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

Superposition — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Ideal flow past a cylinder. A uniform stream past a circular cylinder in a fluid with no viscosity. The solution is exact and closed-form: streamlines part at a stagnation point, run round the surface and close up perfectly behind, and the pressure recovers to exactly what it was in front.

    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.

    part 1 · inviscid
  2. Flow net — a stream past a cylinder. Two families of curves drawn over the same flow: the streamlines, along which the streamfunction is constant, and the equipotentials, along which the velocity potential is constant. They cross at right angles at every point, because they are the two parts of a single analytic function of position.

    Bodies made out of nothing

    Put a source in a stream and a solid nose appears in front of it. Put a sink downstream of the source and the nose closes into a finite body. Nothing was placed in the fluid — the surface is a level set of a function, and it behaves like a wall because nothing crosses it.

    part 2 · inviscid
  3. The pressure of a sum against the sum of the pressures. Ten points around a cylinder with circulation, with the pressure coefficient of the combined flow plotted against what adding the two flows' separate coefficients would give. Nothing lies on the diagonal. The gap is exactly −1 − 2u_A·u_B/U², an identity checked to the last digit at every point, and it is not small: at one of these points the two answers differ by 1.92, which is more than the whole range of a suction peak.

    The one thing that does not add up

    Laplace's equation is linear, so flows can be laid on top of one another and almost every classical result is built that way. The two things anybody actually wants out of a flow — the pressure and the force — are quadratic in the velocity, and neither of them adds at all.

    part 3 · inviscid

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