How this calculator works
The Froude number compares inertia with gravity in a free-surface flow. Values below one allow shallow-water disturbances to travel upstream; values above one indicate supercritical flow. Use hydraulic depth A/T rather than hydraulic radius A/P. They are equal only in special limiting geometries. The classification applies to the shallow-water, hydrostatic wave model.
Formula
Fr = v/sqrt(g Dh); Dh = A/T. v = Fr sqrt(g Dh); Dh = v^2/(g Fr^2). T is water surface width, not wetted perimeter.
Worked example
With v = 3 m/s, Dh = 1 m and g = 9 m/s2, Fr = 1. With v = 1.5 m/s under the same conditions, Fr = 0.5.
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Frequently asked questions
What is the depth for a rectangle?
A = by and T = b, so hydraulic depth equals the actual water depth y.
What does Fr = 1 mean?
Mean flow speed equals shallow-water wave speed. This is critical flow in the model.
Can I use pipe diameter as depth?
Not for a full pressurized pipe. Open-channel hydraulic depth requires a free-surface top width.