Tag Archives: Most efficient trapezoidal section of canal

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