# How to calculate the Balancing Depth of Canal? Technical terms of Canal

For a given canal section, the depth of cutting for which area is equal to the area of filling is called balancing depth. According to the cutting and filling process canal are of three types.

## Types of Canal

1. Fully cutting canal:- The canal whose bed level is below the ground is known as a fully cutting canal.
2. Fully filling canal:- The canal whose bed level is above the ground level is known as fully filling the canal.
3. Partially cutting and partially cutting canal:- The canal which is constructed by partially cutting and partially filling is known as Partially cutting and Partially cutting canal.

Before calculating the balancing depth of the canal you must know some technical terms used for the canal. If you already know then you can skip and move to the bottom of this article.

## Technical terms used in canal Drawing.

1) FSL (Full Supply Level D):- The maximum depth of water supply in the canal is known as full supply level (FSL).

2) Canal Bed: – The bottom surface of the canal on which water flows is known as canal bed.

3) Embankment:-The deposited soil at the side of canal by cutting the bed of the canal is known as embankment.

4) Side Slope:- The slope given to the vertical section of the canal is known as side slope. It make the canal trapezoidal in shape.

It is provided because the soil has low shear strength due to which latter it will cut by the following water and make slope land itself. So, it is better to provide a side slope in the initial state.

5) Berm:- The horizontal distance between the top point of the side slope and the toe of the Embankment is known as Berm.

The distance of the berm is given by 1.5 D. Where d is the full depth of the water supply (FSL) in fully cutting. But if the canal is formed by partially cutting and partially filling then we take 2D as the distance of the berm. If the canal is fully filling then the distance of the berm is taken as 3D.

6) Dowel:- The small rising at the side of the service road and top of the canal for the safety of running vehicles is known as a dowel. Its width is taken 0.5 meters and height is also taken as 0.5 meters.

9) Free Board:- The vertical distance between high flow level and the top level of embankment is known as freeboard.

Let us take an example to calculate balancing depth of canal.

## How to calculate the Balancing Depth of Canal?

Q) An irrigation canal has a bottom width of 8 meters and a side slope of 1.5 H: 1V in cutting and 2 H: 1 V in filling. The width of the crest of the bank is 2 meters and its height above the ground level is 3 meters. Compute balancing depth of the canal and draw net x-section of the various dimensions and level it.

Solution:-

Given,

Bed width (b) = 8 meter

Side Slope (z) = 1.5 in Cutting

Side slope (z1) = 2 in Filling

Width of embankment (w) = 2 meter

Hight of embankment (h1) = 3 meter

Balancing depth (h) =?

Now,

We have area of Trapezoidal Section = b*h + 2*(1/2*h*z*h)

Therefore, Area of cutting = 8h + 2(1/2*h*1.5h) = 8h+1.5h2

Area of filling = 2[2*3+{1/2*(3*2)*3}*2] = 48m2

For balancing depth; we have

Area of cutting = Area of filling

Or,        8h + 1.5h2 = 48

Or,      8h + 1.5h2 – 48 = 0

Solving; we get,

H = 3.58m

Hence, the balancing depth of canal is 3.58 m

Q) A canal has a bed width of 8 meters. The full supply depth of water is 1.5 meters, side slope in cutting 1:1 and filling 1.5:1. The top width of the bank is 1.8 meters and the service bank is 5 meters. Freeboard is kept 0.6 meters. Calculate the balancing depth of the canal so as to get the most economical section.

Solution:-

Given,

Canal Bed (b) = 8 m

Full supply depth (d) 1.5 m

Side slope at cutting = 1

Side slope at filling = 1.5

Top width of embankment = 1.8 meter

Service bank = 5 meter

Free board = 0.6 meter.

Let, service bank (road) is provided 0.4 meter above F.S.L

Therefore,

Area of cutting = b*d + 2*1/2*d*d

Area of cutting = 8d + 2*1/2*d*d= 8d+d2

Area of filling,

Upper Part of embankment = [1.8*0.2+2*1/2{1.5*(0.2)2}]

Lower part of embankment = [(5+1.8+2*1.5*0.2)(1.9-d)+2*1/2*1.5(1.9-d)2]*2

Then total Area =[ Upper Part + Lower part]

= [0.42+7.4(1.9-d)+1.5(1.9-d2)]*2

For balancing depth;

Area of cutting = Area of filling

Or, 8d+d2 = [0.42+7.4(1.9-d)+1.5(1.9-d)2]*2

Solving using calculator, we get ,

d = 1.255 m or 15.85 m (unfeasible)

so , Balancing depth =1.25 m

Happy Learning – Civil Concept

Contributed by,

Civil Engineer – Ranjeet Sahani