What is the Geometric Similarity between the model and proto

What is the Geometric Similarity between the model and prototype? What is the Kinematic Similarity between the model and prototype? What is the Dynamic Similarity between the model and prototype? An underwater missile, of a diameter 2 m and length 10 m is tested in a water tunnel to determine the forces acting on the real prototype. A 1/20th scale model is to be used. If the maximum allowable speed of the prototype missile is 10 m/s, what should be the speed of the water in the tunnel to achieve dynamic similarity? Pick a dimensionless parameter from the lecture, for which you think is very important and explain its meaning.

Solution

1.

Geometric similarity between the model and prototype means that the model and prototype

a) The ratio of all corresponding dimension in the model and prototype
must be equal.

b) Should be identical in shape

2.

Kinematic Similarity: It is the similarity of motion between model and prototype.
Kinematic similarity is existed between the model and the prototype, if the ratios of both velocity and acceleration at the corresponding points at that instant in the model and prototype are the same in both magnitude and directions.

3.

Dynamic Similarity: It is the similarity of forces between model and prototype. Dynamic similarity is existed between the model and the prototype only if the ratios of the forces acting at the corresponding points at a given instsnce in the model and prototype are the same in both magnitude and direction.