Every essay — page 5
Flows and fields Ideal flow Circulation and lift Viscosity Regimes and numbers Compressible flow Transition and turbulence Fluids at work What is taught wrongly Series Concepts Regimes Refutations Search
Fluids at work
Turbines, pipes, weirs, balls, sails, arteries and blades. What the conservation laws say about machines, which is more than a designer expects and less than a brochure claims.
The nozzle that is best at one thing
Put the four losses back into a jet pump and three questions get three answers. The most head comes from a nozzle four-fifths of its throat, in closed form; the best efficiency from one a quarter of it; and the most flow from whichever nozzle is smallest, because flow has no optimum at all.
The wall the suction puts in the curve
A liquid jet pump's lowest pressure is where the entrained stream enters the throat, and when that reaches vapour pressure the pump curve stops being a curve. The flow ratio freezes at a value no lower discharge pressure can move — and raising the motive pressure, the obvious cure, brings the wall closer.
A choke that belongs to two streams
A steam ejector entrains a fixed amount of gas whatever its back pressure, up to a pressure where it stops. The flat part is a choke, and the entrained gas is not at Mach one when it happens: it is at 0.886, because the supersonic jet beside it is part of the same throat. One area ratio then trades that entrainment for compression, and the trade decides how a vacuum train is built.
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.
The vortex a wing leaves behind
A wing at rest has no circulation. A wing in flight has a great deal. Circulation round a circuit of fluid particles cannot change, so the difference had to come from somewhere — and it did, as an equal and opposite vortex dropped on the runway.
Where the lift acts
Lift gets drawn as an arrow, and an arrow has to start somewhere. The pressure is spread over the whole surface, so the choice of where to put the arrow is free — except that exactly one point on the chord has the property of not changing its answer when the wing is pitched.
The price of having ends
An infinitely long wing in a fluid with no viscosity has no drag at all. Cut two ends into it and the drag appears — not from friction, which is still absent, but from the fact that circulation cannot be carried off the end of anything.
How much circulation is too much
Spin a cylinder faster and it lifts harder, with no limit in the equations. What does have a limit is the flow's willingness to stop anywhere on the surface — the two points where the air is at rest slide round towards each other, meet at the bottom, and leave the body altogether.
The wall that pushes back
A wing near the ground carries more lift than the same wing in free air, and the usual explanation — a cushion of compressed air underneath — is not what the equations say. The ground is a mirror, and what changes is not the pressure under the wing but the circulation the wing is forced to carry.