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

Impulse — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The momentum of the fluid, against the shape of the region it is added up over. Momentum of the fluid around a cylinder moving through it, divided by the body's hydrodynamic impulse, against the aspect ratio of the rectangle the integral was taken over. Every rectangle has the same area and contains the same body. A tall region gives minus the impulse, a long one gives plus it, a square gives exactly zero, and the limit of a large region is whichever of those the region was shaped like. The momentum of an unbounded ideal flow is not a number.

    The momentum with no value

    A cylinder is pushed from rest to a steady speed. Work was done, energy went into the fluid, something was pushed. How much momentum does the fluid carry? The integral converges, the answer is finite, and it is a different finite number for every shape of region it is summed over.

    part 1 · inviscid
  2. A body of no volume with a finite added mass. Thin an ellipse towards a plate and the fluid it displaces goes to nothing while its broadside added mass does not move at all — it stays at πρa² to the last digit. Whatever added mass measures, it is not how much fluid a body carries with it: the ratio of the two diverges as the reciprocal of the thickness, reaching a million at a thickness ratio of a millionth.

    The mass a body has to borrow

    Accelerate a sphere through water and it resists as though it were half again as heavy. The half is exact, it is a rational number rather than a measurement, and almost everything a reader infers from it about carried fluid is false.

    part 2 · inviscid
  3. Six ways of reaching one speed. Six velocity histories, all starting from rest and all reaching exactly one at the same moment. Two are ramps, two are eased, one overshoots and comes back, and one goes backwards before it goes forwards.

    Everything about the start, except one vector

    Six ways of accelerating a body from rest to the same speed produce six force histories with nothing in common — peaks spanning a factor of thirty-nine, two of them negative for part of the journey. The impulse left in the fluid is the same ten-figure number in every case, and so is the energy.

    part 3 · inviscid

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