Understanding the Navier-Stokes equations

Jun 2019
2
0
Hi everybody!

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!
 

topsquark

Forum Staff
Apr 2008
2,978
631
On the dance floor, baby!
Hi everybody!

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!
Fluid dynamics is a very active branch of Physics and it's good that you are showing interest. You could have a good career doing just that.

On the other hand, the Navier-Stokes equations are non-linear partial differential equations. Unless you are using some kind of approximation to them? (My field of expertise is in Quantum Field Theory. The Math can be, well, horrible. Be warned: Fluid dynamics equations are worse. You are going to have to take a lot of Math.)

-Dan
 
Jun 2019
2
0
Thanks for the reply!

Right now, I just want to understand (maybe not to the full extent) of the derivation of the equations and just trying to figure out what goes where and why. But I don't know where to start, I know vector calculus is needed so I'm learning up on that but what next?