I'm studying physics (13th grade) and I'm doing some external research and I've been really interested by fluid dynamics, more specifically the Navier-Stokes equations. I want to learn more about them but I don't know where to begin.

I've started by teaching myself vector calculus and vector fields (I'm learning div, curl and grad). I've also researched tensors but I'm a bit confused on

a. how many different equations there are

b. how they are derived (I've seen derivations from F = ma and other ways).

Thanks!