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

Shear stress — where it appears

The tangential force per unit area one layer of fluid exerts on the next, proportional to the rate of strain for a Newtonian fluid. In a straight duct its distribution is fixed by a force balance alone, whatever the fluid turns out to be.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

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.

viscous · Lubrication The core that does not move, and where its edge is. Four velocity profiles at the same pressure gradient and four yield stresses. The shear stress in a pipe is G r/2 whatever the fluid is — that is a force balance and not a constitutive law — so the fluid is unyielded exactly inside r = 2 tau_y/G, and the plug radius is known before anything is solved.

The core that does not move

Toothpaste in a tube has a region in the middle that is not being sheared at all, and its edge is at a radius you can write down before solving anything. Four things about that core are exact, and one of them is that the fluid does not flow below a threshold — not slowly, at all.

viscous · Non-newtonian Four fluids under the same stress, and the four profiles that result. Each fluid carries the same linear stress and answers it differently: a Newtonian fluid with a parabola, a shear-thinning one with a blunter profile, a shear-thickening one with a sharper one, and a Bingham plastic with a plug in the middle where the stress is below its yield point.

The stress a pipe knows

A capillary viscometer measures a pressure drop and a flow rate and reports a viscosity. The first half of that inference is a force balance and is exact for any fluid there is; the second needs the slope of a whole flow curve, which is the experiment the instrument was bought to avoid.

viscous · Non-newtonian

Named alongside it

The objects these essays reach for when they reach for this one.

ViscosityConstitutive lawMeasurementNon-newtonianPipe flowCavitationControl volumeCreeping flowLubrication filmMass conservationMisconceptionModel limit

All concepts