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Open Channel Froude Number and Hydraulic Mean Depth

Find Froude number from flow velocity and hydraulic mean depth, or recover a supported missing measure with unit controls.

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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

With a wetted cross-section of 4 m², top water width 2 m, speed 4 m/s and chosen gravity 8 m/s², hydraulic mean depth is 2 m and Froude number is 1.

D = A/T; Fr = u/√(gD)

Worked example

Enter these known values and leave the other values blank.

Area of cross-section (A)
4 m²
Top water-surface width (T)
2 m
Flow velocity (u)
4 m/s
Acceleration due to gravity (g)
8 m/s²
Hydraulic mean depth (D)
2 m
Froude number (Fr)
1

Assumptions and limitations

  • A is the wetted flow cross-section and T is the top width of the water surface. Hydraulic mean depth D=A/T equals physical water depth for a rectangular section, but differs for an irregular channel. It is not hydraulic radius A divided by wetted perimeter.
  • This retained moving-flow workflow requires strictly positive area, top width, mean depth, speed, gravity and Froude number; stationary zero-speed cases are excluded. Default gravity is an editable approximation: 9.81 m/s² in metric or 32.185 ft/s² in the imperial preference. These rounded defaults describe slightly different numerical values.
  • Enter area and top width to infer D, or supply D directly. With g known, speed and D give Fr, or Fr and D give speed, or speed and Fr give D. Clear g to infer it from speed, D and Fr. Two of A, T and D support their missing third. Fr alone does not fix flow speed or channel geometry.
  • The ideal gravity-wave comparison classifies positive Fr below 1 as subcritical, equal to 1 as critical, and above 1 as supercritical. It does not account for channel roughness, nonuniform velocity, air entrainment, sediment or a detailed hydraulic design.

Common questions

Which channel width belongs in the formula?

Use the water surface top width, not the wetted perimeter or bottom width. Hydraulic mean depth divides the wetted cross-sectional area by that top width.

Does this calculate hydraulic radius?

No. Hydraulic radius is area divided by wetted perimeter; this workflow uses hydraulic mean depth A/T for the gravity-wave Froude relation.

Can I solve a missing speed or depth?

Yes. With gravity supplied, speed and Fr determine D=u²/(gFr²), while D and Fr determine u=Fr√(gD). Clear the unknown first; Fr alone is insufficient.

References

Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor.

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