In open channel flows,  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.  The naval constructor Frederic Reech had put forward the concept much earlier in 1852 for testing ships and propellers but Froude was unaware of it. Speed–length ratio was originally defined by Froude in his Law of Comparison in 1868 in dimensional terms as:
where:
* = flow speed
* = length of waterline
The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. In France, it is sometimes called Reech–Froude number after Frederic Reech.