Froude number is the ratio of

The correct option is inertia forces to gravity forces.

To understand why this is correct, we can analyze the definition of the Froude number.

The Froude number ($F_r$) is a dimensionless quantity used in fluid mechanics to characterize fluid flow behavior, particularly in open channel flows and wave dynamics. It represents the ratio of inertial forces to gravitational forces within the fluid.

Mathematically, the Froude number is defined as:
$$F_r=\frac{V}{\sqrt{gL}}$$
where:
- $V$ is the characteristic flow velocity,
- $g$ is the acceleration due to gravity, and
- $L$ is the characteristic length scale of the flow.

By squaring the formula, we obtain:
$$F_r^2=\frac{V^2}{gL}=\frac{\rho V^2{L}^2}{\rho g{L}^3}$$
Here, the numerator ($\rho V^2{L}^2$) represents the inertial force, and the denominator ($\rho g{L}^3$) represents the gravitational force. Thus, the Froude number is indeed the ratio of inertia forces to gravity forces.