Air, water, blood, magma, the plasma in a star — all of it flows, and all of it obeys the same handful of equations. Fluid dynamics is what happens when you apply Newton's laws not to a single particle but to a continuous, deformable medium with infinitely many of them. The result is some of the richest behaviour in physics: smooth streamlines, swirling vortices, shock waves, and the still-unconquered puzzle of turbulence.
This branch develops the continuum picture — fluid kinematics, the continuity equation, Euler's
and Bernoulli's results, the full Navier–Stokes equations, vorticity and circulation, and the
dimensionless numbers that tell you when a flow goes wild. It draws heavily on the vector calculus
in