How to calculate the volume of water in a pond by a contour map?/ Finding volume of a contour lines.

 Eg:

Following are the different contours at 2m. intervals in a pond up to a water level with their respective areas. 

Sl. No.	Contour	Area in m²
1	550	775
2	552	920
3	554	1145
4	556	1565
5	558	1980
6	560	2650
7	562	3425

 

 

Calculate the volume of water in the pond.

To find:

The volume of water in the pond.

Calculation:

The volume of water is calculated by using the trapezoidal & prismoidal formulas for contour maps. The answer will be nearer to accuracy & slightly differ from each other.

Now, let us calculate the volume of water by using both of them to observe the difference.

1. Trapezoidal formula:

The volume of water in the pond

V = D х [{(A0 + An) ➗2} + (A1 + A2 + A3 + ---- + An - 1)]

Here,

 D = Interval between the successive contours 

 D = {562 - 560} = 2

A0 = area of 1st contour line = 775m²

A1 = area of 2nd contour line = 920m²

Similarly,

A2 = 1145m², A3= 1565m², A4 = 1980m², 

       An  👉 The area of the last contour = A6 =3425m²

(An - 1) 👉 Prior to last contour = A5 = 2650m²

Now,

The volume of water in a pond

V = D х  [{(A0 + A6) ➗2} + {A1 + A2 + A3 + A4 + A5}]

    = 2 х [{(775 + 3425) ➗2} + {920 + 1145 + 1565 + 1980 + 2650}]

    = 2 х [{2100} + {8260}]

     = 2 х [10,360]

 V  = 20,720m³

2. Prismoidal formula:

The volume of water in the pond

V = D/3 [ 1st area + last area + 4 Σ even area + 2 Σ odd area ]

V = [ (D ➗ 3)  х { (A0 + An) + 4  х ( A1 + A3 + A5 ) + 2  х ( A2 + A4)}]

   = [ (2 ➗ 3)  х { (775 + 3425) + 4  х ( 920 + 1565 + 2650 ) + 2  х ( 1145 + 1980)}]

   = [0.6667 х { ( 4200 ) +  4  х ( 5135 ) + 2 х ( 3125)}]

  = [0.6667 х { 4200  + 20540 + 6250 }]

  = [0.6667  х 30,990 ]

V = 20, 660 m³

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

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