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

Terminal velocity — where it appears

The speed at which a body falling or rising through a fluid has its weight exactly balanced by drag, so that it stops accelerating. It depends on which drag law applies, and the same body has different terminal velocities in different regimes.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A falling drop is a bun, not a tear. The shape of a drop pressed on by the air it is falling through, computed by matching the Legendre component of a sphere's own potential-flow pressure distribution against the change in curvature it produces. The result is oblate — flattened along the direction of travel — because the pressure is high at the poles and low round the equator. The teardrop of every illustration has the wrong symmetry entirely: a drop in free fall has no up, and one at terminal speed is being pressed on from in front.

The drop that is not a tear

A falling raindrop is flattened along the direction it is going, by the pressure of the air passing it rather than by its own weight, and the group that decides is the Weber number. The teardrop of every illustration has the wrong symmetry entirely — there is no up in the problem it is drawn for.

regimes · Drop shape Two-thirds to one, and nothing outside it. The drag on a spherical drop as a fraction of Stokes' drag on a rigid sphere of the same size, against the ratio of the viscosities. It runs from exactly two-thirds for a clean gas bubble to exactly one for a rigid particle and takes no value outside that range, however light or heavy the drop is — the formula has no density in it anywhere. A drop of water in air and a drop of mercury in water sit at opposite ends of it.

The surface that moves with the flow

A clean gas bubble feels two-thirds of the drag a rigid sphere of the same size would, and the formula has no density in it anywhere. What buys the third is that the bubble's surface is free to move — and real bubbles in ordinary water do not get it, for a reason that is a millionth of a per cent of the water by mass.

viscous · Mobile interface

Named alongside it

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

DropBoundary conditionBubbleCreeping flowDimensionlessDissipationDragLegendreMobile interfacePerturbationPotential flowPressure coefficient

All concepts