Hydraulics

BFC21103
Prepared by :

Noor Aliza Ahmad

Faculty of Civil Engineering and Built Environment ,
UTHM
Email : aliza@uthm.edu.my
 6 TOPIC FOR THIS SUBJECT

1. Introduction to Open
Channel Flow
2. Uniform Flow in Open Channel
3. Specific Energy and Control
Section
4. Non-Uniform Flow in Open
Channel
5. Hydraulic Structures
6. Hydraulic Machineries
Chapter 1.
Flow in Open Channel
 Learning Outcomes
At the end of this chapter, students should be able to:
i. Define and explain on types and states of flow
ii. Identify types of open channels
iii. Define open channel geometries
Open channel flow is flow of a liquid in a conduit with a free
surface subjected to atmospheric pressure.
Free surface
T

A y

 B
Datum
Figure. Sketch of open channel geometry

Examples: flow of water in rivers, canals, partially full sewers

and drains and flow of water over land.
 Tahan river
rapids

Stormwater Management and Road Tunnel

(SMART), Kuala Lumpur, Malaysia
Siberian meandering
river
Practical applications:
a. flow depth in rivers, canals and other conveyance
conduits,
b. changes in flow depth due to channel controls e.g. weirs,
spillways, and gates,
c. changes in river stage during floods,
d. surface runoff from rainfall over land,
e. optimal channel design, and others
1.1 Flow Parameters and Geometric Elements
a. Depth of flow y is the vertical measure of water depth.
Normal depth d is measured normal to the channel bottom.
d = y cos 
For most applications, d  y when   10%, e.g. cos 1° = 0.9998.

Free surface

Sw = water surface slope

So = bottom slope 
Datum
b. Flow or discharge Q is the volume of fluid passing a cross-
section perpendicular to the direction of flow per unit time.
Mean velocity V is the discharge divided by the cross-sectional
area
Q
V=
A

c. Wetted perimeter P is the length of channel perimeter that is

wetted or covered by flowing water.
T = top width

A = cross sectional area covered by

A y
flowing water
P

B = bottom width
d. Hydraulic radius R is the ratio of the flow area A to wetted perimeter P.

A
R=
P

e. Hydraulic depth D is the average depth of irregular cross section.

flow area A
D= = T
top width T

A y
P

B
Table. Open channel geometries
Area Top width Wetted perimeter
Channel section
A T P
T
y By B B + 2y
B
Rectangular
T

1 y zy2 2zy 2y 1 + z 2
z
Triangular
T
1 y By + zy2 B + 2zy B + 2y 1 + z 2
z
B
Trapezoidal
T
D2
D (2 − sin2 ) Dsin D
2
y 8
Circle
Activity 1.1

1m

2m
60°

3m
Find:
(a) Top surface width T, flow area A, wetted perimeter P, and
hydraulic radius R.
(b) If Q = 2.4 m3/s, determine the state of flow.
(a) Top surface width T, wetted area A, wetted perimeter P
and hydraulic radius R.
1
z= 
= 0.5774
tan60
T = B + 2zy P = B + 2y 1 + z 2

T = 3 + 2(0.5774 )(2) P = 3 + 2(2) 1 + 0.57742

T = 5.309 m P = 7.619 m

A
A = By + zy 2 R=
P
A = 3(2) + 0.5774(2)2 8.309
R=
7.619
A = 8.309 m2
R = 1.091 m
(b) If Q = 2.4 m3/s, determine the state of flow.

Q 2.4
v= = = 0.2888 m/s
A 8.309
V
Fr =
gD

VR
Re =

Activity 1.2

1m A1

A2 A4
2m A3

2m

1m 2m 4m 3m

Find:
(a) Flow area A
(b) Wetted perimeter P
(c) Hydraulic radius R
1.2 Types of Open Channel
• Prismatic and non-prismatic channels
Prismatic channel is the channel which cross-sectional
shape, size and bottom slope are constant. Most of the man-
made (artificial) channels are prismatic channels over long
stretches. Examples of man-made channels are irrigation
canal, flume, drainage ditches, roadside gutters, drop, chute,
culvert and tunnel.
All natural channels generally have varying cross-sections
and therefore are non-prismatic. Examples of natural
channels are tiny hillside rivulets, through brooks, streams,
rivers and tidal estuaries.
• Rigid and mobile boundary channels
Rigid channels are channels with boundaries
that is not deformable. Channel geometry and
roughness are constant over time. Typical
examples are lined canals, sewers and non-
erodible unlined canals.
Mobile boundary channels are channels with
boundaries that undergo deformation due to
the continuous process of erosion and
deposition due to the flow. Examples are
unlined man-made channels and natural rivers.
Canals
is usually a long and mild-sloped
channel built in the ground,
which may be unlined or lined
with stoned masonry, concrete,
cement, wood or bituminous
material.
Terusan Wan Muhammad Saman, Kedah

Griboyedov Canal, St. Petersburg, Russia

Flumes
is a channel of wood, metal, concrete, or masonry, usually
supported on or above the surface of the ground to carry
water across a depression.

This flume diverts water from White River,

Washington to generate electricity Bull Run Hydroelectric Project diversion flume
Open-channel flume in laboratory
Chute
is a channel having steep slopes.

Natural chute (falls) on the left and man-made logging chute on the
right on the Coulonge River, Quebec, Canada
Drop
is similar to a chute, but the change in elevation is within a
short distance.

The spillway of Leasburg Diversion Dam is a vertical hard basin drop structure
designed to dissipate energy
Stormwater sewer
is a drain or drain system
designed to drain excess rain
from paved streets, parkinglots,
sidewalks and roofs.

Storm sewer

Storm drain receiving urban runoff

1.3 Types and Classification of Open Channel
Flows
Open channel flow

Steady flow Unsteady flow

Uniform flow Non-uniform flow

Rapidly-varied flow Gradually-varied flow

Various types of open-channel flow

Open channel flow conditions can be characterised with
respect to space (uniform or non-uniform flows) and time
(steady or unsteady flows).

Space - how do the flow conditions change along the reach

of an open channel system.

a. Uniform flow - depth of flow is the same at every

section of the flow dy/dx = 0

b. Non-uniform flow - depth of flow varies along

the flow dy/dx  0
a. Uniform flow

y
y
x

dy
Depth of flow is the same at every section along the channel, =0
dx

b. Non-uniform flow

y1
y2

dy
Depth of flow varies at different sections along the channel, 0
dx
Time - how do the flow conditions change over time at a
specific section in an open channel system.

c. Steady flow - depth of flow does not change/ constant

during the time interval under
consideration dy/dt = 0

d. Unsteady flow - depth of flow changes with time

dy/dt  0
c. Steady flow
y1 y2 y1 = y2
Time = t1 Time = t2
dy
Depth of flow is the same at every time interval, =0
dt

d. Unsteady flow
t3
t1
y1 t2 y1  y2  y3

dy
Depth of flow changes from time to time, 0
dt
The flow is rapidly varied if the depth changes abruptly over
a comparatively short distance. Examples of rapidly varied
flow (RVF) are hydraulic jump, hydraulic drop, flow over weir
and flow under a sluice gate.

The flow is gradually varied if the depth changes slowly over

a comparatively long distance. Examples of gradually varied
flow (GVF) are flow over a mild slope and the backing up of
flow (backwater).
 RVF GVF RVF GVF RVF GVF RVF

Hydraulic Flow over

Sluice jump weir

Hydraulic
drop
Contraction
below the sluice
 1.4 State of Flow
The state or behaviour of open-channel flow is governed
basically by the viscosity and gravity effects relative to the
inertial forces of the flow.
Effect of viscosity - depending on the effect of viscosity
relative to inertial forces, the flow may be in
laminar, turbulent, or transitional state.
- Reynolds number represents the effect of
viscosity relative to inertia,
VR
Re =
where V is the velocity, R is the hydraulic radius of a

conduit and  is the kinematic viscosity (for water at
20C,  = 1.004  10−6 m2/s, dynamic viscosity  =
1.002  10−3 Ns/m2 and density  = 998.2 kg/m3).
Re < 500 → the flow is laminar
500 < Re < 12500 → the flow is transitional
Re > 12500 → the flow is turbulent

VR
Re =


The flow is laminar if the viscous forces are dominant

relative to inertia. Viscosity will determine the flow
behaviour. In laminar flow, water particles move in
definite smooth paths.

The flow is turbulent if the inertial forces are dominant

than the viscous force. In turbulent flow, water particles
move in irregular paths which are not smooth.
Effect of gravity - depending on the effect of gravity forces
relative to inertial forces, the flow may be
subcritical, critical and supercritical.

- Froude number represents the ratio of

inertial forces to gravity forces,

V
Fr =
gD

where V is the velocity, D is the hydraulic

depth of a conduit and g is the gravity
acceleration (g = 9.81 m/s2).
Fr < 1 , the flow is in subcritical state → V  gD
Fr = 1 , the flow is in critical state
→ V = gD
Fr > 1 , the flow is in supercritical state
→ V  gD
1.5 Regimes of Flow

A combined effect of viscosity and gravity may produce any

one of the following four regimes of flow in an open channel:

a. subcritical - laminar , when Fr < 1 and Re < 500

b. supercritical - laminar , when Fr > 1 and Re < 500

c. supercritical - turbulent , when Fr > 1 and Re > 12500

d. subcritical - turbulent , when Fr < 1 and Re > 12500

Thank You