Topic 4 - Uniform flow in open channel - SS 2021

TOPIC 4

UNIFORM
FLOW IN
OPEN
CHANNEL

This topic introduces the concept

of uniform flow in open channel

and cover identify Manning's

Equation and coefficients for

several types of surface channel

Topic 4

Uniform flow
in Open Channel

LESSON 1

Explain the concept of uniform flow in open channel
i. Describe uniform flow
ii. Explain hydraulic gradient, wet perimeter and hydraulic radius

LESSON 2

Identify Manning's Equation and coefficients for several types of
surface channel
i. Calculate the flow rate, section dimension or channel slope using

Manning's Equation
ii. Distinguish the best hydraulic cross section using Manning’s

Equation

Topic 4

Lesson 1

Introduction

Meaning of Open Channel Flow
✓ Flow in open channels is defined as the flow of a liquid with a free surface.
✓ A free surface is a surface having constant pressure such as atmospheric pressure.
✓ Thus, a liquid flowing at atmospheric pressure through a passage is known as flow

in open channels.
✓ The flow of water through pipes at atmospheric pressure or when the level of water

in the pipe is below the top of the pipe, is also classified as open channel flow.

Topic 4

Lesson 1

To define
1 Open Channel

• Liquid surface is exposed to the atmosphere
• Surface is at atmospheric pressure

Type; • Rivers and streams
• Drainage
• Ditches
• Irrigation canal

Application;

Interest to hydraulic

engineers
• Location of free surface
• Velocity distribution
• Discharge - stage

(depth) relationships
• Optimal channel design

Topic 4 Topic 4

Types of channel Lesson 1

1) Man made • Channel designed and made by
2) Natural human

• Examples : earth or concrete lined
drainage and irrigation

• Prismatic channel (no change in
geometry with distance)

• Changes with spatial and temporal
(non prismatic channel)

• Examples: River and streams

Topic 4

Lesson 1

Comparison between Open Channel &
Pipe Flow

Topic 4

Lesson 1

Open Channel section type

• Flow in Part • Flow in Part • Flow in • Flow in Flat • Flow in Vee
full pipes. full Rectangular bottomed channels.
rectangular channels. channels (with
sections. sloping sides).

Topic 4

Lesson 1

Classification of Flow in
channel

1) Steady flow and
unsteady flow

2) Uniform flow and
non-uniform flow

3) Laminar flow and
turbulent flow

4) Sub-critical, critical
and super critical flow

Classification of Flow in Topic 4
channel
Lesson 1

1) Steady flow and unsteady flow

Steady Flow Mathematically, steady flow means

If the flow characteristics such as depth
of flow, velocity of flow, rate of flow at
any point in open channel flow do not
change with respect to time, the flow is
said to be steady flow.

Unsteady flow Mathematically, unsteady flow means

If at any point in open channel flow, the
velocity of flow, depth of flow or rate of
flow changes with respect to time, the
flow is said to be unsteady flow.

Classification of Flow in Topic 4
channel
Lesson 1

2) Uniform flow and Non-uniform flow

Uniform Flow v1 = v2
d1 = d2
Uniform flow in open channels is when the mean velocity
in a cross section with another does not change. It means vd
that the cross sectional area and depth on any part of
the same.

v1 d1 Non-uniform flow

v2 Non-uniform flow is when the mean
d2 velocity varies along the channel. It can
occur in channels with different cross-
v1 ≠ v2 sectional area, change in slope and
d1 ≠ d2 also with the existence of hydraulic
structures such as embankments,
chipped, gate and so on.

Classification of Flow in Topic 4
channel
Lesson 1
3) Laminar flow and Turbulent flow

• Fluid move in a straight line • Flow lines start changing
• Occurs at low velocity • A state between laminar and
• The flow is called streamline
Laminar flow turbulent flows, called the
Turbulent flow intermediate flow

Reynolds determined that the transition from laminar to turbulent flow occurs at a definite value of
the dimensionally property, called Reynolds number :

Laminar flow when Re < 500

Transition flow when 500 < Re <
2000

Turbulent flow when Re > 2000

Topic 4

Lesson 1

Classification of Flow in channel

4) Sub-critical, critical and supercritical flow

Depending on Froude number, Fr

Subcritical flow Fr = v
gy
• The channel is called as deep channel for sub-critical flow.
• Sub critical flow is also called as slow or tranquil flow. Where;
Fr = Froude Number
Critical flow v = Flowrate (m/s)
g = Acceleration gravity (9.81 m2/s)
• The flow at depth equal to the critical depth is known as y = flow depth (m)
critical flow.
Type Of Flow
Supercritical flow
Slow, Subcritical
• The flow at which depth of the channel is less than critical Critical
depth, velocity of flow is greater than critical velocity and
slope of the channel is also greater than the critical slope is Fast, Super critical
known as supercritical flow.

• The channel is called as shallow channel for supercritical flow.
• Supercritical flow is also called as rapid or fast flow.

Flow Depth Flow Velocity Froude Number

y > yc v < vc Fr < 1
y = yc v = vc Fr = 1
y < yc v > vc Fr > 1

Topic 4

Lesson 1

Term in Open Channel

Hydraulic gradient
Wet perimeter
Hydraulic radius

Topic 4

Lesson 1

1 Hydraulic gradient, So, i – channel slope

Hydraulic gradient is the slope at the bottom or base of the
channel. Movement of fluid flow is also influenced by the
slope.

Topic 4

Lesson 1

2 Wet perimeter, P – depend on
section/types of channel

Wet perimeter is the perimeter or the perimeter of the liquid surface and container
cutting in contact with the liquid

D Wet perimeter, P = B + 2D
B
Where,
B = width of the channel
D = Depth of the liquid

3 Hydraulic radius @ hydraulic

mean depth, R = A/P

Explain Topic 4

depth of slope section, Lesson 1
top width, hydraulic
depth, base slope, free ◇ Depth of flow section (d) : depth of flow normal
board & side slope to the direction of flow.

Top Width, T= Freeboard ◇ Top width (T) : The width of channel section at
the free surface.
Ɵ
◇ Hydraulic depth (D) : D = A/T
Base slope, Bed slope, = tan Ɵ
Hydraulic gradient, So, i = ◇ Base slope (So) : So = tan θ

◇ 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.

◇ Side Slope (Z): The ratio of the horizontal to
vertical distance of the sides of the channel.

UNIFORM FLOW IN OPEN CHANNEL Topic 4

Lesson 1

Shape Area, A Wet Perimeter,R

y By B+2y

B B+[2y√1+z2)]
@
T (B+zy)y
H 1y @ B+2H

z ½ (B+xT) y 2y√(1+Z2)

B

1 y zy2
z

Topic 4

Lesson 1

Section Area, A Wet Perimeter,R
2(1/2.x.y) 2y/(cosϴ)
x
yϴ

Topic 4

Lesson 1

Compile Shape of Open Channel

Topic 4

Lesson 1

COMPANY LOGO

Topic 4

Lesson 1

Example 1

Based on the diagram below evaluate the area A, perimeter P wet
and hydraulic radius R of the channel

a. Area = b x d
= 2 x 4 = 8m2
D = 2m
Wet Perimeter = b + 2d
= 4 + (2 x 2) = 8 m

B = 4m

Topic 4

Lesson 2

Uniform flow
in Open Channel

LESSON 2

Identify Manning's Equation and coefficients for several types of
surface channel
i. Calculate the flow rate, section dimension or channel slope using

Manning's Equation
ii. Distinguish the best hydraulic cross section using Manning’s

Equation

Identify Manning’s Equation and Coefficients Topic 4

Lesson 2

V = 1 R2/3.i1/ 2 Q=AV
N
Where
Q = A. 1 .R2/3.i1/ 2 Q = Discharge
N A = Area
V = flowrate

Where
Q = Discharge
A = Area
v = Flowrate
N = Manning roughness coefficient
R = Hydraulic radius = A / P
i = Slope gradient

Manning n values for the
coefficient varies with the
kind of material. Table
shows N values are listed
which are commonly used.

Topic 4

Lesson 2

Example 2

A rectangular channel is 4 meters deep and 6 meters wide. Find the discharge
through channel, when it runs full. Take slope of the bed as 1 in 1000 and
Manning coefficient of roughness, n = 0.050.

d=4m

b=6m Area; A = 4 x 6 = 24 m2
Wet Perimeter; P = b+2d = 6 + 2 x 4 = 14 m
Q = A. 1 .R 2 / 3 .i1/ 2 Hydraulic radius; R = A/P = 24/14 = 1.71 m
N Slope of bed; S = 1/1000 = 0.001

Topic 4

Lesson 2

Example 3

Water is flowing at the rate of 8.5 m3/s in an earthen trapezoidal

channel with bed width 9 meters, water depth 1.2 meter and side slope

2:1. Calculate the bed slope, if the value of n in the Manning formula be

0.012. y must 1
Then,
Given
y : x 1 yx y = 2/2, x = 1/2 = z
2:1
z

Q = A. 1 .R 2 / 3 .i1/ 2 A = { 9 + (0.5 x 1.2) } 1.2 = 11.52 m2
N P = 9 + { 2 x 1.2 √(12 + 0.52 ) } = 11.683 m
R = A/P = 11.52/11.683 = 0.986

Topic 4

Lesson 2

Example 4

Flow rate of water flow with 0.1m3/s through a half full pipe culvert with
radius 0.5m . Calculate the sewers where the slope of Manning roughness
coefficient is 0.013.

Q = A. 1 .R2/3.i1/ 2
N

0.1 = 0.393. 1 .0.252/3.i1/ 2
0.013

Topic 4

Lesson 2

THE BEST HYDRAULIC CROSS SECTION USING MANNING FORMULA

It’s most economy. This is because they GIVE maximum flow-rate. Has
the smallest of wet perimeter and it will reduce the frictional resistance

THE BEST HYDRAULIC CROSS SECTION Topic 4
USING MANNING FORMULA
Lesson 2
Rectangular section

y

A = by b
b = A/y
P =b +2y (1)
(2)
(3)

Replace equation (2) into equation (3)

Differentiate P =b +2y A=2y2 (4)

Equation (4) into (1)

2y2 = by

b = 2y

Topic 4

Lesson 2

THE BEST HYDRAULIC CROSS SECTION
USING MANNING FORMULA

Trapezoidal section

1 y 1
n b n

ny ny

Q max = ½ [b +2zy] = y √(1+z2)

Topic 4

Lesson 2

SUMMARY

Topic 4

Lesson 2

Example 4

Calculate discharge the most economical cross-section of a rectangular channel with 4 m
wide, when the bed slope is 1 in 1000. Assume the Manning coefficient, N=0.028

Given best cross-section b = 2y, when b = 4m Q = 9.035 m3/s

b = 2y
4 = 2y
y=2m

Area; A = 2y2 = 2(2)2 = 8 m2
Wet Perimeter; P = 4y= 4 x 2 = 8 m

Hydraulic mean depth; R = y/2 = 2 / 2 = 1 m
Slope of bed; S = 1/1000 = 0.001
Used manning formula

Q = A. 1 .m2/3.i1/ 2
N

= 8. 1 .(1) 2 / 3.(1/1000)1/ 2
0.028

Example 5 Topic 4

Lesson 2

A trapezoidal channel flowing of water depth 1.06 m at the minimum

cross section. Get the discharge of the channel if the slope of the base is
1:1200. The slope side at 450 and N = 0.025.

1.06 m 1
0.88 m 1

Hydraulic mean depth; R = y/2 = 1.06 / 2 = 0.53 m

Q = A. 1 .R 2 / 3 .i1/ 2
N

Q = 1.946. 1 Q=

0.025 .0.532 / 3.(1/1200)1/ 2 1.472 m3/s

End of
Topic 4

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