Most efficient trapezoidal section of canal

The most efficient trapezoidal section of canal can be calculated as follows

Let,


Base width of the canal=B


Side slope=m (1V:mH)


Flow depth = h


Wetted perimeter= P

The cross sectional area, A=By+my^2


ie B= (A-m*h^2)/h


ie B=A/h-m*h


Wetted perimeter P= B+2*h *sqrt(m^2+1)


For most efficient channel, dP/dh=0


ie -A-m*y^2+2 y^2 sqrt(m^2+1)=0


ie B= y(2*sqrt(m2+1)-1-m)


Therfoer B/y=2*sqrt(m2+1)-1-m is the required relationship