Physics:Most efficient section

A channel section is considered as the most economical or most efficient when it passes a maximum discharge for given cross section area, resistance coefficient, and bottom slope. From the equation of continuity it is evident that for area of cross section being constant, discharge is maximum when the velocity of discharge is maximum. And from Chézy formula and Manning formula for a certain value of slope and surface roughness, velocity is maximum when the hydraulic radius is maximum. And if we take the area as constant, hydraulic radius is maximum if the wetted perimeter is minimum. A semicircular section is the best economical channel but due to difficulty in creating it, a trapezoidal section can be considered most efficient.