Froude resistance curve

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 (/ˈfruːd/;), the Froude number is based on the speed–length ratio which he 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.

However, in naval architecture the Froude number is a very significant figure used to determine the resistance of a partially submerged object moving through water. Dynamics of vessels that have the same Froude number are easily compared as they produce a similar wake, even if their size or geometry are otherwise different.

The Denny Ship Model Experiment tank in Dumbarton, Scotland, has a bust of Froude near the front door.

In open channel flows, Bélanger (1828) introduced first the ratio of the flow velocity to the square root of the gravity acceleration times the flow depth. When the ratio was less than unity, the flow behaved like a fluvial motion (i.e., subcritical flow), and like a torrential flow motion when the ratio was greater than unity.

Quantifying 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 Ferdinand Reech had put forward the concept in 1852 for testing ships and propellers. Speed/length ratio was originally defined by Froude in his Law of Comparison in 1868 in dimensional terms as:

...
Wikipedia