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Trapezoidal Channel Area Calculator

Civil and hydraulic engineering tool to calculate the flow area ($A$), wetted perimeter ($P$), and hydraulic radius ($R$) for open channels with side slope $z:1$.

Flow Cross-Sectional Area (A)
— m² / ft²
Top Water Width (T) —
Wetted Perimeter (P) —
Hydraulic Radius (R = A/P) —
Bed Width (b) Top Water Width (T = b + 2zy) Depth (y) z:1

Open Channel Hydraulics Formulas (Trapezoidal Cross-Section)

Trapezoidal channels are the most widely used shape for engineered irrigation canals, storm drainage ditches, and culvert cross-sections due to stable soil bank slopes ($z:1$, where $z$ is horizontal distance per 1 vertical foot or meter).

1. Cross-Sectional Flow Area

A = (b + z × y) × y

2. Top Water Surface Width

T = b + 2 × z × y

3. Wetted Perimeter

The total perimeter of the channel bed and banks in contact with fluid:

P = b + 2 × y × √(1 + z²)

4. Hydraulic Radius

R = A / P
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Frequently Asked Questions

How do you calculate the cross-sectional area of a trapezoidal channel?
Add the bottom width and top width of the channel, multiply the sum by the vertical depth, and divide by two. The formula is A = ½(b + T)y, where b is the bottom width, T is the top width, and y is the depth.
How do you calculate the top width of a trapezoidal channel?
For a symmetrical channel with side slope z horizontal to 1 vertical, the top width is T = b + 2zy, where b is the bottom width and y is the depth.
What is the formula for the area of an open trapezoidal channel?
The cross-sectional area is A = y(b + zy) for a symmetrical channel with side slope z:1, bottom width b, and water depth y. This is equivalent to the trapezoid area formula when the top width is calculated as b + 2zy.
Is channel cross-sectional area the same as wetted area?
The cross-sectional flow area is the area occupied by the water. Wetted perimeter is the length of the channel boundary in contact with the water. These are different quantities used in hydraulic calculations.
Can I calculate the area of a partially filled trapezoidal channel?
Yes. Use the water depth rather than the full channel depth, along with the bottom width and side slopes, to calculate the water's cross-sectional area.
Can this calculator calculate water flow rate?
Cross-sectional area alone does not determine flow rate. To calculate discharge, you also need the average flow velocity or sufficient additional hydraulic information to estimate it.
What does a channel side slope of 2:1 mean?
A side slope of 2:1 usually means two horizontal units for every one vertical unit. Confirm the convention used by the calculator before entering the side slope.