CHAPTER SIX:

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CHAPTER SIX

• DESIGN OF CHANNELS AND IRRIGATION STRUCTURES

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6.1 DESIGN OF CHANNELS FOR STEADY UNIFORM FLOW

• Channels are very important in Engineering
  projects especially in Irrigation and, Drainage.
  
• Channels used for irrigation are normally called
  canals
• Channels used for drainage are normally called
  drains.

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6.1.1 ESTIMATION OF CANAL DESIGN FLOWS (Q)

• For Irrigation Canals, Design Flows are
  estimated Using the Peak Gross Irrigation
  Requirement
• For Example, in a Location with the Peak Gross
  Irrigation Requirement of 7.69 mm/day.
• Peak flow (Q) 7.69/1000 m x 10000 x
  1/3600 x 1/24 x 1000
• 0.89 L/s/ha
• For a canal serving an area of 1000 ha, canal
  design flow is then 890 L/s or 0.89 m 3 /s.
• Typically, for humid areas, magnitude of
  discharges are in the range of 0.5 to 1.0
  L/s/ha.

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6.1.2        Dimensions of Channels and
Definitions
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Definitions

• a) 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.
•  
• b) Side Slope (Z) The ratio of the
  horizontal to vertical distance of the sides of
  the channel. Z e/d e/D

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Table 6.1 Maximum Canal Side Slopes (Z)
Sand, Soft Clay 3 1 (Horizontal Vertical)
Sandy Clay, Silt Loam, Sandy Loam 21
Fine Clay, Clay Loam 1.51
Heavy Clay 11
Stiff Clay with Concrete Lining 0.5 to 11
Lined Canals 1.51
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• 6.1.3 Estimation of Velocity in Channels
• The most prominent Equation used in the design is
  the Manning formula described in 6.1.3. Values
  of Manning's n can be found in standard texts
  (See Hudson's Field Engineering).
• 6.1.4 Design of Channels
• Design of open channels can be sub-divided into
  2
• a) For Non-Erodible Channels (lined)
• b) Erodible Channels carrying clean water

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Design of Non-Erodible Channels
When a channel conveying clear water is to be
lined, or the earth used for its construction is
non-erodible in the normal range of canal
velocities, Manning's equation is used. We are
not interested about maximum velocity in design.
Manning's equation is  
Q and S are basic requirements of canal
determined from crop water needs. The slope of
the channels follows the natural channel.
Manning's n can also be got from Tables or
estimated using the Strickler equation n
0.038 d1/6 , d is the particle size
diameter (m)
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Design of Non-Erodible Channels Contd.

• LHS of equation (1) can be calculated in terms of
  A R2/3 termed section factor. For a
  trapezoidal section
• A b d Z d2 P b 2 d (1
  Z)1/2
• The value of Z is decided (see Table 6.1) and the
  value of b is chosen based on the material for
  the construction of the channel.
• The only unknown d is obtained by trial and
  error to contain the design flow. Check flow
  velocity and add freeboard.
•  

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Example 6.1

• Design a Non-Erodible Channel to convey 10
  m3/s flow, the slope is 0.00015 and the mean
  particle diameter of the soil is 5 mm. The side
  slope is 2 1.
• Solution Q 1/n AR 2/3 S 1/2 .. (1)
• With particle diameter, d being 5 mm, Using
  Strickler Equation, n 0.038 d 1/6
• 0.038 x 0.005 1/6
  0.016

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Solution of Example Contd.
Z 2. Choose a value of 1.5 m for 'b For
a trapezoidal channel, A b d Z d2
1.5 d 2 d2 P b 2 d (Z2 1)1/2
1.5 2 d 51/2 1.5 4.5 d Try
different values of d to contain the design flow
of 10 m3/s  
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Soln of Example 6.1 Contd.
d(m) A(m2 ) P(m) R(m) R2/3
Q(m3/s) Comment 2.0 11.0
10.5 1.05 1.03 8.74 Small
flow 2.5 16.25 12.75 1.27 1.18
14.71 Too big 2.2 12.98
11.40 1.14 1.09 10.90 slightly
big 2.1 11.97 10.95 1.09 1.06 9.78
slightly small 2.13 12.27 11.09 1.11 1.07
10.11 O.K. The design parameters
are then d 2.13 m and b 1.5 m
Check Velocity Velocity Q/A 10/12.27
0.81 m/s Note For earth channels, it is
advisable that Velocity should be above 0.8 m/s
to inhibit weed growth but this may be
impracticable for small channels. Assuming
freeboard of 0.2 d ie. 0.43 m, Final design
parameters are D 2.5 m
and b 1.51 m
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Final Design Diagram
T 11.5 m
D 2.5 m
Z 21
d 2.13 m
b 1.5 m
T b 2 Z d 1.5 2 x2 x 2.5 11.5 m
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Design of Erodible Channels Carrying Clean Water

• The problem here is to find the velocity at which
  scour is initiated and to keep safely below it.
  Different procedures and thresholds are involved
  including maximum permissible velocity and
  tractive force criteria.
• Maximum Permissible Velocities The maximum
  permissible velocities for different earth
  materials can be found in text books e.g.
  Hudson's Field Engineering, Table 8.2.

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Procedure For Design

• i) Determine the maximum permissible velocity
  from tables.
• ii) With the permissible velocity equal to
  Q/A, determine A.
• iii) With permissible velocity 1/n S1/2 R2/3
  
• Slope, s and n are normally given.
• iv) R A/P , so determine P as A/R
• v) Then A b d Z d and
• P b 2 d (Z2 1)1/2 ,
• Solve and obtain values of b and d

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Example 6.2

• From previous example, design the channel using
  the maximum permissible velocity method.
• Solution Given Q 10 m3 /s , Slope
  0.00015 , n 0.016
• , Z 2 1
• i) From permissible velocity table, velocity
  0.75 m/s
• A Q/V 10/0.75 13.33 m
• iv) P A/R 13.33/0.97 13.74 m
• v) A b d Z d2 b d 2 d2
• P b 2 d (Z2 1)1/2 b
  2 d 51/2 b 4.5 d
• ie. b d 2 d2 13.33 m 2
  ........(1)
• b 4.5 d 13.74 m
  ........ (2)

From previo
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Solution of Equation 6.2 Contd.
From (2), b 13.74 - 4.5 d
.......(3) Substitute (3) into (1), (13.74 -
4.5 d)d 2 d2 13.33
13.74 d - 4.5 d2 2 d
13.33
13.74 d - 2.5 d2 13.33 ie. 2.5 d2 -
13.74 d 13.33 0 Recall the quadratic
equation formula
d 1.26 m is more
practicable From (3), b 13.74 - (4.5 x
1.26) 8.07 m Adding 20 freeboard, Final
Dimensions are depth 1.5 m and width 8.07
m

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6.1.5 Classification of Canals Based on Capacity

• Canals can be classified as
• (a)   Main Canal It is the principal channel of
  a canal system taking off from the headworks or a
  reservoir or tail of a feeder.
• It is a large capacity channel and usually there
  is no direct irrigation from it.
• Small capacity ditch distributaries running
  parallel to the canal are taken off from the main
  canal to irrigate adjoining areas.
• Main canals deliver supply to branch canal and
  main distributaries.

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Canals Contd.

• (b)   Branch or Secondary Canal
• Branch canals take their supply from the main
  canal and convey to the distributaries.
• Very little direct irrigation is done from the
  branch canals.
• Sub-branch is a canal, which takes off from the
  branch canal but has capacity higher than a
  distributary.

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Canals Contd.

• (c)   Major Distributary
• It is a distributing channel, which may take off
  from a main canal, branch canal or sub-branch and
  has discharge capacity less than that of a branch
  canal.
• It supplies water to another distributary.
• Distributaries and minors take off from it.
• Irrigation is done through outlets fixed
  along it.

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Canals Contd.

• (d)   Distributary
• It is a channel receiving supply from branch
  canal or major distributary and has discharge
  less than that of major distributary.
• Minors take off from it, besides irrigation is
  done from it through outlets.

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IRRIGATION STRUCTURES

• Structures are widely used in Irrigation, water
  conservation, flood alleviation, river works
  where water level and discharge regulation are
  required.
• These are hydraulic structures that are used to
  regulate, measure, and/or transport water in open
  channels.
• These structures are called control structures
  when there is a fixed relationship between the
  water surface elevation upstream or downstream of
  the structure and the flow rate through the
  structure.
• Hydraulic structures can be grouped into three
  categories

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IRRIGATION STRUCTURES
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Hydraulic Structures Contd.

• (i)  Flow measuring structures, such as weirs
• (ii) Regulation structures such as gates and
• (iii) Discharge structures such as culverts.

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Weirs

• Weirs Weirs are elevated structures in open
  channels that are used to measure flow and/or
  control outflow elevations from basins and
  channels.
• There are two types of weirs in common use
• Sharp-crested weirs and the broad-crested weirs.
  
• The sharp-crested weirs are commonly used in
  irrigation practice

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Sharp-Crested Weirs

• Sharp-crested or thin plate, weirs consist of a
  plastic or metal plate that is set vertically
  across the width of the channel.
• The main types of sharp-crested weirs are
  rectangular, V-notches and the Cipolletti or the
  Trapezoidal weirs.
• The amount of discharge flowing through the
  opening is non-linearly related to the width of
  the opening and the depth of the water level in
  the approach section above the height of the weir
  crest.

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Sharp Crested Weirs Contd.

• Weirs can be classified as being contracted or
  suppressed depending on whether or not the nappe
  is constrained by the edges of the channel.
• If the nappe is open to the atmosphere at the
  edges, it is said to be contracted because the
  flow contracts as it passes through the flow
  section and the width of the nappe is slightly
  less than the width of the weir crest (see
  figure).
• If the sides of the channel are also the sides of
  the weir opening, the streamlines of flow are
  parallel to the walls of the channel and there is
  no contraction of flow.

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Figure 6.2 Rectangular Weirs
(b) Unsuppressed Weir (Contracted)
(a) Suppressed Weir
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Sharp Crested Weirs Contd.

• In this case, the weir is said to be suppressed.
  Some type of air vent must be installed in a
  suppressed weir so air at atmospheric pressure is
  free to circulate beneath the nappe. (See Figure
  6.2 for suppressed and unsuppressed weirs).

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Sharp Crested Weirs Contd.
The discharge, Q (m3/s) over a rectangular
suppressed weir can be derived as

Where Cd is the discharge coefficient, b is the
width of the weir crest, m (see Figure 6.2 above)
and H is the head of water (m) above weir crest.
According to Rouse (1946) and Blevins( 1984),

..(2) Where Hw is the height of the
crest of the weir above the bottom of the
channel.
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Weirs Contd
This equation is valid when H/Hw lt5, and is
approximated up to H/Hw 10. If H/Hw lt 0.4,
Cd can be approximated as 0. 62 and equation (1)
reduces to Q 1.83 b H1.5
. (3)
This equation is normally used to compute flow
over a rectangular suppressed weir over the usual
operating range. It is recommended that the
upstream head, H be measured between 4H and 5H
upstream of the weir. For the unsuppressed
(contracted) weir, the air beneath the nappe is
in contact with the atmosphere and venting is not
necessary. The effect of side contractions is to
reduce the effective width of the nappe by 0.1 H
and that flow rate over the weir, Q is estimated
as Q 1.83 (b 0.2 H) H1.5
(4) This equation is acceptable as long as b is
longer than 3 H
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Cipoletti Weir

• A type of contracted weir which is related to the
  rectangular sharp-crested weir is the Cipoletti
  weir (see Figure 6.3 below) which has a
  trapezoidal cross-section with side slopes 14
  (HV). The advantage of a Cipolletti weir is
  that corrections for end contractions are not
  necessary.

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Cipolletti Weir Contd.
The discharge formula can be written as   Q
1.859 b H1.5 .. (5)   Where b is the
bottom width of the Cipolletti weir. The minimum
head on standard rectangular and Cipolletti weirs
is 6 mm and at heads less than 6 mm, the nappe
does not spring free of the crest.  
   
Figure 6.3 A Trapezoidal of Cipolletti Weir
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Example 6.3

• A weir is be installed to measure flows in the
  range of 0.5 to 1.0 m3/s. If the maximum depth
  of water that can be accommodated at the weir is
  1 m and the width of the channel is 4 m,
  determine the height of a suppressed weir that
  should be used to measure the flow rate.

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Solution to Example 6.3
The flow over the weir is shown in the Figure 6.4
below. The height of water is Hw and the flow
rate is Q. The height of water over the crest of
the weir, H is given by H 1
Hw Assuming that H/Hw , 0.4, then Q is related
to H by equation (3), where   Q 1.83 b H 1.5


Figure 6.4 Weir Flow
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Solution to Example 6.3Concluded
Taking b 0.4 m, Q 1m3/s (the maximum flow
rate will give the maximum head, H), then  
The height of the weir, Hw
is therefore given by Hw 1 0.265 0.735
m   And H/Hw
0.265/0.735 0.36   The initial assumption
that H/Hw lt 0.4 is therefore validated, and the
height of the weir should be 0.735 m.  
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V-Notch Weir
A V-notch weir is a sharp-crested weir that has a
V-shaped opening instead of a rectangular-shaped
opening. These weirs, also called triangular
weirs, are typically used instead of rectangular
weirs under low-flow conditions ( mainly lt 0.28
m3/s), where rectangular weirs tend to be less
accurate. It can be derived that the flow rate,
Q over the weir is given by    

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V-Notch Weirs Contd.
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Parshall Flume

• Although weirs are the simplest structures for
  measuring the discharge in open channels, the
  high head losses caused by weirs and the tendency
  for suspended particles to accumulate behind
  weirs may be important limitations.
• The Parshall flume provides an alternative to the
  weir for measuring flow rates in open channels
  where high head losses and sediment accumulation
  are of concern.
• Such cases include flow measurement in irrigation
  channels.
• The Parshall flume (see Figures 6.7 and 6.8
  below) consists of a converging section that
  causes critical flow conditions, followed by a
  steep throat section that provides for a
  transition to supercritical flow.

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Parshall Flume
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Parshall Flumes
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Parshall Flume Contd.

• The unique relationship between the depth of flow
  and the flow rate under critical flow conditions
  is the basic principle on which the Parshall
  flume operates.
• The transition from supercritical flow to
  subcritical flow at the exit of the flume usually
  occurs via a hydraulic jump, but under high tail
  water conditions the jump is sometimes submerged.

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Parshall Flume Contd

• Within the flume structure, water depths are
  measured at two locations, one in the converging
  section, Ha and the other at the throat section,
  Hb. The flow depth in the throat section is
  measured relative to the bottom of the converging
  section as illustrated in the figure below.
• If the hydraulic jump at the exit of the Parshall
  flume is not submerged, then the discharge
  through the flume is related to the measured flow
  depth in the converging section, Ha by the
  empirical discharge relations given in Table 6.2,
  where Q is the discharge in ft3/s, W is the width
  of the throat in ft, and Ha is measured in ft.

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Parshall Flume Contd

• Submergence of the hydraulic jump is determined
  by the ratio of the flow depth in the throat, Hb,
  to the flow depth in the converging section, Ha,
  and critical values for the Hb/Ha are given in
  Table 6.3.
• Whenever, the ratio exceeds the critical values
  in the table, the hydraulic jump is submerged and
  the discharge is reduced from the values given by
  the equations in Table 6.2.
• Corrections to the theoretical flow rates as a
  function of Ha and the percentage of submergence,
  Hb/Ha are given in the Figures 6.8 and 6.9 below
  for throat widths of 1 ft and 10 ft.

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Parshall Flumes Contd.
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Parshall Flumes Contd.

• Flow corrections for the 1 ft flume are applied
  to larger flumes by multiplying the correction
  for the 1 ft flume by a factor corresponding to
  the flume size given in Table 6.4.
• Similarly, flow corrections for flume sizes
  greater than 10 ft. are applied to larger flumes
  by multiplying the correction for the 10 ft flume
  by a factor corresponding to the flume size
  given in Table 6.5.
• Parshall flumes do not reliably measure flow
  rates when the submergence ratio, Hb/Ha exceeds
  0.95.

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Parshall Flume Correction
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Tables For Parshall Flume Correction
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Example 6.4

• Example 6.4 Flow is being measured by a
  Parshall flume that has a throat width of 2 ft.
  Determine the flow rate through the flume when
  the water depth in the converging section is 2.00
  ft and the depth in the throat section is 1.70ft.

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Solution to Example 6.4
From the given data W 2 ft, Ha 2 ft,
and Hb 1.7 ft. According to Table 6.2, Q
is given by In this
case Hb/Ha 1.7/2 0.85 Therefore,
according to Table 6.3, the flow is submerged.
Figure 6.8 gives the flow rate correction for a
1 ft flume as 2ft3/s, and Table 6.4 gives the
correction factor for a 2 ft flume as 1.8. The
flow rate correction, dQ for a 2 ft flume is
therefore given by DQ 2 x 1.8
3.6 ft3/s And the flow rate through the
Parshall flume is Q dQ, where Q dQ 23.4
3.6 29.8 ft3/s
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Gates

• Gates are used to regulate the flow in open
  channels.
• They are designed for either over-flow or
  underflow operation, with overflow operation
  appropriate for channels in which there is a
  significant amount of floating debris.
• The common types of gates are vertical and radial
  (Tainter) gates, which are illustrated below.
• Vertical gates are supported by vertical guides
  with roller wheels, and large hydrostatic forces
  usually induce significant frictional resistance
  to raise and lower the gate

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Diagrams of Gates
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Gates Contd.
Flow, Q through a gate could be
established to be Cc
Cc coefficient of contraction, y2/yg
0.61 for most vertical gates. For For Tainter
gates, Cc is generally greater than 0.61 and is
commonly expressed as a function of the angle
(degrees) shown in the diagram above.
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Gates Concluded
It can be expressed as This equation
applies as long as the angle is least than 900.
All the equations apply where there is free flow
through the gates. See texts for situations
where the flows through the gates are submerged.
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Drop Structures

• Drop structures, typically constructed out of
  concrete, can accommodate a sudden change in
  elevation of the channel bottom while maintaining
  control of the flow.
• Drop structures are used in channels, which must
  be laid along relatively steep gradients to allow
  for dissipation of energy without causing scour
  in the channel itself.
• In such applications, the drop structure allows
  the main channel to be laid on subcritical slope
  while the excess potential energy of the flow due
  to the steep topography is absorbed in the drop
  structure. See Figure 6.12 of a drop structure
  below

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Diagram of Drop Structure
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Example 6.5

• An irrigation channel with a design discharge of
  2.265 m3/s is to be laid along a terrain having
  an average slope of 0.005 m/m. To maintain
  subcritical flow in the channel section, the
  bottom of the channel must be limited to 0.001
  m/m. The extra fall is to be absorbed by drop
  structures such as the one shown above in the
  diagram having a width of 3.048 m. Compute the
  number of structures required in a 16.09 km
  length of line if the drop height (dZ) is equal
  to 1.829 m.

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Solution of Example 6.5

• Solution The total drop to be absorbed by
  structures, ZT (St - So) L
• Where St is the terrain slope, L is total
  distance, and So is the slope of the channel.
• ZT ( 0.005 m/m - 0.001 m/m ) 16.09 km
  64.36
• The number of drop structures required,
• N ZT/dZ 64.36/1.829 36 Structures.