And the dimensions ratios which are most commonly used in

fluid mechanics as showed here.

The Reynolds number which is important in situations where friction or

viscous forces are important.

The Froude number which is important where flows gravity forces are important.

Which are often flows with a free surface.

The Mach number is important when compressibility is important.

The Weber number is important, where you have surface tension forces.

Pressure coefficient, where pressure differences are important, and

Drag coefficient, when you're interested in drag forces.

So, these are the most common numbers that are used in fluid mechanics.

And strictly speaking for similitude,

we must have all of these dimensionless groups equal in model and prototype.

In other words, Reynolds number model equals Reynolds number prototype, etc.