Which law is applied for comparison of model and prototype where the predominant force is the gravity force? 

When comparing a model and a prototype where the predominant force is gravity, the Froude Model Law is applied. This law is based on the principle that the ratio of inertial forces to gravitational forces should be the same for both the model and the prototype. The Froude number (Fr) is a dimensionless number that compares the inertial force to the gravitational force and is given by:

Fr = V / √(gL)

where:

• V = velocity
• g = gravitational acceleration
• L = characteristic length (such as depth of water)

The Froude Model Law ensures dynamic similarity between the model and the prototype when gravity is the dominant force. This is particularly important in hydraulic models and fluid dynamics involving free-surface flows, such as in the design of ships, spillways, and river modeling.

Analyzing the Given Options

1. 1) Mach Model Law (Incorrect)

   • The Mach Model Law is used for scenarios where compressibility effects are significant, and the Mach number (ratio of flow velocity to the speed of sound) is used for dynamic similarity. It is not primarily concerned with gravitational forces.

2. 2) Euler Model Law (Incorrect)

   • The Euler Model Law applies to scenarios where pressure forces dominate, and the Euler number (ratio of pressure forces to inertial forces) is used. This law is not suitable for situations where gravity is the predominant force.

3. 3) Weber Model Law (Incorrect)

   • The Weber Model Law is concerned with surface tension forces and is used when studying phenomena like capillary waves and droplet formation. It involves the Weber number, which is the ratio of inertial forces to surface tension forces, and is not applicable for gravity-dominated situations.

4. 4) Froude Model Law (Correct)

   • The Froude Model Law is specifically used for scenarios where gravitational forces are predominant. It ensures dynamic similarity between the model and the prototype by maintaining the same Froude number. This makes it the appropriate choice for the given situation.