Dynamic similarity

Remarks

When the dimensionless problem has a unique solution, dynamically similar flows have the same dimensionless velocity and pressure fields, so measurements on the model can be scaled to the prototype. Example: for steady incompressible flow past a body, the only parameter is the Reynolds number. A model at scale $1/10$ in the same fluid at ten times the speed has the same $UL/\nu$, so the two flows are dynamically similar. Non-example: take a ship model at scale $1/10$ in water. Equal Froude number needs the speed scaled by $\sqrt{1/10}$, while equal Reynolds number needs it scaled by $10$. Both cannot hold, so the model and the ship are not fully dynamically similar. In practice one matches the dominant number and corrects for the others.