Depth

Series — page 10

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.

How hot seven films get. The peak temperature rise inside the film itself, on a logarithmic axis, for seven lubricated contacts with ordinary engineering numbers. A journal bearing runs tens of kelvin above its own housing, which is why lubrication systems are designed around heat rather than around load; a water-lubricated bush runs at a hundredth of a kelvin, because water conducts six hundred times better per unit of viscosity. The air bearing is marked: its gap is smaller than air's mean free path, so its film is not a continuum at all.

Viscous heating

1 The film that heats itself

1 essay · viscous

Four corners, and what the flow does in each. The local flow in corners of four different interior angles, drawn from the exact local solution ψ = r^(π/α) sin(πθ/α). The exponent of the speed is π/α − 1 and depends on nothing else: at a right angle the corner is stagnant, at a flat wall nothing happens, and at any angle greater than a straight line the speed has no bound at the corner. The last panel, at 360 degrees, is the flow round the edge of a plate.

Wedge flow

1 Nothing turns a sharp corner

1 essay · inviscid

The wake, and the velocity it gives itself. The cross-section of the wake far behind a wing with turned-up tips, with the velocity the wake induces on itself drawn as arrows normal to the trace. Induced drag is the integral of the circulation against that velocity and nothing else — this picture contains the entire quantity. It also contains no information whatever about where the surfaces were: two wings a chord apart and two wings ten chords apart produce the same picture and therefore the same drag, which is Munk's stagger theorem stated as a fact about what the arithmetic can see.

Winglet

1 A wing that leaves the plane

1 essay · circulation