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

Fanno flow — where it appears

Adiabatic flow of a gas through a constant-area duct with wall friction, in which friction drives the Mach number towards one from either side. A duct long enough for the flow to reach Mach one is choked, and any extra length reduces the mass flow the duct can carry.

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

The Fanno line, which has only one direction on it. The entropy relative to the sonic state, against Mach number, for both branches. Friction raises the entropy, so a duct flow moves to the right along this curve whichever branch it is on — up in Mach number from below and down from above — and it stops at the sonic point.

A duct that cannot be run backwards

Friction drives a compressible duct flow towards the speed of sound from either side, and the entropy rises the whole way. So the state of the gas at a station is an odometer: it records how much duct is behind it, and no amount of further duct can take it back.

compressible · Fanno rayleigh A long line empties from the break backwards. The pressure along a gas line three hundred friction lengths long — fL/D = 300 — at five times after it breaks at its far end into still air at a twentieth of its pressure, the break on the right. Half a transit time in, the rarefaction has crossed half the line and the gas beyond it has not moved. Friction then holds the pressure in a slope that lengthens back towards the closed end; at six transit times the closed end is at 0.55 of its starting pressure, at fifteen 0.21, and the break has long since stopped being choked.

A broken line empties at the pace of its friction

When a gas line breaks, its open end chokes and the textbook stops there: a choked outlet passes gas at its own speed of sound and nothing downstream can change that. On a long line the choke is the least of it. The break stays choked only while friction lets enough gas reach it, which on a line a thousand friction lengths long is the first eighth of the time to half pressure. The pressure falls at a pace friction sets, the half-time grows as the square root of the line's length in friction lengths, and the wall's heat — negligible in the steady line — makes the blowdown a third slower.

compressible · Fanno rayleigh

Named alongside it

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

ChokingCharacteristicsConserved quantityDuctEntropyFrictionFriction factorIrreversibilityIsothermal flowMeasurementMemory kernelModel limit

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