Trapezoidal Channel Cross-Sectional Area
Trapezoidal Channel Cross-Sectional Area
Trapezoidal channels are the standard shape for earthen canals and many concrete-lined channels because sloped sides are self-stable in loose soil, unlike a vertical-walled rectangular channel. Before any hydraulic calculation such as Manning's equation can be applied, the wetted cross-sectional area at a given depth has to be known from simple channel geometry. This area calculation is purely geometric and unit-homogeneous, independent of the flow itself, which is why it is normally the first step before computing velocity or discharge — getting the geometry wrong propagates directly into every downstream hydraulic result.
The trapezoidal area is A = (b + z*y)*y, the average of the bottom and top widths times the depth. where b_bot is the channel bottom width, y_dep is the flow depth, and z_side is the side slope expressed as horizontal run per unit vertical rise (dimensionless).
Inputs
b_bot := 3 m=3 m
y_dep := 1.2 m=1.2 m
z_side := 1.5=1.5
The top water width exceeds the bottom width by z*y on each side combined, so the water surface width is b + z*y, and the average of top and bottom widths times depth gives the trapezoid area.
A_trap := (b_bot + z_side·y_dep)·y_dep=5.76 m^2
Results
A cross-sectional area of a few square metres is typical for a small-to-medium irrigation canal at this depth, and this area feeds directly into Manning's equation to get velocity and discharge. Steeper side slopes (larger z) add area quickly for the same depth, so channel capacity is often increased by flattening the sides rather than deepening the channel, especially where excavation depth is constrained.
Assumptions & limitations
- Trapezoidal, prismatic (constant cross-section) channel assumed.
- Side slope z is the same on both banks.
- Purely geometric relation — no flow or roughness information used here.
- Flow depth assumed uniform across the channel width.