Free · Physical and mathematical models

Wetted Hydraulic Radius for Five Cross Sections

Find flow area divided by wetted perimeter for full or part-filled pipes and rectangular, triangular or trapezoidal open channels.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Find flow area divided by wetted perimeter for full or part-filled pipes and rectangular, triangular or trapezoidal open channels.

Rh=A/Pwet; the free water surface is excluded from Pwet

Worked example

Enter these known values and leave the other values blank.

Shape
Pipe (full)
Radius (r)
2 mm
Area
12.566 mm²
Wetted perimeter
12.566 mm
Hydraulic radius
1 mm

Assumptions and limitations

  • Hydraulic radius is a geometric ratio of flow area to wetted boundary length. It is not the pipe radius or hydraulic depth and does not determine discharge by itself.
  • Open-channel perimeter includes only contact with the solid boundary; the free surface is excluded.
  • Triangular and trapezoidal sections have equal positive side slopes, measured horizontal run per unit vertical rise.
  • Part-filled pipe uses a circular segment with fill strictly between zero and the full diameter. Positive-root inverse branches choose one geometric solution.
  • Area or perimeter can recover a full-pipe radius. Hydraulic radius alone remains incomplete in the retained constraint graph.

Common questions

How should I use an inverse?

Leave the required unknown empty and supply compatible known values. Multiple mathematical solutions or zero denominators can prevent a unique inverse.

What does this model assume?

Hydraulic radius is a geometric ratio of flow area to wetted boundary length. It is not the pipe radius or hydraulic depth and does not determine discharge by itself.

References

Replace explanatory external images with original accessible descriptions preserving every image condition and control relationship. Restrict part-filled pipes to a water depth strictly below the diameter, where the circular segment model has a real wetted arc.

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