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

Nucleation — where it appears

The first appearance of a new phase, such as a vapour cavity in a stretched liquid, which must pay the surface energy of a small nucleus before it can grow. Its threshold is set by the largest nucleus already present, or in a perfectly pure liquid by thermal fluctuations, which put water's at about −150 MPa.

Named by 6 essays across 2 fields — each of them below, with the objects they name alongside it.

A threshold that is a curve, not a pressure. The tension a rectangular pulse has to reach to make a five-micron bubble run away, against how long the pulse lasts. At a tenth of a microsecond it takes forty bar; at a hundred microseconds it takes 1.05, which is within about one per cent of the static threshold. There is no such thing as the cavitation pressure of this bubble on its own.

A threshold that is also a duration

The cavitation number treats inception as a pressure: below it the liquid tears, above it does not. A five-micron bubble asked to grow in 0.3 microseconds needs 43 bar of tension and the same bubble given a hundred needs 1.05, because it has to make a journey and not merely respond.

applied · Cavitation A tube 10 cm across, spun: the lowest pressure is on the axis. The absolute pressure along a water-filled tube spun about its middle, open to the air at both ends, 5 cm from the axis. In the spinning frame the water is at rest under a centrifugal pull, so the pressure falls from atmospheric at each meniscus to its lowest on the axis, as a parabola. 10 thousand rpm puts −1.3 MPa there, 20 thousand rpm puts −5.4 MPa there, 30 thousand rpm puts −12.2 MPa there and 45 thousand rpm puts −27.6 MPa there. The place the water is stretched hardest is the place furthest from both free surfaces, which is the whole merit of the method: a gas cannot reach the liquid where it is weakest.

A breaking strength that is the size of a flaw

Water can be stretched, and how far is a measurement people have made for a century and a half with instruments that agree with one another and not with the theory. Spinning a tube puts the stretch where no gas can reach it, sealing one caps the stretch at water's density maximum, and every measured number turns out to name the size of the worst cavity in the sample.

misconceptions · Suction A litre of water at the crown carries 77 mL of gas it cannot hold. The volume of free gas a litre of air-saturated water can release at a siphon's crown, at the crown's own pressure, against that pressure, on a logarithmic scale, at three temperatures. It is zero at atmospheric and grows without limit towards the vapour pressure. At the reference siphon's starting crown pressure of 51.5 kPa it is 20.6 mL, a supersaturation of 2.02; at the frictionless floor of 23.0 kPa it is 76.7 mL, a supersaturation of 4.79. Cold water carries more: 87.4 mL at 5 °C. This is the equilibrium bound — what would come out if the water stayed long enough, which it does not.

The air that breaks a siphon nothing else can

A running siphon's heights cannot break it, and its friction only postpones the moment it is most exposed. What does break a siphon that has run for a day is the air dissolved in its water, which the crown's low pressure leaves the water carrying far more of than it can hold — and which gathers only once the flow is too slow to carry a bubble away.

misconceptions · Siphon The largest nucleus decides how tall a siphon can be. The tallest crown a siphon of degassed water can run over, above the upper reservoir's surface, against the radius of the largest gas nucleus the water carries, for outlets 0.2, 1 and 3 m below the upper reservoir. Nuclei of ten microns and more leave the ordinary limit of about ten metres, where the crown reaches the vapour pressure. A largest nucleus of one micron lets a slow siphon stand 14.4 m tall; of three-tenths of a micron, 27.3 m. The water's own strength is never the limit: its dirt is.

A degassed siphon is as tall as its largest nucleus allows

The textbook says a siphon cannot lift water more than about ten metres, because above that the pressure at its crown would fall below zero. Water can hold a pressure below zero — a tension — and siphons of degassed water have run over crowns taller than the barometric height. How much taller is not set by the water's strength, which is enormous, but by the largest speck of gas it carries. A nucleus of a micron lets a slow siphon stand fourteen metres tall; three-tenths of a micron, twenty-seven. And the flow's own speed takes metres off every limit.

misconceptions · Siphon Dissolved gas takes height from the largest nuclei first. The tallest crown a siphon runs over, against the radius of its largest nucleus at the reservoir, when a nucleus at the crown must neither break the water at once nor grow to break it by diffusion, for water at 0, 10, 30, 60 and 100 per cent of saturation. Fully degassed water gives the static limit. For a one-micron nucleus, gas below about a fifth of saturation changes nothing — 14.41 m against 14.41 — and saturated water brings it to 10.7 m. A five-micron nucleus in saturated water breaks the siphon at 2.4 m.

A crown dissolves its nuclei or breaks on them, and fast

A siphon of degassed water runs until its crown's tension reaches the breaking threshold of its largest nucleus. A nucleus lodged at the crown does not stay the size it arrived: it gains or loses gas by diffusion, and across a micron diffusion takes milliseconds, so the crown gives its verdict almost at once. Every stable nucleus loses gas unless the water holds more than half the crown's tension, and past a knee in gas content, dissolved air takes height from a siphon's crown that no amount of further degassing gives back.

misconceptions · Siphon The pocket escapes at the least pressure its states can stand. The liquid pressure each equilibrium of the pocket needs, against the pocket's volume, for a crevice with a one-micrometre mouth in a wall the water wets at 40° and one it does not, at 110°. As the crown's pressure falls the pocket follows its curve to the right: the rim slides out of the cone, pins at the mouth, and the meniscus bulges into a cap. The curve's minimum is the escape threshold — -106 kPa for the wetting wall and -138 kPa for the non-wetting one — and below it no state exists: the pocket becomes a cavity.

A crevice keeps the nucleus a free bubble loses

A free bubble at a siphon's crown dissolves in milliseconds, so it cannot be what breaks a siphon that has run for an hour. A pocket of gas in a crack of the hose wall can be, because its meniscus is curved by the wall and need not dissolve. Followed through its equilibria, the pocket escapes at a tension set almost entirely by the crack's mouth. What the wall's wettability decides is slower and more consequential: whether the crack fills, or keeps drawing gas in until the siphon breaks.

misconceptions · Siphon

Named alongside it

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

CavitationModel limitSurface tensionVapour pressureLiquid tensionSiphonThresholdAbsolute pressureBubbleDiffusionMisconceptionBlake threshold

All concepts