Illustrated Physics
physics, drawn
Concept

No slip — where it appears

The condition that a fluid in contact with a solid moves with it, which is what makes viscosity produce a velocity gradient at all. It is an experimental fact rather than a derivable one, and it fails for a rarefied gas whose free path approaches the size of the apparatus.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as velocity gradient — the same set of essays touches all of them, so they are one junction rather than several.

The straight line between two plates. A layer of water 10 mm deep with its top plate drawn along at 1 m/s. In the steady state the velocity is a straight line from zero at the fixed surface to the plate's speed at the moving one, and the stress needed to keep it going is μ times that slope: 0.100 Pa. The fluid at each wall is at rest with respect to it, which is an experimental fact rather than a consequence of anything above.

Momentum going sideways

Viscosity is usually described as friction between layers of fluid, which gets the effect right and the mechanism wrong. What is actually happening is that momentum is being conducted across the flow — by the same equation, with the same solutions, as a drop of ink spreading.

fluids · Viscosity The parabola in a pipe, and what it integrates to. Steady flow in a round pipe: the velocity is a parabola, zero at the wall and greatest on the axis, and its average over the cross-section is 0.500 of the peak — exactly a half, by integration. Because the profile scales with r² and the area with r² as well, the flow goes as the fourth power of the radius: widening a pipe from 1 to 2 mm multiplies it by 16.

The fourth power in a pipe

Halve a pipe's radius and the flow through it falls to a sixteenth. The exponent is four rather than two, because narrowing a pipe both removes cross-section and slows what is left — and one law with that exponent in it governs a blood vessel, a hypodermic needle and a water main.

fluids · Viscosity

Named alongside it

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

Shear stressVelocity gradientViscosityDiffusionFlow resistanceKinematic viscosityMean free pathMomentum diffusionPoiseuille flowPressureScaling

All concepts