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

The thread: A smooth picture proves nothing

Streamlines are smooth whatever nonsense produced them. A flow figure is only worth as much as the conservation laws it was checked against.
the upper surface is 1.7% longerso equal transit needs the flow over it 1.7% fasterit is actually 76.5% fasterthe premise is false and the number it predicts is wrongsurface lengths and speeds measured on the solved field6° incidence What is taught wrongly

The story about air meeting up again

The most repeated explanation of lift says that air parting at the nose must rejoin at the tail, so the longer upper path forces a higher speed. The premise is false, and the speed it predicts is wrong by a factor of twenty.

 thin: streamlines, frozen at one instantthick: the path one particle actually takesunsteady flow — the three families differincompressible Flows and fields

Streamlines are not the paths particles take

Three different curves get drawn through a flow and they are routinely treated as one. In steady flow they coincide, which is why the confusion survives; in unsteady flow they are as different as a photograph and a long exposure.

 frontback+1−30angle round the bodycomputed drag-1.1e-16not “small” — zeroideal flow — inviscid, irrotational, steadyany Reynolds number Ideal flow

The exact theory says nothing has any drag

Solve the flow past a body in a fluid with no viscosity and the answer is beautiful, closed-form, and predicts that a cyclist needs no legs and an airliner no engines. This is not a small error, and it is the most useful failure in the subject.

 0.871.330.85ideal flow — incompressible, so the tube's area sets the speed Flows and fields

Mass has nowhere to go

Squeeze a stream of fluid and it speeds up, not because anything pushes it but because the same amount has to get through a smaller gap every second. Almost every result in the subject is that observation with more machinery attached.

 creepingattachedseparated, sheddingturbulentbacterium swimmingshedding begins, Re ≈ 47a thrown ballan airliner winga whaleReynolds numberinertia ÷ viscositylog₁₀ Rethe ratio decides the regime, not the size or the speed alone Regimes and numbers

The Reynolds number, and the length in it

The most useful number in fluid mechanics has an arbitrary quantity buried in it, and quoting one without saying which length was used makes it meaningless. That detail is where most misuse comes from.

 ideal flow — closes up, no dragreal flow at Re 100 — separatedleft: exact closed form · right: solved on a gridRe = 100 Viscosity

The two theories, side by side

The exact solution and the real flow, for the same body in the same stream. One is beautiful and predicts nothing has drag; the other is approximate and has a wake in it. Where they agree and where they part is the whole map of the subject.

 length ∝ speedideal flow past a cylinderfastest 1.91U Flows and fields

What a flow is

A fluid is made of molecules and nobody models it that way. Treating it as a continuous field with a velocity at every point is an approximation, an extremely good one, and knowing why it works is knowing where it stops.

All themes