ANS:D - Froude number

The Froude number (Fr) is a dimensionless parameter used in fluid mechanics to characterize the relative significance of inertial forces to gravitational forces in a flowing fluid. It is named after the British engineer William Froude. Here's an explanation of the Froude number:

1. Definition: The Froude number is defined as the ratio of the inertial force to the gravitational force, or equivalently, the ratio of the flow velocity to the square root of the product of the gravitational acceleration (g) and a characteristic length scale (L) of the flow: 𝐹𝑟=𝑉𝑔𝐿Fr=gL​V​ Where:
   • 𝑉V = flow velocity
   • 𝑔g = gravitational acceleration (approximately 9.81 m/s29.81m/s2)
   • 𝐿L = characteristic length scale (e.g., depth of flow, diameter of a pipe, or chord length of a ship)
2. Interpretation: The Froude number compares the kinetic energy associated with the flow velocity to the potential energy associated with the gravitational field. It indicates whether the flow is dominated by inertial effects (high Fr) or gravitational effects (low Fr).
3. Regimes:
   • 𝐹𝑟<1Fr<1: Subcritical flow - Gravity dominates, and the flow is controlled by the depth of the flow. Waves propagate upstream.
   • 𝐹𝑟=1Fr=1: Critical flow - The flow velocity is equal to the wave velocity, and surface waves are stationary.
   • 𝐹𝑟>1Fr>1: Supercritical flow - Inertial forces dominate, and the flow velocity is greater than the wave velocity. Waves propagate downstream.
4. Applications:
   • Open-channel flow: The Froude number is commonly used in the analysis of open-channel flow in rivers, streams, canals, and spillways to determine flow regimes, such as subcritical, critical, and supercritical flow.
   • Ship hydrodynamics: In naval architecture, the Froude number is used to scale model tests of ship hulls to predict their performance in full-scale conditions. The Froude similarity law states that dynamic similarity between the model and prototype is achieved when the Froude number is the same for both.
5. Limitations: The Froude number is applicable to flows with significant gravitational effects, such as open-channel flow and ship motion. It may not be relevant for flows where other forces, such as surface tension or viscous forces, dominate.

In summary, the Froude number is a dimensionless parameter used to characterize the relative importance of inertial forces to gravitational forces in a flowing fluid. It is widely used in fluid mechanics to analyze flow regimes and predict the behavior of flowing systems, particularly in open-channel flow and ship hydrodynamics.