Froude Number Calculator
Calculate the Froude number for open-channel flow: Fr = v / sqrt(g * d), the ratio of flow velocity to gravitational wave speed.
Froude Number
0.957990
Froude Number vs Flow Velocity
Formula
## Froude Number The Froude number characterises the ratio of flow inertia to gravitational effects in open-channel flow. ### Formula **Fr = v / sqrt(g d)** - *v* = mean flow velocity - *g* = gravitational acceleration - *d* = hydraulic depth (cross-section area divided by top width) Fr < 1: subcritical (tranquil). Fr = 1: critical. Fr > 1: supercritical (rapid).
Esempio Risolto
River at 3 m/s with 1 m depth.
- 01Fr = v / sqrt(g d)
- 02Fr = 3 / sqrt(9.807 * 1)
- 03Fr = 3 / 3.131
- 04Fr = 0.958 (subcritical, but nearly critical)
Domande Frequenti
What is the physical meaning of the Froude number?
It compares the speed of the flow to the speed of surface gravity waves. When Fr > 1, flow moves faster than waves can propagate upstream, so upstream conditions cannot influence downstream.
How does the Froude number relate to ship design?
For ships, the Froude number (based on hull length) determines wave-making resistance. Ships are most efficient below the hull speed, roughly Fr = 0.4.
What happens at Fr = 1?
Critical flow, with minimum specific energy for a given discharge. This condition is used in weir design to measure flow rates.
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