What this calculator does
Froude Number works out ratio of flow inertia to gravity in open-channel or ship-hull flow. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaFr = u / √(g·Hd), Hd = A/W
The inputs explained
| Field | What to enter |
|---|---|
| Flow velocity (u) (m/s) | A number, measured in m/s. Starts at 2.5. |
| Cross-section area (A) (m²) | A number, measured in m². Starts at 6. |
| Channel width (W) (m) | A number, measured in m. Starts at 4. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with flow velocity (u)
Every other input is held at the calculator’s starting values while flow velocity (u) varies. Select any row to load that scenario into the calculator.
How the answer changes with flow velocity (u)
| Flow velocity (u) (m/s) | Froude number (Fr) | Flow regime | Hydraulic mean depth |
|---|---|---|---|
| 1.25 | 0.3259 | Subcritical (tranquil flow) | 1.500 m |
| 1.88 | 0.4902 | Subcritical (tranquil flow) | 1.500 m |
| 2.5 | 0.6518 | Subcritical (tranquil flow) | 1.500 m |
| 3.75 | 0.9777 | Subcritical (tranquil flow) | 1.500 m |
| 5 | 1.304 | Supercritical (rapid flow) | 1.500 m |
| 7.5 | 1.955 | Supercritical (rapid flow) | 1.500 m |