I started learning fluid mechanics with a pretty good textbook. The original motivation was to better simulate the fluid using shader, besides that I also feel interested to learn it as I like math/physics.

Have you guys learned that before or any comments?

If you have an interest for it, then do it!

Various forms of fluid simulation are used in current gen games, from ocean rendering to particle based fluid simulations. I did some investigation into particle based fluid simulation on the GPU at my workplace as an investigation in making an over the top crazy looking blood splatter simulation, which was lots of fun.

Yeah, I'm already enjoying it.
So that I won't regret not studying physics in college.

Oh don't worry. You're pretty much required to study physics anyways.

Fluid Dynamics won't be too helpful on it's own if you want to use it in real time simulations. You'll probably find yourself combining it with Numerical Analysis. What it basically does is it breaks up larger problems that would normally be impossible to solve, into smaller problems that can be quickly solved. This is typically what's used in Auto Cad simulations. Like having a car smash into a wall... many pieces of it bend, deform, or go break off and go flying through the air. Just a normal soft body simulation would provide a result that would make the car scrunched up... but not very realistic... and still operable if not programmed otherwise. And even then a small ding could easily make the car no longer operable.