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

Lubrication — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 20.45 MPa out of a film 25 µm thick. The pressure along a tapered pad, from the closed-form solution of Reynolds' equation, with the same equation's tridiagonal grid solve drawn over it as points. The peak is 20.45 MPa — enough to yield mild steel — and it sits at 69 per cent of the way along rather than in the middle, because the pressure gradient vanishes where the film equals the harmonic mean of its two ends and the harmonic mean is biased towards the thinner one. The pad's own shape is drawn along the top, to a vertical scale of its own. Nothing pumps this oil: the runner drags it into a narrowing gap and the gap does the rest.

    Nothing but the shape of the gap

    A machine that holds a steel shaft off its bearing with a film of oil twenty-five microns thick has no pump in it, and the pressure it generates would yield mild steel. The mechanism is not the oil and not the speed; it is that the gap narrows.

    part 1 · viscous
  2. A pure number with no fluid in it. The load a plane slider bearing carries, divided by everything dimensional in it. What is left is a function of the convergence ratio alone — no viscosity, no speed, no size, no material — so the tilt that carries the most load is decided before anything about the machine is known. It is the root of one transcendental equation, at 2.1887048.

    The gap that carries the most

    A bearing's most consequential dimension is decided by a number with no oil in it, no speed and no size — the root of one transcendental equation, at 2.1887048. And the maximum it sits on is flat enough that the value printed in every handbook is not it.

    part 2 · viscous

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