1) For dynamic similarity between the model and the prototype the ratio of the corresponding forces acting at the corresponding points in model and prototype should be equal.

2) The ratio of the forces are dimensionless numbers.

3) That means, for dynamic similarity between the model and prototype the dimensionless numbers should be same for models and prototype.

4) But it is difficult to satisfy the condition that all the dimensionless numbers are same for the model and prototype.

5) The laws on which the models are designed for dynamic similarities are called model laws or laws of similarity.

Some important model laws:-

a) Reynolds Model law:-

The law in which models are based on Reynolds number are called as Reynolds model law

Model based on this law:-

1) Pipe flow

2) Resistance experiences by sub-marines, airplanes, fully immersed bodies. etc

Let

$V_{m}$= Velocity if fluid in model

$\rho_{m}$= Density of fluid in model

$L_{m}$= Length or linear dimensions of the model

$\mu_{m}$= Viscosity or fluid in model

similarly

$V_{p}$= velocity of fluid in prototype

$\rho_{p}$= Density of fluid in prototype

$L_{p}$= Length of Prototype

$\mu_{p}$= Viscosity in prototype