The Froude number is defined as

$$

Fn = \frac{v}{\sqrt{g LWL}} where $v$ is the speed in m/s, g is the acceleration due to gravity, and $LWL$ is the Length on the Waterline.

The Froude number is used to compare the Wave Making component of resistance between bodies of various sizes and shapes.

In fluid dynamics, the Froude number is the reciprocal of the square root of the Richardson number.

When used in the context of the Boussinesq approximation it is defined as

$\{u\backslash over\; \backslash sqrt\{g\text{'}\; h\}\}$

where g' the reduced gravity (see Boussinesq approximation) and $h$ a representative vertical lengthscale. Strictly, this is known as the densimetric Froude number.

The densimetric Froude number is usually preferred by modellers who wish to nondimensionalize a speed preference to the Richardson number which is more commonly encountered when considering stratified shear layers.

For example, the leading edge of a gravity current moves with a front Froude number of about unity.

Origins

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The quantification of the resistance of floating objects is generally credited to William Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. Froude's observations led him to derive the Wave-Line Theory which first described the resistance of a shape as being a function of the waves caused by varying pressures around the hull as it moves through the water. The Naval Constructor Reech put forward the concept in 1832 but had not demonstrated how it could be applied to practical problems in ship resistance. Speed length ratio was originally defined by Froude in his 'Law of Comparison' in 1868 in dimensional terms as :

$\backslash textrm\{Speed\; Length\; Ratio\}\; =\backslash frac\; \{V\}\{\backslash sqrt\; \backslash textrm\{LWL\}\; \}$

where:

v = speed in knots

LWL is in feet

The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did.

It is sometimes called Reech-Froude number after Ferdinand Reech.

Dimensionless numbers | Fluid dynamics

Froude-Zahl | Número de Froude | Frouden luku | Numero di Froude | Getal van Froude | Число Фруда | 福祿數