ORIGIN OF THE FROUDE NUMBER

In the summer of 2002, while researching the writing of Milestones of Hydrology. I noticed that Ven Te Chow had mentioned the Froude number in his popular textbook, but had not elaborated on its origins.1 The Froude number, a fundamental principle of open-channel hydraulics, is defined as the ratio of the mean velocity of the flow (Manning or Chezy) to the relative celerity of dynamic waves.

In an effort to tell the story accurately, I consulted several books and, to my surprise, learned that Froude had not developed the Froude number per se. Froude's major work, published in 1861, had dealt with the hydrodynamics of ship stability.

Between 1863 and 1867, Froude showed that scaling between model and prototype was possible only when the speed (V) of the ship was proportional to the square root of its length (L). He called this concept the "Law of Comparison." The constant of proportionality k [with dimensions L1/2 T -1] is the number that applies to both model and prototype.

V = k L1/2

Froude's contributions to society, however, were of such importance that he was highly regarded by his peers. After his death, to honor his memory, they attributed to him the concept which now bears his name. This concept states that the mean velocity V of the flow [L T -1 units] is proportional to the relative celerity of dynamic waves:

V = F (gD)1/2

in which F = Froude number, dimensionless; D = hydraulic depth [L units]; and g = gravitational acceleration [L T -2 units].


 1 Chow, V. T. (1959). "Open-channel hydraulics," McGraw-Hill, New York.
 

Ski-jump spillway at Tocantins dam, Para, Brazil

Ski-jump spillway at Tocantins dam, Para, Brazil.