Wetted Perimeter Calculator - Channel Flow & Pipe Design

What Is Wetted Perimeter?

The wetted perimeter is the length of a channel's or pipe's cross-section that touches flowing water. It is measured along the boundary of a pipe, ditch, or river, wherever water is in direct contact with a solid surface. Engineers use it to size drainage channels, irrigation ditches, sewers, and culverts. This calculator finds the wetted perimeter for three common shapes: a circular pipe, a rectangular channel, and a trapezoidal channel.

How the Calculator Works

Pick a shape, then enter its dimensions and the depth of the water.

• Circular pipe: enter the diameter and the fill height (how deep the water sits in the pipe).
• Rectangular channel: enter the width and the fill height.
• Trapezoidal channel: enter the top width, the bottom width, the channel depth, and the fill height.

All values must be positive numbers. For a circular pipe, the fill height cannot be greater than the diameter. For a trapezoidal channel, the fill height cannot be greater than the depth. If a value breaks these rules, the calculator shows an error instead of a result.

Wetted Perimeter Formulas

Circular Pipe Formula

For a pipe with diameter D and water fill height y:

• Partially filled (y < D): P = D × arccos((D − 2y) / D)
• Fully filled (y = D): P = πD, the pipe's full circumference

The calculator does not accept a fill height greater than the diameter.

Rectangular Channel Formula

For a channel with width b and water depth y:

P = b + 2y

The two sides each contribute a length equal to the water depth, and the flat bottom contributes the width.

Trapezoidal Channel Formula

A trapezoidal channel is not a fixed shape until its dimensions are set. The calculator asks for the top width, the bottom width, and the channel depth, then works out the side slope from those three numbers:

z = (topWidth − bottomWidth) / (2 × depth)

Here z is the "side slope," the horizontal distance a bank moves for every unit it rises. Once z is known, the wetted perimeter uses the fill height y (how deep the water actually is, which can be less than the full channel depth):

P = bottomWidth + 2y × √(1 + z²)

How to Calculate Wetted Perimeter: Worked Examples

Example 1: Circular Pipe

A pipe has a diameter of 10 m and a fill height of 2 m. Since 2 m is less than 10 m, the pipe is only partially full.

acos((10 − 2×2) / 10) = acos(0.6) ≈ 0.9273 radians

P = 10 × 0.9273 ≈ 9.27 m

Example 2: Rectangular Channel

A channel is 5 m wide and holds water 2 m deep.

P = 5 + 2 × 2 = 9.00 m

Example 3: Trapezoidal Channel

A channel has a top width of 8 m, a bottom width of 5 m, and a depth of 2 m. First find the side slope:

z = (8 − 5) / (2 × 2) = 0.75

If the channel is filled to the brim (fill height = 2 m):

P = 5 + 2 × 2 × √(1 + 0.75²) = 5 + 4 × 1.25 = 10.00 m

If the same channel holds only 1 m of water, the side slope stays the same (it depends on the channel's shape, not the water level), but the perimeter changes:

P = 5 + 2 × 1 × 1.25 = 7.50 m

Wetted Perimeter and Hydraulic Radius

Wetted perimeter is rarely the final answer engineers want. It is usually a step toward the hydraulic radius, R = A / P, where A is the cross-sectional area of the flowing water and P is the wetted perimeter. A smaller wetted perimeter for the same flow area gives a larger hydraulic radius, which means less friction between the water and the channel walls. Hydraulic radius feeds directly into Manning's formula, the equation most commonly used to estimate flow velocity in open channels and partially filled pipes.

Where Wetted Perimeter Matters

Irrigation engineers use it to size ditches that move water without excessive loss. Stormwater engineers use it to check that drainage channels and culverts can carry a flood without overflowing. Wastewater engineers use it to keep flow fast enough in sewers to stop solids from settling. Wetted perimeter also appears in river studies, where it helps model how a natural channel carries floodwater.

History

The wetted perimeter became a standard part of open-channel hydraulics in the 18th and 19th centuries, when engineers such as Antoine Chézy and Robert Manning built formulas that linked channel shape to flow velocity. The Chézy formula appeared in 1769, and the Manning formula followed in 1889. Both treat the wetted perimeter, through the hydraulic radius, as a main driver of how much friction slows the water down. The same relationship still underlies modern channel and pipe design.

Frequently Asked Questions

What is wetted perimeter?

It is the length of the boundary of a channel or pipe that touches the water flowing through it, measured around the cross-section.

How is wetted perimeter different from hydraulic radius?

Wetted perimeter is a length. Hydraulic radius is the flow area divided by the wetted perimeter (R = A/P). Hydraulic radius, not wetted perimeter alone, goes directly into Manning's formula.

Does a fuller pipe always have a larger wetted perimeter?

Yes, up to the point where the pipe is completely full. As fill height increases from empty to full, the wetted perimeter increases steadily, reaching πD (the full circumference) exactly when the pipe is full.

Why does the trapezoid formula need both a depth and a fill height?

Depth and top width fix the shape of the channel's banks, which sets the side slope. Fill height is how deep the water actually sits, which can be less than the full depth. The calculator uses depth and top width to find the slope, then uses fill height to find the perimeter.

Can wetted perimeter be used for pipes as well as open channels?

Yes. A fully filled pipe's wetted perimeter is simply its circumference, πD. A partially filled pipe uses the arccos formula shown above.

What units does this calculator use?

All inputs and results are in meters. The formulas work with any consistent unit of length, as long as the same unit is used for every input.

References

1. "Wetted Perimeter." Wikipedia, Wikimedia Foundation, https://en.wikipedia.org/wiki/Wetted_perimeter.
2. "Manning Formula." Wikipedia, Wikimedia Foundation, https://en.wikipedia.org/wiki/Manning_formula.