Illustrated Physics
physics, drawn
Concept

Gauge pressure — where it appears

Pressure measured against the local atmosphere rather than against vacuum, which is what almost every instrument reads. The distinction matters wherever the absolute value enters — in the ideal gas law, in a boiling point, and in any calculation of whether a liquid will cavitate.

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

Three vessels, one pressure. Three vessels filled to the same depth of 3 m. The pressure on each base is 29.4 kPa — identical, because pressure is set by depth — while the weight of water each holds differs by a factor of 4.7. The base of the flaring vessel carries more force than the water standing over it weighs.

The pressure that only knows depth

A litre of water and a swimming pool press equally hard on a floor at the same depth. Pressure in a still fluid is a scalar with no direction of its own, it depends on how far down and on nothing else, and the shape of the container falls out of the arithmetic entirely.

fluids · Hydrostatics The surface a spin decides. The free surface of a liquid in a dish of radius 0.5 m turning at 10, 20, 40 revolutions a minute. In the rotating frame the surface is a level set of gz − ½ω²r², so it is a paraboloid exactly and not to some approximation, and nothing about the liquid appears in its shape: the same curve is got with mercury, water or oil. The rim stands 14.0 mm, 55.9 mm, 223.6 mm above the centre at those rates. A parabola z = r²/4f has focal length f, so these surfaces are mirrors of focal length g/2ω² — 4.47 m at 10 rpm, 1.12 m at 20 rpm, 0.28 m at 40 rpm. That is checked here on the drawn curves rather than quoted: a vertical ray reflected off the surface at a quarter, a half, three quarters and the whole of the radius crosses the axis at the same height to 0.00%, which is what a mirror with no spherical aberration means. Doubling the spin quarters the focal length, and there is no other adjustment: the dish can only ever look straight up.

The surface a spin decides

Spin a dish of liquid and its surface settles into a paraboloid — exactly, with nothing about the liquid in the shape. A parabola of that form has a focal length of g over twice the spin rate squared, so a bucket of mercury turning at twenty revolutions a minute is a telescope mirror figured by a clock instead of by grinding.

fluids · Hydrostatics One height inside the bottle where the pressure is the air's. Gauge pressure against height inside a sealed bottle with an open tube reaching down to 10 cm above its outlet, while it is bubbling, at three water levels: 30.0, 22.0, 13.0 cm. Each line rises at the same hydrostatic slope, ρg, from the air pocket at the top, which is below atmospheric, to the outlet at the foot. All three cross atmospheric pressure at the tube's tip — 7.4 mm below it, the extra a bubble needs to leave a 2 mm tube — and so all three reach the outlet at the same 906 Pa above atmospheric, whatever the level. Dashed: an open bottle at the same levels, whose pressure at the outlet is 2937, 2154, 1273 Pa.

The bottle that pours at one rate however full it is

Water running from a hole in the foot of an open bottle slows as the bottle empties, because the pressure at the hole is the depth of water above it. Seal the bottle and push an open tube through the stopper, down into the water, and it stops slowing: the flow holds steady from full until the level reaches the bottom of the tube. Nothing regulates it. The tube's tip is the one point inside where the pressure is the atmosphere's, the water above it hangs from an air pocket below atmospheric, and the outlet sees only the height of the tip.

fluids · Hydrostatics

Named alongside it

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

Free surfaceHydrostatic equilibriumApparent weightAtmospheric pressureCapillary lengthCentre of pressureCentrifugal forceConic sectionContinuumDensityEquipotentialFocal length

All concepts