## Types of similarities between model and prototype

There are three types of similarities between model and prototype in hydraulic similitude:

- Geometric.
- Kinematic.
- Dynamic.

## Geometric similarity in Hydraulic Similitude

Geometric similarity means that the model and prototype

- Corresponding dimensions must bear the same ratio.
- Be identical in shape.

The models are generally prepared with the same scale ratio in different directions. These are geometrically true models in Hydraulic Similitude. However, sometimes, it is not possible to use a true model and different convenient scales are used in different directions. These are geometrically distorted models.

## Kinematic similarity in Hydraulic Similitude

Kinematic similarity is the similarity of motion. It requires that the velocities of corresponding points in the prototype and model must have the same ratio.

Velocity ratio = Velocity of prototype / velocity of model

Corresponding points in different direction must have the same ratio.

## Dynamic Similarity in Hydraulic Similitude

Dynamic similarity is the similarity of forces and requires that the corresponding forces in prototype and model must be in the same ratio.

Force ratio = Force in prototype / Force in model

In the various type of fluid flow phenomenon, there could be one or more of the following forces involved:

- Force due to viscosity.
- Force due to gravity.
- Force due to pressure.
- Force due to elasticity.
- Force due to surface tension.
- Force due to inertia.

Force of inertia would play role when the sum of other forces is not equal to zero. When sum is not equal to zero then sum is equal to force of inertia.

The dynamic similarity requires that;

Force of inertia in prototype / Force of inertia in model = Sum of all other forces in prototype / Sum of all other forces in model

It is found that in all cases of fluid flow, there is one force which is most important as compared to others. That most important force is called most significant or predominant force.

In the design of model, only the predominant force is taken into account.

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