Concept

Liquid tension — where it appears

A negative absolute pressure in a liquid, in which the liquid pulls on its surroundings rather than pushing. A liquid with no cavity or free surface near it can hold megapascals of it, as water does at the top of every tall tree, and its floor is set by the largest cavity present rather than by the vapour pressure.

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

Two heights, and only one of them is in the answer. A siphon, with the two heights that get confused. The drop from the source surface to the outlet is what drives the flow: the exit speed is √(2gΔz) = 4.43 m/s and nothing else enters it. The rise to the crown decides the pressure at the top — 72.0 kPa absolute here, against an atmosphere of 101.3 — and therefore whether the column holds together at all. A siphon over a high wall and one over a kerb, draining to the same place, flow at exactly the same rate.

The siphon that does not need the air

A siphon is explained everywhere by the atmosphere pushing the liquid over the hump. The flow rate says otherwise, in the flattest way available — the height of the hump does not appear in it at all. What the atmosphere does is hold the column together, which is a different job with a different limit.

misconceptions · Siphon

100 metres of water, −1.98 MPa absolute at the top. The absolute pressure up a transpiring column 100 metres tall, with the sap rising at 0.25 mm/s through conduits 40 µm across. It starts at 1.3 kPa at the root, falls by 9.79 kPa a metre for gravity and 10.02 for friction, and reaches −1.98 MPa at the top — below zero, which is not a low push but a pull. The pale line is the same column with nothing flowing. The floor is not the vapour pressure but the pore a gas bubble could be drawn through: −2.81 MPa for a 50 nm pore, which this column would reach at 142 metres. A suction pump lifting the same water from a free surface stops at 10.1 metres, because it offers the water somewhere to boil.

Where a liquid does pull

A fluid cannot pull, and the essays that settle what suction is are right about every gas and every liquid with a free surface near it. A liquid with nothing in it to boil on is another matter. Every tree taller than ten metres depends on the difference, and the floor under it is set by the size of a pore rather than by the vapour pressure.

misconceptions · Suction

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

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.

Cavitation Model limit Vapour pressure Surface tension Absolute pressure Misconception Nucleation Siphon Barometric height Bubble Diffusion Threshold

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