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This set of Irrigation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Stable Channels Design in India”.

1. Design of alluvial channels in India is based on Kennedy and Lacey theories.
a) True
b) False

Explanation: The direct accurate mathematical solution based on the resistance equations given by Chezy’s formula and Manning’s formula is very complicated in Indian based alluvial channels. So, therefore hypothetical theories given by Kennedy and Lacey are used, as these theories are based on experiments and experience from existing channels over the years.

2. On what condition does the resistance equations of Chezy’s formula and manning’s formula are applicable?
a) τo
b) τc
c) τo < τc
d) τo > τc

Explanation: The average shear stress (τo) which is acting on the boundary of an alluvial channel should be less than the critical shear stress (τc), then the channel shape remains unchanged, and hence the channel is considered having rigid boundary. So based on this condition Chezy’s formula and Manning’s formula can be applied.

3. What is the problem in India for artificial channels?
a) Formation of Depressions
b) Formation of Alluvial Soil
c) Untimely Rains
d) Improper Usage of Channels

Explanation: In prehistoric periods, the area starting from the Himalayas to Vindhya mountains is used to in the form of depressions with water flowing over it. But over the ages these depressions got filled with fine silt particles, thereby forming into alluvial soil. So the rivers present in this area of north India flow in alluvial soil carrying silt. So, therefore the artificial channels carrying water from such rivers thus have to carry silt sediment.

4. The velocity of flow in a channel should not more or less, but instead it should be adequate.
a) True
b) False

Explanation: The given velocity of flow of a channel and certain depth can carry in suspension, some amount of silt. But if the velocity is more and depth is not fully charged with silt it will erode the bed and sides of the channel. And if the velocity is less, the silt cannot be carried in suspension by the flow, hence it is dropped.

5. What is the effect of scouring in channels?
a) The Channel Section gets reduced
b) Reduces Discharge Capacity
c) Improper Working of Channel
d) Breaching of Canal Banks

Explanation: Scouring is not a rare phenomenon in channels. It is very understandable and can be controlled or avoided by proper designing of channels. Scouring causes loss of command in channels and lowers full supply level of channel. This causes breaching of canal banks and in turn causes failure of foundations of irrigation structures.
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6. What is the effect of silting in channels?
a) Reduced Discharge Capacity of Channel
b) Causes Loss of Command
c) Breaching of Canal Banks
d) Failure of Irrigation Structures

Explanation: The silting problem is very common in any kind of artificial channels, or we can say there is no natural or artificial channel with the silting problem. Silting interferes with the proper working of a channel, as it causes reduction in the channel section due to siltation, which thereby reduces the discharge capacity of the channel.

7. Which type of state is achievable in artificial channels but not in rivers?
a) Turbulent State
b) Laminar State
c) Regime State
d) Uniform State

Explanation: The channel is said to be in regime state, when the flow of the channel is such that silting and scouring effects need no special attention. This state is not easy to achieve in rivers but can be achieved in artificial channels, by proper designing of the channels.

8. On what basis for designing the regime state is obtained?
a) Silt and Velocity of Flow
b) Silt
c) Velocity
d) Depth of Channel

Explanation: The basis for designing a channel to be in regime state, whatever the amount of silt has entered the channel has to be kept in suspension, so that it does not settle down and get deposited in the channel anywhere. And the velocity of the flow in the channel should be such that it does not produce silt by eroding the banks and beds of the channel.

9. What vital factor is not considered in regime theories during the design of regime channels?
a) Velocity of Flow in the Channel
b) Type of Flow in the Channel
c) Quantity of Sediment Entering a channel
d) Area in which the Channel flows

Explanation: The quantity of sediment load entering the channel from the head works plays an important role in designing the regime channels, as it controls the cross-section and shape of the regime channel. Moreover the design of regime channel is not complete until provisions are made for the effects produced by the actual quantity of sediment load present in the channel.

10. According to Kennedy the silting action in channels is due to?
a) Generation of Eddies
b) Slope of the Bed
c) Area of Channel
d) Type of Flow in the Channel

Explanation: From the observations of his research, he concluded that the silting action in channels is due to the generation of eddies, rising to the surface. These eddies are in turn generated by the friction of flowing water with the channel surface.

11. Based on his research what factor is given by Kennedy for free silting and scouring actions in a channel?
a) Critical Velocity (Vo)
b) Bed Slope of Channel
c) Hydraulic Mean Depth
d) Rugosity Coefficient

Explanation: Eddies affect the formation of silting action in a channel brief investigation shows that the vertical component of these eddies try to move sediment up and the weight of sediment tries to bring it down, thus keeping the sediment in suspension. So, silting is avoided if sufficient velocity is generated to form eddies and keep the sediment in suspension. This velocity is called critical velocity.

12. Given to design the irrigation channel to carry 80 cumecs of discharge. The channel slope is 1 in 3000. The critical velocity ratio is 1.3. Take rugosity coefficient as 0.021.
a) Depth = 3 m, Base width = 15 m
b) Depth = 3.5 m, Base width = 15.5 m
c) Depth = 3.3 m, Base width = 15.2 m
d) Depth = 3.2 m, Base width = 15.1 m

Explanation: Given Q = 80 cumecs, S = 1/3000, m = 1.3, n = 0.021
Critical velocity (Vo) = 0.55my0.64 (y = depth of the channel)
= 0.55 x 1.3 x (2)0.64
= 1.114 m/sec
Area (A) = Q/Vo = 80 / 1.114 = 71.8 m2
Now assume side slope as (1/2): 1(1/2H: V)
Now, A = y (b + y x 1/2)
71.8 = 2(b + 2 x 1/2)
71.8 = 2(b + 1)
b = 34.9 m
Perimeter (P) = b + 2 x √5/2y
= 34.9 + 4.47
= 39.37 m
Now R = A/P = 71.8 / 39.37 = 1.82 m
V = ((1/n + (23 + 0.00155/s)) / (1 + (23 + 0.00155/s)n/$$\sqrt{RR}$$))$$\sqrt{RSRS}$$
V = 0.78 m/sec
Now calculating for critical velocity,
Vo = 0.55 x 1.3 x y0.64
= 0.715 x y0.64
Now assume y = 2.5 m
Vo = 0.715 x (2.5)0.64 = 1.28 m/sec
A = 80 / 1.28 = 62.5 m2
62.5 = 2.5 (b + 1/2(2.5))
b = 23.75 m
P = 23.75 + 2 x √5/2(2.5) = 29.35 m
R = A/P = 2.13
√R = 1.46
V = 75.27/1.4 x (1.46/54.8) = 1.432 m/sec
V > V0
Now assume y = 3.2 m
Vo = 0.715 x (3.2)0.64 = 1.51 m/sec
A = 80 / 1.5 = 53.33 m2
53.33 = 3.2 (b + 1.6)
b= 15.1 m
P = 15.1 + √5(3.2)
P = 22.2 m
R = A/P = 53.33/22.2 = 2.4 m
√R = 1.56
V = (75.27/1.4) x (1.56/54.8)
= 1.53 m/sec
Therefore V = Vo
Hence use the depth equal to 3.2 m and base width 15.1 m with slope 1/2:1.

13. Design a regime channel for a discharge of 90 cumecs and silt factor is 1.3 use Lacey’s Theory.
a) Depth = 2.2 m, Base width = 40.5 m, Slope = 1/4670
b) Depth = 2.12 m, Base width = 40.42 m, Slope = 1/4675
c) Depth = 2.135 m, Base width = 40.3 m, Slope = 1/4676
d) Depth = 2.123 m, Base width = 40.1 m, Slope = 1/4672

Explanation: Given Q = 90 cumecs, f = 1.3
V = [Qf2/140]1/6 = 1.014 m/sec
A = Q/V = 90/1.014 = 88.76 m2
R = 5/2 x V2/f = 2 m
P = 4.75√Q = 45.06 m
For a trapezoidal channel with 1/2H: 1V slopes
P = b +√5y and A = (b + y/2) y
45.06 = b + √5y, 88.76 = (b + y/2) y
b = 45.06 – 2.24y, substitute this value in area equation
88.76 = (45.06 – 2.24y + y/2) y
Y = 2.135 m
b = 45.06 – 2.24 x 2.135 = 40.3 m
S = (f5/3 / 3340Q1/6) = 1/4676.

14. According to Lacey what factor is needed to have a true regime in an artificial channel?
a) Flow is Uniform
b) Critical Velocity = Actual Velocity
c) No Silting or Scouring Action
d) Lining of the Channel Bed

Explanation: For a channel to be in regime condition it should not have silting and scouring action. To obtain this the silt entering the channel must be carried away through the channel, by the channel section. The artificial channel to be in a regime it must have a fixed slope and fixed section. So, therefore to achieve this flow in the channel should uniform flow.

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