Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Pressure drag — where it appears

The part of a body's drag contributed by the pressure acting on its surface rather than by friction. It is zero in ideal flow and dominates for a bluff body, and the difference between the two is the pressure that separation prevents from recovering.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

Flow past a cylinder at Re 100. A real fluid past a circular cylinder. At low Reynolds number the flow closes up behind the body much as the ideal theory says; as it rises the flow separates and a region of reversed flow appears behind, which is where drag comes from.

When the flow lets go

Every body asks the air behind it to slow down and climb back up to the pressure it started at. Sometimes the air cannot, and the moment it refuses is separation — the source of most drag, the cause of stall, and the reason a golf ball has dimples.

viscous · Separation The cliff a rough ball reaches sooner. The drag coefficient of a sphere against Reynolds number, on log axes. The smooth curve is Morrison's correlation, which is a fit to measurements and is drawn in the colour this site reserves for a borrowed claim. The other is the same curve shifted along the Reynolds axis by a factor of 6 — a stated model of what roughness does, which is to trip the boundary layer early, and not a measurement of any real ball.

The drag that falls as it speeds up

There is a band of speeds in which a smooth ball experiences less drag the faster it goes. Not a smaller coefficient — a smaller force. Dimples move that band down to where a golf ball actually flies, and they do it by making the friction worse.

applied · Sport ball The Kirchhoff flow past a flat plate. A uniform stream meeting a flat plate held across it, with two streamlines leaving the edges and never returning. Between them is a wake of fluid at rest at a constant pressure. The equations solved are the same equations that give d'Alembert's paradox for a closed body, and this flow has a drag coefficient of 0.8798.

Drag in the theory that forbids it

d'Alembert's paradox is a theorem about flows that close behind the body. Stop requiring that, let two streamlines leave the edges and never come back, and the same equations — no viscosity, no vorticity — produce a drag coefficient of 0.8798.

inviscid · Free-streamline

Named alongside it

The objects these essays reach for when they reach for this one.

SeparationWakeAdverse pressure gradientBoundary conditionBoundary layerCavitationCorrelationd'Alembert's paradoxDrag coefficientDrag crisisFree-streamlineModel validity

All concepts