In 1945, the US conducted its first atomic bomb test. Reporters from Time magazine were present, and months later published the image below – an innocuous demonstration of the new weapons’ power for the American public. Lore holds that just weeks later, Soviet physicists knew more or less exactly the explosive power of the bomb - a datum known at the time only to those with the highest security clearance. Regardless of the veracity of this rumor, it is quite plausible, as the simple scaling behavior of shockwaves makes it quite easy to determine the equivalent TNT kilotonnage of Gadget, the plutonium bomb detonated during the Trinity test. It’s just simple fluid dynamics.
We will start with the basics of Bernoulli’s equation, with a brief stopover to finally dispel all the rumors and poor physics on the internet of why planes actually fly. We will turn to the Euler and Lagrange formulations of fluid dynamics proper, working our way towards the formulation of the Navier-Stokes equation. We will cover wave mechanics, and touch on the wide variety of its applications (water waves, density waves, entropy waves, electromagnetism, quantum mechanics, gravitational waves, and an endless list further). Next, we will discuss streamlines, streaklines, laminar flow, and the crucially important Reynolds number. We will cover the basics of shockwaves and go over exactly how the Time magazine photo gives away so much information. We will then turn to the topics of viscosity and turbulence, touching on the poorly understood 3/5 law. Time permitting, we will go over a few of the active research problems physicists currently work on.
Recommended Prerequisites: Geometry, calculus, the basics of linear algebra, and mechanics.