Froude number Formula

The Froude number is a dimensionless value that describes the different flow regimes of an open channel flow. The Froude number is a ratio of inertial and gravitational forces. This is written as:

Froude number = Velocity of the fluid / √ (gravity acceleration * depth of flow)

The equation is

Fr = v / √ (g l)

We have:

Fr: Froude number

v: Velocity of fluid

l: Depth of flow

g: Gravitational acceleration

Froude number equation Questions:

1) A fluid flows through a tube with a men depth of 0.1 m with velocity 5m/s. What is the Froude number associated with the fluid system?

Answer: The Froude number is found from the equation:

Fr = v / √ (g l)

Fr = 5 m/s / √ (9.8 m/s² * 0.1 m) = 5.05

Fr = 5.05

2) If the Froude number of the problem above is 10 and only the velocity can change. What would be the velocity?

Answer: The velocity is found from the equation of Froude:

v = Fr √ (g l)

then substituting the values,

v = (10)² * √ (9.8 m/s² * 0.1 m ) = 9.9.2 m/s

v = 9.9 m/s.