In
continuum mechanics, the
Froude number (
Fr) is a
dimensionless number defined as the ratio of the flow inertia to the external field (the latter in many applications simply due to
gravity). Named after
William Froude (;), the Froude number is based on the
speed–length ratio as defined by him, and is defined as:
where
u0 is a characteristic
flow velocity,
g0 is in general a characteristic
external field, and
l0 is a characteristic length. The Froude number has some analogy with the
Mach number. In theoretical
fluid dynamics the Froude number is not frequently considered since usually the equations are considered in the high Froude limit of negligible external field, leading to homogeneous equations that preserve the mathematical aspects. For example homogeneous Euler equations are
conservation equations.