Hydraulics Notes 1 - One Slide On A Page

CE 356
HYDRAULIC ENGINEERING
Dr. Kwaku Amaning Adjei
Department of Civil Engineering
KNUST
Kumasi
Introduction to Hydraulics
The term hydraulics refers generally to

the study of the behaviour of Liquids.
The word “hydraulics” comes from the
Greek word hydraulikos meaning water.
Definition: It is the study of the
mechanical behaviour of water in
physical systems and processes. It
involves flows in open channels,
conduits, porous media, sediments and
other contaminants transported with
water.
2
Applications of Hydraulic Engineering
Hydraulic topics range through some

part of science and most of engineering
modules, and cover concepts such as:
Pipe flow,
Dam design,
Pumps, turbines, hydropower
Computational fluid dynamics
Flow measurement
River channel behavior and erosion etc
3
Hydraulic Engineering Projects
Provision of water
distribution and
wastewater
collection networks
Hydropower
China, Ghana...
Discharge of water
into the
environment
Flood control
Stream restoration
4
Differences Between Fluid Mechanics and Hydraulics
Fluid Mechanics Hydraulics

1. Theoretical 1. Empirical
2. Refers to both liquids 2. Refers to liquids (often
and gasses refers to Water)
3. Compressible and 3. Incompressible flows
incompressible Flows
5
Objective of this study
The application of engineering
principles and methods to the planning,
control, transportation, conservation
and utilization of water.
Scope of study
• Free surface flow (Open Channel Flow)
• Pipe Flow and Pipe Networks
• Hydrodynamic Machines (Emphasis on
Pumps)
• Dimensional Analysis and Hydraulic
Similitude
6
Open Channel Flow
Classification of Flows
Liquids are transported from one location to

another using
 Natural conveyance
 Constructed (artificial) conveyance
structures.
Flow passages may have cross sections that are
 Open
 Closed at the top.
 The structures with the closed tops are
referred to as closed conduits
 The structures with open tops are called
open channels.
8
Open-channel Flow (Free Surface Flow)
Flow in an open channel or closed conduit

having a free surface is referred to as
free-surface flow or open channel flow
(open channel Hydraulics).
If there is no free surface and the
conduit is flowing full, the flow is
called pipe flow, or pressurized flow.
Open channel flow occurs when a liquid
flows as a result of gravity, has a free
surface, and is also not under pressure
other than that caused by its own weight
and atmospheric pressure.
9
Examples of Open Channel Flow
Common examples of open channel flows:

Rivers.
Canals
Storm water drains
Irrigation canals
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Properties of Open Channels
Free water surface

Position of water surface can change in
space and time
Many different types
River, stream; canal, flume, or ditch; culverts
Many different cross-sectional shapes
11
Various Sections of Open Channels
12
Elements of Channel Section
Flow in an open channel is due to gravitational

forces; hence the channel bottom should have
a slope in the direction of………….?
Flow
UNIFORM FLOW
B
y
A
So
13
Definition of Geometric Elements
Gupta, Fig. 10.1
y = depth of flow A = flow area
d = depth of flow section R = hydraulic radius = A/P
T = top width D = hydraulic depth = A/T
P = wetted perimeter
Example 1
Compute the hydraulic radius and

hydraulic mean depth for a trapezoidal
channel
15
Example 2
Compute the hydraulic radius and

hydraulic mean depth for a smooth
concrete-lined channel
16
Velocity Distribution in Open-Channels
In an open channel,
Velocity is zero at the bottom and sides of the
channel due to no-slip condition
Velocity is maximum at the mid-plane of the
free surface
In most cases, velocity also varies in the
stream-wise direction
17
Velocity Distribution in Open-Channels
18
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) are
encountered in long
straight sections where
head loss due to friction
is balanced by elevation
drop.
Depth in UF is called
normal depth yn
For uniform flow, the velocity, depth, and

cross sectional area are constant along
the channel;
whereas for non-uniform flow, they vary in
the direction of the flow. The depth
associated with uniform flow is called the
normal depth.
20
Non-uniform flow can be further divided into
Rapidly-varied flow: Depth changes suddenly
Gradually-varied flow: Depth changes
gradually
Open-channel flow can also be classified as
steady and unsteady flow.
The flow is steady when the velocity and flow
depth at a given point do not change with time.
On the other hand, the velocity and flow depth
vary with time for unsteady flow.
21
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.’
State of Flow
Flow in open channels is affected by

viscous and gravitational effects
Viscous effects described by Reynolds
number, Re = VR/n
Gravitational effects described by Froude
number, F = V/(gD)1/2
23
Viscous Effects
For Re < 500, viscous forces dominate

and flow is laminar
For Re > 2000, viscous forces are weak
and flow is turbulent
For Re between 500 and 2000, there is a
transition between laminar and turbulent
flow
24
Gravitational Effects
Critical Velocity
Froude Number
V The mean velocity

Dm Hydraulic mean depth, A/B
Physically, the Froude number represents the
ratio of inertial forces to gravitational forces. It
also represents the ratio of fluid velocity to the
wave celerity.
25
Gravitational Effects
Critical flow is the point where velocity is

equal to the speed of a wave in the water
For F = 1, flow is critical
For F < 1, flow is subcritical
Wave can move upstream
For F > 1, flow is supercritical
Wave cannot move upstream
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A pebble is dropped into a channel
27
A pebble is dropped into a channel
28
Equations of Motion
There are three general principles used in

solving problems of flow in open channels:
Continuity (conservation of mass)
Energy
Conservation of Momentum
For problems involving steady uniform
flow, continuity and energy principles are
going to be applied
29
Conservation of Mass
Since water is essentially incompressible,

conservation of mass (continuity) reduces
to the following: discharge in = discharge
out
Stated in terms of velocity and area:
Q = V1A1 = V2A2
30
Control Volume for Open Channels
Gupta, Fig. 10.4

Conservation of Energy
Conservation of energy applied to

control volume results in the following:
2 2
V V
Z 1  y1   1  Z 2  y2   2
1
 hf 2
2g 2g
where Z1,Z2 are elevations of the bed,
y1, y2 are depths of flow,
V1, V2 are velocities,
1, 2 are kinetic energy corrections, and
hf is the frictional loss.
32
Energy Coefficient
The term associated with each velocity

head () is the energy coefficient
This term is needed because we are using
the average velocity over the depth to
compute the total kinetic energy
33
Uniform Flow
Equations are developed for steady-state

conditions
Depth, discharge, area, velocity all constant
along channel length
Rarely occurs in natural channels (even
for constant geometry) since it implies a
perfect balance of all forces
Two general equations in use: Chezy and
Manning formulas
34
Chezy Equation
Balances force due to weight of water in

direction of flow with opposing shear
force V  C RS
Note: V is mean velocity, R is hydraulic

radius (area/wetted perimeter), S is the
slope of energy gradeline, and C is the
Chezy coefficient
C is a function of the roughness of the
channel bottom
35
Manning Equation
The Manning equation is an empirical

relationship similar to Chezy equation:
1 2 / 3 1/ 2
V R S
n
Note: V is mean velocity (m/s), R is

hydraulic radius (m), S is the slope of
the energy gradeline (m/m), and n is the
Manning roughness coefficient
36
Manning’s Roughness (n)
Roughness coefficient (n) is a function of:

Channel material
Surface irregularities
Variation in shape
Vegetation
Flow conditions
Channel obstructions
Degree of meandering
37
Manning’s Equation
Using continuity equation (Q=VA),

Manning’s equation for English units
can be written as
1.486 2 / 3 1/ 2
Q AR S
n
 And for metric units

1 2 / 3 1/ 2
Q  AR S
n
39
Conveyance
For uniform flow, A, R and n are

constant thus
1 /2
Q  KS
The term K is conveyance, given as
K is a measure of the carrying capacity of a

channel. It is usually used when computing
discharge in compound channels.
40

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CE 356

The term hydraulics refers generally to

Hydraulic topics range through some

Fluid Mechanics Hydraulics

Liquids are transported from one location to

Flow in an open channel or closed conduit

Common examples of open channel flows:

Free water surface

Flow in an open channel is due to gravitational

Gupta, Fig. 10.1

y = depth of flow A = flow area

d = depth of flow section R = hydraulic radius = A/P

T = top width D = hydraulic depth = A/T

Compute the hydraulic radius and

Compute the hydraulic radius and

Flow in open channels is

For uniform flow, the velocity, depth, and

Flow in open channels is affected by

For Re < 500, viscous forces dominate

V The mean velocity

Critical flow is the point where velocity is

There are three general principles used in

Since water is essentially incompressible,

Gupta, Fig. 10.4

Conservation of energy applied to

The term associated with each velocity

Equations are developed for steady-state

Balances force due to weight of water in

Note: V is mean velocity, R is hydraulic

The Manning equation is an empirical

Note: V is mean velocity (m/s), R is

Roughness coefficient (n) is a function of:

Using continuity equation (Q=VA),

 And for metric units

For uniform flow, A, R and n are

K is a measure of the carrying capacity of a

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