocity and is usually
described as rapid, shooting, and torrential.

20. Basic Hydraulic Principles
• Geometric elements are properties of a channel section
that can be defined entirely by the geometry of the section
and depth of flow.
• These elements are very important and are used
extensively in flow computation.
• The definition of several geometric elements of basic
importance are given below.
 Geometric Elements of Channel Section

21. • Depth of flow (y) :is the vertical distance
of the lowest point of a channel section
from the free surface.
• Depth of flow section (d) :depth of flow
normal to direction of flow.
• Stage (h) :elevation of the free surface
from a datum.
• Top width ( T) :width of the channel
section at the free surface.
• Wetted area (A) :cross sectional area of
flow normal to the direction of flow.

22. Continuity principle
• Matter cannot be created nor destroyed.
• Hence, fluid must be entering a control volume at the same rate at
which it leaves.
• Rate implies a rate of mass transfer.
• For incompressible fluid ‘rate’ can be interpreted as rate volumetric
transfer.
• Therefore, the equation of continuity for steady flow of an
incompressible fluid is given by
• A = the cross-sectional area in sections 1 and 2,
• V = the mean velocity in sections 1 and 2
2
2
1
1 A
V
A
V
Q





23. Application of the continuity principle to
unsteady channel flow
• In unsteady open channel flow the
water surface will change over a certain
distance ∆X and during a certain time
∆t.
• During ∆t : Inflow-Outflow = Storage
• As the velocity and the discharge will
change over a distance.
S
B
x
y
t
Q 




  .
/
: 1
2 x
x
Q
Q
Q
Q
x 




 

0



t
y
B
x
Q
S




24. Reading Assignment
Energy Principle
• The energy equation is used in addition to
the continuity equation in analyzing fluid-
flow situations. It is derived from Newton’s
second law of motion.
Momentum Principle
• According to Newton's second law of

25. Specific Energy and Critical Depth
• If the datum coincides with the channel
bed at the cross-section, the resulting
expression is know as specific energy
and is denoted by E.
• Thus, specific energy is the energy at a
cross-section of an open channel flow
with respect to the channel bed.
• The “Specific energy” is the average
energy per unit weight of water with
g
V
y
ES
2
2




26. • For a given section and constant
discharge (Q), the specific energy is a
function of water-depth only, since
Q=vA .
• When the depth of flow is plotted
against the specific energy for a given
channel section and discharge, a
specific-energy curve is obtained
2
2
2
2 S
s
B
y
g
Q
y
E 



27. • Two Limbs, (AC & CB) Line , OD (450)
• At any point P on this curve, the ordinate
represents the depth, and the abscissa

28. Cont.
• The curve shows that for a certain discharge Q two flow regimes
are possible, viz. slow and deep flow or a fast and shallow flow,
• i.e. for a given specific energy, there are two possible depths, for
instance, the low stage y1 and the high stage y2.
• The low stage is called the alternate depth of the high stage, and
vice versa.
• At pint C, the specific energy is minimum. It can be proved that
this condition of minimum specific energy corresponds to the
critical state of flow.
• Thus, at the critical state the two alternate depths apparently
become one, which is known as the critical depth (YC).

29. The Critical Flow Condition
• The condition of minimum specific energy
is known as the critical flow condition and
the corresponding depth yc is known as
critical depth.
• At critical depth, the specific energy is
minimum. Thus differentiating the above
Equ. with respect to y (keeping Q1
constant) and equating to zero,
2
2
2 A
g
Q
y
ES 

dy
dA
A
g
Q
dy
E
d S
3
2
1

 The basic equation governing the critical flow conditions in a channel

30. Critical Depth and Velocity for Rectangular Section

31. Exercise: 1
A flow of 5.0 m3/sec is passing at a depth of 1.2m through
a rectangular channel of width 2.0 m. What is the specific
energy of the flow? What is the value of the alternate
depth to the existing depth?

32. Exercise: 2
A rectangular channel 3 m wide has a specific energy of 1.7
m when carrying a discharge of 5 m3/sec. Calculate the
alternate depths and corresponding Froude numbers.
B=
3

33. Transitions
Channel with a Hump
a) Subcritical Flow
Consider a horizontal, frictionless rectangular
channel of width B carrying discharge Q at
depth y1.
Let the flow be subcritical. At a section 2 (Fig.
below) a smooth hump of height ΔZ is built
on the floor. Since there are no energy losses
between sections 1 and 2, construction of a
hump causes the specific energy at section 2
to decrease by ΔZ.
Channel Transition with a Hump

34. • Thus the specific energies at sections 1 and
2 are,
• Since the flow is subcritical, the water
surface will drop due to a decrease in the
specific energy. In (Fig. below), the water
surface which was at P at section 1 will
come down to point R at section 2. The
depth y2 will be given by,
Specific energy diagram

35. It is easy to see from Fig. (5.13) that as the
value of ΔZ is increased, the depth at
section 2, y2, will decrease. The minimum
depth is reached when the point R
coincides with C, the critical depth. At this
point the hump height will be maximum,
ΔZmax, y2 = yc = critical depth, and E2 = Ec
= minimum energy for the flowing
discharge Q. The condition at ΔZmax is
given by the relation,

36. If y1 is in the supercritical flow regime, (Fig.
below) shows that the depth of flow
increases due to the reduction of specific
energy. In Fig. (5.13) point P` corresponds to
y1 and point R` to depth at the section 2. Up
to the critical depth, y2 increases to reach yc
at ΔZ = ΔZmax. For ΔZ > ΔZmax , the depth
over the hump y2 = yc will remain constant
and the upstream depth y1 will change. It
will decrease to have a higher specific
energy E1`by increasing velocity V1. The
b) Supercritical Flow
Variation of y1 and y2 in supercritical flow over a hump

37. Uniform Flow
Uniform flow in open channels has the following main characteristics
a. the depth, water area, velocity, and discharge at every section of
the channel are constant;
b. the energy line, water surface, and channel bottom are all parallel;
i.e. their slopes are all equal Sf = Sw = So
 Uniform flow is considered to be steady only, since unsteady
uniform flow is practically nonexistent. In natural streams,
even steady uniform flow is rare, for rivers and streams in
natural states scarcely ever experience a strict uniform flow
condition.

38. Establishment of uniform flow
• When flow occurs in an open channel,
the water encounters resistance as it
flows downstream.
• This resistance is generally
counteracted by the components of
gravity forces acting on the body of the
water in the direction of motion.
• A uniform flow will be developed if the
resistance is balanced by the gravity
forces
• In general, uniform flow can occur only

39. Computation of Uniform flow

40. The Manning equation is given by the SI
system of units
V = 1/n R2/3 S1/2
Where
V = average velocity
R = hydraulic radius
S = channel longitudinal slope
n = Channel roughness /resistance

41. Example 1
Find the velocity of flow and rate of flow
of water through a rectangular channel of
6m wide and 3m deep, when it is running
full. The channel is having bed slope as
1:2000. take chezy’s constant C=55. Ans.
V= 1.5m/s Q=27.1 m3/s
Example 2
Find the bottom slope for a rectangular channel which have
3m width and 2m depth. The unit flow rate is 1.5 m2/s. take
manning roughness of the channel 0.04.