The Froude Number is a dimensionless number that is used in fluid mechanics to analyze the flow behavior of a fluid. It is defined as the ratio of inertia force to gravity force and is named after the English engineer William Froude.

Inertia Force:
The inertia force is the force that resists changes in the motion of a fluid element. It is a result of the fluid's mass and acceleration and is given by the equation F = m * a, where F is the inertia force, m is the mass of the fluid element, and a is the acceleration of the fluid element.

Gravity Force:
The gravity force is the force exerted on a fluid element due to gravity. It is given by the equation F = m * g, where F is the gravity force, m is the mass of the fluid element, and g is the acceleration due to gravity.

Ratio of Inertia Force to Gravity Force:
The Froude Number (Fr) is defined as the ratio of the inertia force (F) to the gravity force (Fg), i.e., Fr = F / Fg. By substituting the equations for F and Fg, we get Fr = (m * a) / (m * g). The mass of the fluid element cancels out, resulting in Fr = a / g.

Explanation of the Correct Answer:
The Froude Number is the ratio of inertia force to gravity force. This means that it quantifies the relative importance of inertia forces compared to gravity forces in a fluid flow. When the Froude Number is less than 1, the flow is considered subcritical, and gravity forces dominate. On the other hand, when the Froude Number is greater than 1, the flow is supercritical, and inertia forces dominate.

The Froude Number is particularly important in open channel flow analysis, such as rivers and canals, where gravity forces play a significant role. By comparing the magnitude of inertia forces to gravity forces, engineers can assess the flow conditions and predict the behavior of the fluid. This information is crucial for designing structures like dams, spillways, and channels, as well as for understanding the stability and movement of sediments in rivers.

Overall, the Froude Number provides valuable insights into the flow behavior of fluids and allows engineers to make informed decisions in the design and analysis of hydraulic systems.