Design of Canals MCQ Quiz in मराठी - Objective Question with Answer for Design of Canals - मोफत PDF डाउनलोड करा

Concepts:

Garret's diagram

• It is graphical representation of design of canal dimensions based on Kennedy theory.
• The diagram is discharge plotted on abscissa (X-axis), and slope of the channel on the left side of ordinate (Primary Y-axis) and depth of the channel and critical velocity on the right side of the ordinate. (Secondary Y-axis).
• Garret's diagram is applicable only for side slope of the channel of 0.5: 1.
• The diagrams are specified for manning's coefficient (N) of 0.0225. However, these charts can be extended to any value of N using a nomogram at the top of each diagram.

Explanation:

Lacey followed Lindley’s hypothesis, which states that “dimensions and slope of a channel to carry a given discharge and silt load in easily erodible soil are uniquely determined by nature”.

Option 1 & 2 are correct and option 3 is incorrect.

According to Lacey:

1) He considered the channel section semi-elliptical.

2) He considered the channel cannot be in the true regime. So, the channel only can be the initial and final regime.

3)  Section is wider and shallower.

4) Silt is kept in suspension by the vertical component of eddies generated at all points of forces normal to

the wetted perimeter. So the eddies are generated from the bottom as well as the side of the channel.

Regime Channel

5) A channel is said to in regime if there is neither silting nor scouring.

According to Lacey, there may be three regime conditions:

(i) True regime;

(ii) Initial regime; and

(iii) Final regime.

Accordingly, he proposed the following four basic equations for designing of the alluvial channels:

1. Relationship between velocity (V) and Hydraulic Mean Depth (R)

\({V^2} = \frac{2}{5}fR\)

2. Relationship between Area (A) and Velocity of flow in channel (V)

\(A{f^2} = 140\;{V^5}\)

3. Grain size (d) of silt and silt factor (f)

\(f = 1.76\;\sqrt {d\left( {\;in\;mm} \right)} \)

4. Relationship between Regime Slope (S) and discharge (Q)

\(S = \frac{{{f^{5/3}}}}{{3340{Q^{1/6}}}}\)

Concept:

Meander Length (M_L) - The tangential distance between the crests or trough of a mender in plan view.

Meander belt width (M_B) - Distance between top and bottom portion of successive crests and trough of a member in plan view.

The value of the meander belt (MB) for the river (in m) = 150 √Q 

Calculation:

Given

Q = 1600 m3/sec

M_B = 150 √Q = 150 √1600

 = 150 × 40 = 6000 m = 6 km

Concept:

Lacey proposed that rugosity coefficient is dependent on grade and density of boundary material against the idea of Kutter and Manning, who defined rugosity coefficient to be dependent solely on surface roughness.

He also established relationship between rugosity coefficient (N) and silt factor (f) as below:

N α f^1/4 and f = 1.76 \(\sqrt d\)

Where, d is the diameter average silt particle in ‘mm’.

Explanation:

From the below relations:

1. Velocity is proportional to Q1/6
2. Bed Slope is proportional to Q-1/6
3. Wetted Perimeter is proportional to Q1/2

​So, the correct answer is option 2.

According to Lacey, the design formulas for canal design is as follows:

1) silt factor ⇒ \(\rm{f = 1.76\sqrt {{d_{mm}}}}\)

2) velocity of flow ⇒ \(V = {\left[ {\frac{{Q{f^2}}}{{140}}} \right]^{\frac{1}{6}}}\)

3) bed slope ⇒ \(S = \frac{{{f^{\frac{5}{3}}}}}{{3340 \times {Q^{\frac{1}{6}}}}}\)

4) wetted perimeter ⇒ \(P = 4.75\sqrt Q\)

5) hydraulic mean depth ⇒ \(R = \frac{{5{V^2}}}{{2f}}\)

6) Lacey's Normal Regimed depth ⇒ \(R_r' = 0.473{\left[ {\frac{{Q}}{{f}}} \right]^{\frac{1}{3}}}\)

7) Lacey's Normal depth ⇒ \(R_r' = 1.35{\left[ {\frac{{Q^2}}{{f}}} \right]^{\frac{1}{3}}}\)

Diversion head works like Weir or barrage is constructed across a perennial river to raise water level and to divert the water to canal, is known as diversion head work Flow of water in the canal is controlled by canal head regulator. It controls the entry of silt into canals and provides some poundage by creating small pond. However, the most appropriate will be option ‘1’.

Concept:

Hydraulic mean radius as per Lacey’s theory is given by:

\(R = \frac{5}{2}\left( {\frac{{{V^2}}}{f}} \right)\)

Where,

V = mean velocity 

f = silt factor

Calculation:

Given,

V = 2 m/sec

f = 1

\(R = \frac{5}{2}\left( {\frac{{{V^2}}}{f}} \right)\)

\(R = \frac{5}{2}\left( {\frac{{{2^2}}}{1}} \right) = 10\;m\)

According to Lacey, the design formulas for canal design are as follows:

1) silt factor ⇒ \(\rm{f = 1.76\sqrt {{d_{mm}}}}\)

2) velocity of flow ⇒ \(V = {\left[ {\frac{{Q{f^2}}}{{140}}} \right]^{\frac{1}{6}}}\)

3) hydraulic mean depth ⇒ \(R = \frac{{5{V^2}}}{{2f}}\)

4) wetted perimeter ⇒ \(P = 4.75\sqrt Q\)

5) bed slope ⇒ \(S = \frac{{{f^{\frac{5}{3}}}}}{{3340 \times {Q^{\frac{1}{6}}}}}\)

6) Lacey's regime scour depth ⇒ \(R_r' = 1.35{\left[ {\frac{{Q^2}}{{f}}} \right]^{\frac{1}{3}}}\)

Explanation:

1. Ridge Canal 

• It is also called a watershed canal.
• Aligned along the ridge or natural watershed line.
• Can irrigate areas on both sides of the ridge.
• Cross drainage work not requires.
• They are economical.

2. Contour canal

• Aligned nearly parallel to the contours of the country.
• Can irrigate areas only on one side.
• Cross drainage works are required.

3. Side Slope Canals

•  Aligned roughly at right angles to the contour of the country.
• It is neither on the watershed nor in the valley.
• In can irrigate areas only on one side.
• It is roughly parallel to the drainage of the country, so cross drainage works are not required.
• It has a very steep bed slope.

Concept:

Exit gradient, \({G_E} = \frac{H}{d} \times \frac{1}{{\pi \sqrt \lambda }}\)

Where,

H = Maximum seepage head

d = Vertical cut off depth at downstream end

\(\lambda = \frac{{1 + \sqrt {1 + {\alpha ^2}} }}{2}\;and\;\alpha = \frac{b}{d}\)

b = length at downstream end

Calculation:

\({\rm{\alpha }} = \frac{{20}}{5} = 4\)

\({\rm{\lambda }} = \frac{{1 + \sqrt {1 + {4^2}} }}{2} = 2.56\)

Concept: 

Lacey's scour depth is given by:

\(R\; = \;1.35{\left( {\frac{{{q^2}}}{f}} \right)^{\frac{1}{3}}}\; \)

Where, q = Discharge per meter width, f = silt factor

Calculations:

Given, q = 3 cumec, f = 1.2

\(R\; = \;1.35{\left( {\frac{{{3^2}}}{1.2}} \right)^{\frac{1}{3}}}\;=\;2.64\;m\)

Important Points

Various formulas deduced by lacey is given below:

1) silt factor ⇒ \(\rm{f = 1.76\sqrt {{d_{mm}}}}\)

2) velocity of flow ⇒\(V = {\left[ {\frac{{Q{f^2}}}{{140}}} \right]^{\frac{1}{6}}}\)

3) hydraulic mean depth ⇒\(R = \frac{{5{V^2}}}{{2f}}\)

4) wetted perimeter ⇒ \(P = 4.75\sqrt Q\)