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Apart from the complex math we do to find that most effective cross section of a canal for a common man the explanation can be
1. It is easier to build. As trapezoidal cross section does not need vertical walls made of concrete and the lining can be easily done.
2. This trapezoidal section offers least frictional resistance. 
3. This offers a minimal flow speed even when the quantum of flow is very low. As rectangular section will have stagnent water.
4. The increase in flow depth is not equal to increased flow but the depth raised gradually increases even if water quantity is suddenly increased, thus ensures safety of canal and afjrcent areas.. This is because as depth increases the cross section area increases.
5. Finally , It is easy to maintain such as dredging and tile work in trapezoidal canal can be done by even unskilled labour and less equipments.

Aftr all civil engineering is to ease and secure the lives of people apart from just math.

by:-Er.sanjay kumar

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just a guess.. because it would lessen the impact of water or other objects to its sides? Instead of directly exerting force perpendicular to the walls, some of the the force would be redirected up.

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Common types of cross-sections for irrigation canals are trapezoid, parabolic, triangular, circular, and irregular (natural). Square / rectangular cross sections are used normally for concrete ducts.Out of these trapezoidal cross section is widely used due to following reasons :-

1)Heavy rains - The trapezoid has its width gradually increasing towards the top. In case of heavy rains , since the water level increases ,the trapezoid geometry ensures that the channel doesn’t overflow as the water is accommodated in the larger areas at the top of the trapezoid.

2) Velocity - The ratio of flow area to the contact area with the wall is very high. This decreases the effect of viscous forces on the flow velocity of water,thus making it move faster.

3) Safety - If someone or something falls into the canal by mistake, it is easier to climb a wall with a gradual gradient like the trapezoid unlike a vertical wall.

4.)Discharge-The best thing about a trapezoidal channel is that it has maximum discharge i.e., maximum volume of water flows through it within 1 second, when compared to rectangular, circular and triangular channels.

5.)This trapezoidal section offers least frictional resistance. 

6.)It is easy to maintain such as dredging and tile work in trapezoidal canal can be done by even unskilled labour and less equipments.

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