# Froude Number Formula

Froude Number Formula

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

$Fr=\frac{v}{c}$

Where, the characteristic velocity is v and

the characteristic wave velocity is c,

gravity in terms of the Froude number is articulated as,

$Fr=\frac{v}{(gl)^{\frac{1}{2}}}$

Where,
Froude number is Fr,

velocity is v,

gravity is g,

characteristic length is l.

It is used to specify the resistance of a body which is immersed partially moving along with water.

Froude Number Solved Problems

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

Problem 1: Find the Froude number if the length of the boat is 2m and velocity is 10 m/s.

Known: length l = 2m, velocity v = 10 m/s

The Froude number is articulated as,

$Fr=\frac{v}{(gl)^{1/2}}=\frac{2m/s}{(9.8m/s^{2}\times&space;2m)^{1/2}}=0.451$

Thus, the Froude number of the boat is 0.451.

Problem 2: Compute the velocity of the moving fish in the water if its length 0.5 m and Froude number is 0.72.

Known: l (length) = 0.5m, Fr (Froude number) = 0.72

The Froude number is given by,

$Fr=\frac{v}{(gl)^{1/2}}$

$The\;velocity\;of\;the\;moving\;fish\;is$

$v=Fr\times&space;(gl)^{1/2}$

$v=0.72\times&space;(9.8\times&space;0.5)^{1/2}$

$v=1.59m/s$

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

#### Practise This Question

A truck has a mass of 8000 kgs, a car has a mass of 1000 kgs and a bike has a mass of 100 kgs. Both the truck and car are moving on a level road at 45m/s.The bike, however, is going on the same level road at 55m/s. The kinetic energy will be more for the _______.