Most efficient trapezoidal section of canal

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

canal section.JPG
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

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