Every essay
Flows and fields
Streamlines, particle paths and the field that carries them. What is conserved, what a picture of a flow can show, and what it cannot.
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.
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.
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.
Ideal flow
The exact theory of a fluid with no viscosity — closed-form, elegant, and predicting no drag at all. Its failure is the most useful thing in the subject.
The theory that solves everything
Throw away viscosity and assume nothing is spinning, and fluid mechanics collapses into a linear problem with closed-form answers. The price is one term, and the term turns out to matter more than everything kept.
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.
Flows add up
The equations of ideal flow are linear, so solutions can be laid on top of one another. A uniform stream plus a doublet produces a cylinder that nobody put there, and almost every classical result is built this way.
Fast means low pressure
The trade between speed and pressure is the most useful relation in the subject and the most misused. Where it comes from, what it costs, and why the pressure over a wing is negative almost everywhere.
Circulation and lift
Where lift actually comes from. The Kutta condition, the Joukowski aerofoil, and lift derived rather than asserted.
What actually holds a wing up
Not the shape, and not the story about air meeting up again behind. A wing lifts because there is circulation round it, and the sharp trailing edge is what decides how much.
The sharp edge decides
Ideal flow round a wing admits infinitely many solutions, each with a different lift, and all of them exact. One extra requirement — that the air leaves the trailing edge instead of whipping round it — picks a single one.
The lift curve, and why it is a straight line
Lift against angle of attack is a straight line, it does not pass through the origin, and its slope is very close to a number that has no business being there. All three facts fall out of the theory.
Lift with no wing at all
A spinning cylinder has no camber, no aerofoil section and no trailing edge, and it lifts exactly as hard as its circulation says it should. Which settles what lift is caused by.
Viscosity
The thin layer next to a surface that ideal flow ignores, and which supplies drag, separation and the wake.
Everything happens in a layer you cannot see
Air has so little viscosity that ignoring it works almost everywhere. Almost everywhere leaves out a film next to the surface, perhaps a millimetre thick, and that film decides drag, stall and whether an aircraft flies at all.
When the flow lets go
Every body asks the air behind it to slow down and climb back up to the pressure it started at. Sometimes the air cannot, and the moment it refuses is separation — the source of most drag, the cause of stall, and the reason a golf ball has dimples.
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.
Regimes and numbers
Reynolds, Mach, Froude, Strouhal. One number decides whether a flow creeps, separates or shocks, and the same shape behaves differently at each.
One number decides which physics applies
A bacterium and a whale both swim, and they are not doing the same thing at different sizes. The ratio of inertia to viscosity separates them, and crossing it changes the rules rather than the magnitudes.
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.
When air stops being incompressible
Air is a gas and can obviously be squeezed, yet most of aerodynamics treats its density as fixed. The assumption holds until the flow approaches the speed at which pressure information travels — and then everything changes at once.
What is taught wrongly
Equal transit time, Bernoulli misapplied, and the rest. Each stated fairly, then tested against a solved flow and found false.
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.
Where Bernoulli's equation applies
The equation is right. Its hypotheses are strict, and almost all misuse is a correct formula carried somewhere it does not hold — across streamlines, through a fan, or into the one layer where friction is the whole story.