Trapezoidal Cross Section
A trapezoid shape is sometimes used for manmade channels and the cross section of natural stream channels are often approximated by a trapezoid area. The diagram at the right shows a trapezoid and the parameters typically used for its shape and size in open channel flow calculations. Those parameters, which are used to calculate the trapezoid area and wetted perimeter, are y, the liquid depth; b, the bottom width; B the width of the liquid surface; λ, the wetted length measured along the sloped side; and α, the angle of the sloped side from vertical. The side slope is usually specified as horiz:vert = z:1.
The cross sectional area of flow is the trapezoid area: A = y(b + B)/2, or
A = (y/2)(b + b + 2zy), because B = b + 2zy, as can be seen from the diagram.
Simplifying, the trapezoid area is: A = by + zy2.
The wetted perimeter is: P = b + 2λ, but by Pythagoras Theorem:
λ2 = y2 + (yz)2, or λ = [y2 + (yz)2]1/2, so the wetted perimeter is:
P = b + 2y(1 + z2)1/2, and the hydraulic radius for a trapezoid is:
RH = (by + zy2)/[b + 2y(1 + z2)1/2]