Fluid and Motion Physics: Buoyancy, Terminal Velocity, and Reynolds Number

Objects moving through fluids and gravity fields follow predictable physics — these four calculations describe some of the most commonly encountered scenarios.

Buoyancy: Archimedes' principle in action

Buoyant force equals the weight of fluid displaced: fluid density × volume displaced × gravity. An object displacing 0.05 m³ of water experiences an upward buoyant force of 1,000 × 0.05 × 9.8 = 490 N — if that exceeds the object's own weight, it floats; if not, it sinks.

Terminal velocity: where gravity and drag balance

A falling object accelerates until air resistance drag equals gravitational force, at which point it stops accelerating — its terminal velocity. This balance point depends on mass, shape (via drag coefficient and cross-sectional area), and air density, which is why a feather and a bowling ball reach very different terminal velocities despite falling under the same gravity.

Escape velocity: the speed needed to leave for good

Escape velocity is the minimum speed needed to escape a body's gravity without further propulsion, based on the body's mass and radius. Earth's escape velocity works out to roughly 11.2 km/s — significantly higher than the ~7.67 km/s needed just to maintain low Earth orbit, since escaping gravity entirely requires more energy than merely orbiting within it.

Reynolds number: predicting laminar versus turbulent flow

Reynolds number is (density × velocity × characteristic length) / viscosity. Water flowing at 2 m/s through a 5cm pipe gives a Reynolds number of 100,000 — well above the roughly 4,000 threshold that indicates turbulent (rather than smooth, laminar) flow.

Predicting fluid and gravitational behavior

Buoyancy, terminal velocity, escape velocity, and Reynolds number each predict a distinct physical behavior from a handful of known inputs. Try the buoyancy calculator, terminal velocity calculator, escape velocity calculator, and Reynolds number calculator.