Froude number

The Froude number (Fr) is a dimensionless number that relates the force of inertia and the force of weight. It owes its name to the English hydrodynamic engineer and naval architect William Froude (1810 – 1879). Froude number has an important kinematic meaning because depending on the value that it assumes a current can be subcritical or supercritical.

Moreover, always starting from Froude number, it can be demonstrated that for the motions of an incompressible liquid confined in a channel, the height of the free surface depends on Froude number. The force of inertia F can be written, according to the second principle of dynamics, as the product of mass and acceleration:

\[F=\dfrac{m}{a}=\dfrac{\rho L^4}{t^2}\]

The weight P turns out to be the product between mass and the acceleration of gravity.

\[P=\dfrac{m}{g}=\rho gL^3\]

The ratio between the two forces:

\[\dfrac{F}{P}=\dfrac{L}{gt^2}\]

Is proportional to Froude number:

\[\textrm{Fr}=\sqrt{\dfrac{V^2_0}{gL_0}}\]

Where: ρ is density; L0 is a reference length; V0 is a reference velocity; g is the reference acceleration of gravity. Froude number can also be expressed as a function of Richardson number which is in fact the reciprocal of its square root.

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