Transcript Open Channel Flow

ERT 349 SOIL AND WATER
ENGINEERING
Open Channel Flow
Siti Kamariah Md Sa’at
PPK Bioproses, UniMAP
Topic Learning Outcomes
At the end of this topic, student should be able
to:
1. Design the open channel in uniform and nonuniform flow
2. Design the most efficient section channel
3. Calculate the flow in open channel
Introduction
“Occur when free water surface in the channel is
at atmosphere pressure”
Example of open channel:
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Rivers and streams
Drainage
Ditches
Irrigation canal
Application
Interest to hydraulic engineers
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location of free surface
velocity distribution
discharge - stage (depth) relationships
optimal channel design
Types of channels
1. Man made
•
•
•
Channel designed and made by human
Examples: earth or concrete lined drainage and
irrigation
Prismatic channel (no change in geometry with
distance)
2. Natural
•
•
Examples: River and streams
Changes with spatial and temporal (non prismatic
channel)
FLOW IN OPEN CHANNEL
TEMPORAL (Time)
STEADY FLOW
UNIFORM FLOW
UNSTEADY FLOW
NON-UNIFORM FLOW
RAPIDLY VARIED FLOW
SPATIAL (Space)
GRADUALLY VARIED FLOW
Types of flow
Based on temporal (Time, t) and Spatial
(Space,x)
Time Criteria
 Steady flow (dy/dt = 0). Water depth at one point
same all the time. (Flow constant with time)
 Unsteady flow (dy/dt ≠ 0). Water depth changes all
the time. (Flow variation with time)
Space criteria
 Uniform flow (dy/dx = 0). Water depth same along
the whole length of flow.
 Non-uniform flow (dy/dx ≠ 0). Water depth changes
either rapidly or gradually flow
Flow Rate
Steady
Unsteady
Time
Steady and Non-Steady Flow
Uniform and Non-Uniform Flow
V1 = V2
A1
= A2
V1
A1
Uniform Flow
V2
A2
V1
A1
V2
A2
Non-Uniform Flow
States of flow
Flow vary with following forces:
 Viscous
 Inertia
 Gravity
Defines by Reynolds number (Re) and Froude
numbers (Fr)
Reynolds Number
To determine:
 Laminar flow
 Transitional flow
 Turbulent flow
: Re < 500 (viscous > inertia)
: 500 < Re < 1300
: Re > 1300 (inertia > viscous)
Froude Number
The Froude Number, Fr describes the following
states of flow:
Fr < 1 : flow is subcritical
Fr = 1 : flow is critical ( inertia < gravity)
Fr > 1 : flow is supercritical ( inertia > gravity)
Froude Number
A flow is called critical if the flow velocity is equal
to the velocity of a gravity wave having small
amplitude.
The flow is called subcritical flow, if the flow
velocity is less than the critical velocity
The flow is called supercritical flow if the flow
velocity is greater than the critical velocity.
4
Critical Flow
 Unstable surface
 Series of standing waves
 Difficult to measure depth
y
Characteristics
3
2
1
0
Occurrence

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
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0
1
2
3
E
Broad crested weir (and other weirs)
Channel Controls (rapid changes in cross-section)
Over falls
Changes in channel slope from mild to steep
Used for flow measurements
 Unique relationship between depth and discharge
4
Parameters of Open Channels
Wetted Perimeter (P) :The Length of contact
between Liquid and sides and base of Channel
Hydraulic Mean Depth or Hydraulic Radius
(R): If cross sectional area is A, then R = A/P.
Depth of flow section (d) : depth of flow
normal to the direction of flow.
Parameters of Open Channels
Top width (T) : the width of channel section at
the free surface.
Hydraulic depth (D)
: D = A/T
Base slope (So)
: So = tan θ
Parameters of Open Channels
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.
Table 1: Maximum Canal Side Slopes (Z)
Sand, Soft Clay
3: 1 (Horizontal: Vertical)
Sandy Clay, Silt Loam, Sandy
Loam
2:1
Fine Clay, Clay Loam
1.5:1
Heavy Clay
1:1
Stiff Clay with Concrete Lining
0.5 to 1:1
Lined Canals
1.5:1
M.Hanif Chaudry, Open Channel Flow 2nd Edition, Springer, 2008
Continuity Equation
Inflow
3
3a
A
Change in Storage
3b
Outflow
1
A
2
Section AA
Inflow – Outflow = Change in Storage
General Flow Equation
Q = vA
Equation 1
Area of the
cross-section
Flow rate
(m3/s)
Avg. velocity
of flow at a
cross-section
(m/s)
(m2)
Uniform flow in Open
Channel
Uniform flow in Open Channel
Energy lines
i
Water Surface
Sw
Flow
yo
So
For uniform flow (in prismatic channel), i = Sw = So
yo= normal depth for uniform flow only
Resistance Equation
1. Chezy Equation
 By Antoine Chezy (France), 1768
2. Manning Equation
 By Robert Manning (Irish), 1889
Chezy Equation
Introduced by the French engineer Antoine
Chezy in 1768 while designing a canal for the
water-supply system of Paris
v  C Ri
 Because i = So, so
v  C RSo
Q  AC RSo
Chezy Equation
 where C = Chezy coefficient
= L1/2/T (Unit m1/2/s)
m
m
60
< C < 150
s
s
where 60 is for rough and 150 is for smooth
Manning Equation
 Most popular in for open channels around the world
V 
1
1/2
R 2/3
S
h
o
n
V 
1.49
1/2
R 2/3
S
h
o
n
Q  VA
1
Q  ARh2 / 3 S o1 / 2
n
C = R1/6 / n
SI Unit
Dimensions of n? T
(English system)
Bottom slope
very sensitive to n
/L1/3
n = Manning
roughness coefficient
= T/L1/3 (Unit s/m1/3)
Manning roughness coefficient, n
Lined Canals
Cement plaster
Untreated gunite
Wood, planed
Wood, unplaned
Concrete, trowled
Concrete, wood forms, unfinished
Rubble in cement
Asphalt, smooth
Asphalt, rough
Natural Channels
Gravel beds, straight
Gravel beds plus large boulders
Earth, straight, with some grass
Earth, winding, no vegetation
Earth , winding with vegetation
n
0.011
0.016
0.012
0.013
0.012
0.015
0.020
0.013
0.016
0.025
0.040
0.026
0.030
0.050
n = f (surface
roughness, channel
irregularity, stage...)
Example 1:
Trapezoidal channel:
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Bottom width = 3.0 m
Side slope = 1: 1.5
Base slope = 0.0016
Manning coefficient = 0.013
Determine Q if yo = 2.6m.
M.Hanif Chaudry, Open Channel Flow 2nd Edition, Springer, 2008
Determination of yo
 If Q, So and n given or known and you need to
estimate yo, direct calculation cannot give you
answer. So there are another method can be
use:
1. Try and error
2. Graphical
3. Curves chart
Example 2:
 A rectangular channel with n = 0.017 with width
6 meter, base slope 0.0016 and to carry
10 m3/s flowrate.
Determine yo with:
1. Try and error
2. Graphical
3. Curves chart