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,

\(\begin{array}{l}F_{r} = \frac{v}{\left ( gl \right )^{\frac{1}{2}}}\end{array} \)
\(\begin{array}{l}F_{r} = \frac{20}{\left ( 9.8\times 5 \right )^{\frac{1}{2}}}\end{array} \)
\(\begin{array}{l}F_{r} =\frac{20}{4.427}\end{array} \)

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,

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

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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