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

Hydrostatic — where it appears

A pressure distribution equal to the weight of the fluid above, which holds when the vertical acceleration is negligible. Every one-dimensional open-channel calculation assumes it, and it fails wherever the streamlines curve sharply.

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

How big before gravity shows. A drop's height over its width against the Bond number, which is the ratio of its weight to the force its own skin can supply. The number is one where those two are equal, and by then the drop is a bun: it is one per cent from a ball at Bo = 0.0079, five per cent at 0.054 and ten at 0.13. Every one of those is below one, and the first is below it by a factor of a hundred and twenty-six.

The size a drop is allowed

The Bond number sets a drop's weight against the force its own skin can supply, and it is one when they are equal. By then the drop is a bun — it is a per cent from being a ball at Bond number 0.0079, which is a water drop half a millimetre across.

regimes · Bond The depth at the edge, against how much pressure is left there. The brink depth as a fraction of the critical depth, against the share of the hydrostatic pressure the brink is taken to retain. A free jet — no pressure at all — gives exactly two thirds, to 1e-16. The measured ratio of 0.715 is met at 40 per cent of hydrostatic, which is more residual pressure than a falling nappe looks as though it should have.

The depth at the edge is not the critical one

Every open-channel calculation assumes the pressure is hydrostatic, and usually says so nowhere. At a free overfall it is not, the assumption's failure can be measured, and the measurement is one number — a brink depth that is 0.715 of the critical depth where a hydrostatic reading would make it one.

applied · Open-channel

Named alongside it

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

Bond numberCapillary lengthConservationContact angleCritical depthCurvatureDimensionlessDropFlow meteringFroude numberMeasurementModel limit

All concepts