Froude Number Calculator (Open Channel Flow Regime)
Froude number of flow in a channel, a river or a spillway from the speed and depth, with whether the flow is subcritical or supercritical and the critical depth.
Results
The dashed line marks the value you entered.
What this tool does
The Froude number compares the flow speed with the speed √(g·h) at which a small wave travels over water of that depth. Below 1 the flow is subcritical — slow and deep, and ripples can travel upstream; above 1 it is supercritical — fast and shallow, and ripples are swept downstream. Near 1 the surface is unstable and waves form. A hydraulic jump is what happens where supercritical flow slows to subcritical, as at the foot of a spillway. Use the hydraulic depth (area ÷ surface width) for a non-rectangular channel.
Formula
Fr = v ÷ √(g × h) · Fr < 1 subcritical, Fr = 1 critical, Fr > 1 supercritical · specific energy E = h + v² ÷ 2g
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v | Speed | m/s |
h | Depth | m |
FR | Froude number | — |
CL | Flow regime | — |
CW | Speed of a small surface wave | m/s |
SE | Specific energy of the flow | m |
YC | Critical depth (rectangular channel, same flow per metre of width) | m |
Worked example
- Speed2 m/s
- Depth1 m
- Froude number0.639
- Flow regimeSubcritical (slow and deep) — disturbances can travel upstream
- Speed of a small surface wave3.13 m/s
- Specific energy of the flow1.204 m
- Critical depth (rectangular channel, same flow per metre of width)0.742 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.