CHAPTER SIX:. DESIGN OF CHANNELS AND IRRIGATION STRUCTURES. 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
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DESIGN OF CHANNELS AND IRRIGATION STRUCTURES
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)
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.
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
d(m) A(m2 ) P(m) R(m) R2/3Q(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
T = 11.5 m
D = 2.5 m
Z = 2:1
d = 2.13 m
b = 1.5 m
T = b + 2 Z d = 1.5 + 2 x2 x 2.5 = 11.5 m
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
Distributaries and minors take off from it.
Irrigation is done through outlets fixed along it.
(b) Unsuppressed Weir
(a) Suppressed Weir
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),
Where: Hw is the height of the crest of the weir above the bottom of the channel.
This equation is valid when H/Hw <5, and is approximated up to H/Hw = 10. If H/Hw < 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
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
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
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 < 0.4 is therefore validated, and the height of the weir should be 0.735 m.
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 < 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:
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
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.
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.