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Froude Number Formula

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  • Last Updated : 25 Apr, 2022

Dimension analysis does not include such shapes which do not have any dimensions. The composition of the values having measurements is used to define these dimensionless quantities. Strain, for example, is a measure of deformation that may be expressed as the proportion of change in length to the original length. A strain has no dimensions since the unit is ‘L’ in both circumstances.

Froude Number

The Froude number is a non-dimensional number that represents the ratio of typical speed to gravity wave velocity. It was named after the physicist William Froude. The prototypes are analyzed using dimensionless numbers. Reynolds numbers, Weber’s number, and Froude’s number are all examples of these numbers. The Froude number determines dynamic similarity in circumstances when the gravitational pull is significant. Flow across open channels, flow over the dam’s spillway, and so on are some instances.

Formula

Fr = \frac{v}{\sqrt{gl}}

where,

  • v denotes the velocity
  • g denotes the acceleration due to gravity
  • l denotes the length

Sample Problems

Problem 1. Calculate the Froude number for an object of length 10 m and velocity 40 m/s.

Solution:

l = 10 m

v = 40 m/s

F_r = \frac{v}{\sqrt{gl}}

= 40/8.854

= 4.51

Problem 2. Calculate the Froude number for an object of length 0.3 m and velocity 1.5 m/s.

Solution:

l = 0.3 m

v = 1.5 m/s

F_r = \frac{v}{\sqrt{gl}}

= 0.9

Problem 3. Calculate the Froude number for an object of length 1 m and velocity 1.5 m/s.

Solution:

l = 1 m

v = 1.5 m/s

F_r = \frac{v}{\sqrt{gl}}

= 0.47

Problem 4. Calculate the Froude number for an object of length 5 m and velocity 1.5 m/s.

Solution:

l = 5 m

v = 1.5 m/s

F_r = \frac{v}{\sqrt{gl}}

= 0.21

Problem 5. Calculate the Froude number for an object of length 10 m and velocity 1.5 m/s.

Solution:

l = 10 m

v = 1.5 m/s

F_r = \frac{v}{\sqrt{gl}}

= 0.15

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