Froude number

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In fluid dynamics, the Froude number (named after William Froude) is the reciprocal of the square root of the Richardson number.

It is sometimes called Reech-Froude number after Ferdinand Reech, who introduced it for testing ships and propellers in 1852. Also, a number of other French researchers used this number before Froude.

The Froude number is defined as

<math>

u\over\sqrt{gh} </math> where <math>u</math> is a representative speed, g the acceleration due to gravity, and <math>h</math> a representative length scale.

The Froude number gives the ratio of inertial forces to gravitational forces, and is used by ship designers to determine the size and speed of models for tank testing, when wave-making behaviour is the primary interest and frictional forces may be neglected. When frictional forces are of primary interest, the Reynolds number is the appropriate scaling factor.

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

<math> {u\over \sqrt{g' h}}</math>

where g' the reduced gravity (see Boussinesq approximation) and <math>h</math> 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.de:Froude-Zahl es:Número de Froude fi:Frouden luku it:Numero di Froude nl:Getal van Froude zh:福祿數