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

Domain of dependence — where it appears

The region whose state can affect a given point, bounded by the paths signals may travel along. In supersonic flow it is a cone, which is what makes a supersonic body's influence unable to reach the fluid ahead of it.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A source at Mach 2.00, and the sound it has already made. Each circle is one pressure pulse, expanding at the speed of sound from the point the source was at when it left. Below the speed of sound every circle still contains the source, so the pressure disturbance reaches every point of the fluid before the source does. Above it the circles have an envelope, and outside that envelope nothing has been heard at all.

When the warning cannot arrive

Supersonic flow is not fast flow. It is flow in which the fluid ahead has been told nothing, because the body is outrunning its own pressure signals — and that single change turns an equation of one type into an equation of another.

compressible · Speed of sound The throat stops listening: mass flow against back pressure. Mass flow through a convergent nozzle, normalised on its choked value, as the back pressure is lowered. It rises until the throat reaches Mach one and then stops, exactly. Below that pressure the throat is sonic and nothing downstream can send a signal upstream to ask for more, so the flow does not respond however far the back pressure falls.

The throat that stops listening

Lower the pressure downstream of a nozzle and more gas flows through it. Keep lowering it and, at a definite point, the flow stops responding — not gradually, but completely, because the news that the pressure has fallen can no longer travel upstream.

compressible · Area mach The backwater curve behind a weir. The depth at the control is 1.6 times the normal depth; integrating upstream the profile relaxes onto normal depth over about seven hundred metres and stays there. That relaxation is the reach forgetting the weir, and nothing about the weir survives past it.

The section that decides the river

A reach of open channel has a normal depth and a critical depth, and the water has neither. What it has is a profile obeying a first-order equation, which needs exactly one condition — and whether that condition belongs at the upstream end or the downstream end is not a choice, because the equation is stable in one direction and unstable in the other.

applied · Open-channel

Named alongside it

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

Signal speedHyperbolicMach numberArea machBoundary conditionCharacteristicsChokingde Laval nozzleFree surfaceFroude numberHydraulic jumpMach cone

All concepts