Concept

Stress — where it appears

Force per unit area within a material, which is a local equilibrium rather than a resultant. Unlike a force on a closed body it keeps the pressure datum, because it is the difference between what pushes on one side of a panel and what pushes on the other.

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

Identical lift at every altitude, and the skin load nearly doubles. The same wing at the same dynamic pressure at seven altitudes. The lift is identical at every one of them — the flat line, computed from the absolute pressures rather than assumed, because a net force cannot depend on where the pressure datum is set. The load on a vented panel is identical too, at 4.86 kPa, because both sides of it moved together. The load on a sealed panel with 75.26 kPa inside is not: it is 28.27 kPa at sea level and 60.84 kPa at twelve kilometres. The datum cancelled in the force and it is one of the two numbers in the stress.

A force forgets the datum, a stress cannot

Nothing sucks, because the pressure datum cancels — the normals of a closed body sum to nothing, so the lift is the same in gauge or absolute pressure. That identity is about a resultant, and it is routinely carried one step too far. The load on a panel of skin has the ambient in it as one of two numbers, not as a datum.

misconceptions · Suction

A blade root at 412.51 megapascals, and the chord is not in it. The centrifugal stress at a blade root against shaft speed, for one annulus of 0.36 m², in four materials. Integrating the blade's own weight outward gives σ = 2π ρ_b A N² with a taper relief — and the chord has cancelled, the blade count has cancelled, and every property of the gas has cancelled. What is left is an area times the square of a speed, capped by a material. The horizontal lines are each material's allowable stress, and where a curve crosses its own line is the fastest that annulus may be turned in that metal. At 12000 rpm this blade carries 412.51 MPa with a tip speed of 439.82 m/s.

The stress that picks the aerodynamics

The free term in a rotor's pressure rise wants radius and speed, and both are capped by something with no fluid in it. Integrate a blade's own weight outward and the root stress comes out as the annulus area times the square of the shaft speed — with the chord cancelled, the blade count cancelled, and every property of the gas cancelled.

applied · Turbomachine

The flow stops and the stress does not. Shear stress against time for a fluid sheared at a constant rate for two seconds and then left alone. Nothing is moving after the second mark and the fluid is still stressed: 37 per cent of the peak one relaxation time later, and 0.7 per cent after five.

The fluid that has not finished its last deformation

Shear a polymer solution for two seconds and stop. Nothing is moving and the fluid is still stressed — 37 per cent of the peak one relaxation time later, and still measurably stressed after five. Two histories imposing exactly the same total strain leave it in states differing by a factor of 3.7.

viscous · Non-newtonian

Named alongside it

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

Model limit Absolute pressure Annulus Closed body Convolution Correlation Deborah number Dimensionless Dynamic pressure Gauge pressure Measurement Memory kernel

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