Froude Number Formula

Froude number was titled after William Froude is a dimensionless number known as the ratio of characteristic velocity to the gravity wave velocity.

Froude Number Formula -1

Where the characteristic velocity is v and

the characteristic wave velocity is c,

gravity in terms of the Froude number is articulated as,

Froude Number Formula -2

Froude number is Fr,

velocity is v,

gravity is g,

characteristic length is l.

It is used to determine the resistance of partially moving body that is immersed in water.

Froude Number Solved Problems

Underneath are some of the solved problems based on Froude Number:

Problem 1: Find the  Froude number if the boat’s length is 5 m and the velocity is 20 s.


Known: length l = 5m,

velocity v = 20 m/s

The Froude number is articulated as,


\(F_{r} = \frac{v}{\left ( gl \right )^{\frac{1}{2}}}\)


\(F_{r} = \frac{20}{\left ( 9.8\times 5 \right )^{\frac{1}{2}}}\)


\(F_{r} =\frac{20}{4.427}\)


Fr = 2.86

Thus, the Froude number of the boat is 2.86.

 Problem 2: Calculate the velocity of the fish moving through the water if its length 0.3 m and Froude number is 0.9.


Known: l (length) = 0.3m

Fr (Froude number) = 0.9

The Froude number is given by,


\(F_{r} = \frac{v}{\left ( gl \right )^{\frac{1}{2}}}\)


The velocity of the moving fish is

v= Fr × (gl)(1/2)

v = 0.9 × (9.8 × 0.3)(0.5)

v = 0.9 × 1.71

v = 1.539 m/s

Thus, the velocity of the moving fish is 1.59 m/s.


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