# 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.

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

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
ItÂ isÂ usedÂ toÂ determineÂ theÂ resistanceÂ ofÂ aÂ partiallyÂ movingÂ bodyÂ thatÂ isÂ immersedÂ inÂ water.

### Froude Number Solved Problems

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

Problem 1:Â FindÂ theÂ Â FroudeÂ numberÂ ifÂ theÂ boat’sÂ lengthÂ isÂ 5Â mÂ andÂ theÂ velocityÂ isÂ 20Â mÂ /Â s.

Answer:

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.

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

Answer:
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= FrÂ Ã— (gl)(1/2)

v = 0.9Â Ã— (9.8Â Ã— 0.3)(0.5)

v = 0.9Â Ã— 1.71

v = 1.539 m/s

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

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