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### Froude Number Equations and Calculator

Froude Number, Equations and Calculator

The Froude number is a dimensionless ratio, relating inertial forces to gravitational forces. The Froude number represents the effect of gravity on the state of flow in a stream (Chow 1959). This useful number was derived by a nineteenth century English scientist, William Froude, who studied the resistance of ships being towed in water. He observed wave patterns along the hull of a moving ship and found that the same number of waves would occur as long as the ratio of the ship’s speed to the square root of its length were the same. Applied in hydraulics, the length is replaced by hydraulic depth,

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Froude Number, Equation

F = V / ( g d )0.5

Where:

V = velocity (ft/s)
g = acceleration due to gravity (32.2 ft/s2)
d = flow depth (ft)

When:

F = 1,     critical flow,
F > 1,     supercritical flow (fast rapid flow),
F < 1,     subcritical flow (slow / tranquil flow).

If the Froude number is less than one, gravitational forces dominate and the flow is subcritical, and if greater than one, inertial forces dominate and the flow is supercritical. The Froude number is used to determine the state of flow, since, for subcritical flow the boundary condition is downstream, and for supercritical flow it is upstream. When the Froude number equals one, the flow is at the critical state.

Reference:

National Engineering Handbook, Part 654
United Staes Department of Agriculture
Natural Resources Conservation Service

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