The Verification Venue · a thing every textbook draws wrong
The Water That Is Pulled, Not Pushed
Put a perfect vacuum pump on top of a pipe and it will lift water 10.33 metres. Not 10.4. That is not an engineering limit, it is all the weight one atmosphere has to push with. A coast redwood measured at 115.55 m in 2006 moves water to its top before breakfast. Something is happening up there that no pump can do.
The picture most people carry is a straw: the leaves suck, the water comes up. The straw picture is not approximately right and then breaks down. It is arithmetically dead above ten metres, and you can watch it die in one drag. Below, the required pressure at the top of the column is computed from the height and the weight of water. Watch where it crosses zero.
Layer one · the column
Water potential at the top
–1.133 MPa
gravity alone
Absolute pressure there
–1.032 MPa
Patm + Ψ, and a vacuum is 0
Suction ceiling
10.33 m
Patm / (ρg)
no pump can do this
Ticks mark real measurements. Cross 10.33 m and the bar leaves the region any pump can reach and never comes back.
Gravity is fixed by the weight of water. Friction is not: it rises with transpiration and falls to nearly nothing at night. This slider is a free choice, and the check panel says so.
Wet soil is near zero. Dry soil starts the column already in tension, and everything above it inherits that.
A free choice worth about two centimetres of ceiling. The famous 10.33 m is the 1000 kg/m³ version.
Why it is not suction, and not capillarity either
The 10.33 m is the mercury barometer wearing different clothes. One standard atmosphere was originally defined as the pressure under 760 mm of mercury, and mercury is 13 595 kg/m³, so 101 325 Pa is also the pressure under 10 332 mm of water. Suction cannot beat it because suction is not a force. Pulling a piston up does not pull the water; it gets out of the water's way, and the atmosphere pushes the water in behind it. Once the column weighs more than the atmosphere can push, the piston separates from the water and you have made a vacuum, not a lift. Farm well pumps hit this every day.
The other standard escape is capillarity: water climbs a narrow tube on its own, so make the tube narrow enough. That is a real effect with a real number, so here is the number rather than the hand wave. Capillary rise is h = 2γcosθ / (ρgr), and xylem conduits are not narrow enough by one and a half to three orders of magnitude:
| conduit radius | what it is | capillary rise | fraction of 10.33 m |
|---|
Nothing in a stem lifts water even three metres by capillarity. But look at the last row. The menisci that matter are not in the conduits at all, they are in the cell walls of the leaf, whose pores are a few nanometres across. A meniscus that small can hold a column kilometres tall. It cannot lift the water, because lifting is the atmosphere's job and the atmosphere has quit. What it can do is hold on, and that is a different verb: the leaf's evaporating surfaces grip the top of the column and the whole thread hangs from them, in tension, like a wire. That is the cohesion-tension mechanism, proposed by Dixon and Joly in 1894, and it is the accepted account of how sap moves.
Layer two · the objection from physics
Liquid at minus three megapascals should not exist
Here is the objection, and it is not a bad one. Water under negative absolute pressure is metastable. It is stretched past the point where the vapour phase is the stable one, and it survives only because forming a bubble has an energy barrier. Every textbook of liquid-state physics says such a liquid is living on borrowed time. So how does a redwood run a column at negative pressure continuously, for a thousand years, without flashing to vapour? This is the objection Zimmermann, Canny and others pressed hard through the 1990s, some of them arguing that the tension was an artefact of the pressure chamber itself.
The answer, and it is the whole of layer two: xylem does not fail by homogeneous nucleation. Pure water in a clean vessel is famously strong, and would need far more tension than a tree ever generates. What actually fails is the seal between one conduit and the next. Neighbouring conduits share a pit membrane, a porous mesh of cell wall. When one conduit is already gas-filled and its neighbour is under tension, the air-water meniscus sitting in a pit pore is pushed on from both sides. Past a threshold pressure difference, it pops through, and air seeds into the water-filled conduit. Nothing nucleated. Air was pulled through a hole.
Which turns the whole question into geometry. The threshold for pushing a meniscus through a pore of diameter D is Young-Laplace: ΔP = 4γcosθ/D. Dial the pore and read off the pressure a plant can survive.
Pore diameter
92 nm
radius 46 nm
Air seeds at
–3.17 MPa
4γcosθ/D, with θ assumed 0
Tallest tree that survives it
323 m
on gravity alone, which no tree has
Choat, Cobb and Jansen (2008) report mean pit-membrane pore diameters of about 5 to 20 nm from colloidal gold perfusion. On the rare-pit hypothesis, wider pores too rare for that method to resolve set the air-seeding threshold, and quoted maxima run to a couple of hundred nanometres across the literature. We could not pin a single sourced upper bound, so read this slider's top end as a literature-wide span, not a measured maximum.
Pure water at 20 °C is 72.75. Xylem sap is not pure water: it carries lipids and surfactants, and its value in place is not well constrained. This is the loosest bolt on the page and it moves every pore estimate.
The point of that dial is not the dial. It is that, on the air-seeding account, one length scale predicts the species. Choat and colleagues measured vulnerability curves on four co-existing dry rainforest trees in 2003 and, from the same equation, reported the pore diameter each species' threshold implies. Those diameters were calculated from the P50s, not observed, so recomputing them here is a check on our arithmetic against theirs rather than an independent measurement. It lands:
| species | P50 (MPa) | ours: D = 4γ/|P50| | published D | Δ |
|---|
That is why pore structure is the dominant term in embolism resistance, and why a desert shrub and a streamside willow, made of much the same water, part company by a factor of ten. It is not the only term. Zhang and colleagues (2020), whose 20 nm figure this page cross-checks two sections down, argue the opposite direction on the residual: pure water in a 20 nm constriction should hold to about 7.2 MPa, far past where real plants actually embolise. They expect surface-active substances known to occur in sap to lower γ, but even their lipid value of 2.4 MPa leaves most species failing sooner, and they read the gap as a question for the classic air-seeding mechanism. The γ slider above is the surfactant part of that argument made operable. Structure sets the ranking between species. Chemistry is a live candidate for the offset.
Layer two · the curve, and how much room is left
The vulnerability curve, and the margin nobody has
Nothing fails all at once. Push a stem to a given tension, measure how much of its water conductivity is gone, and you get a sigmoid: the vulnerability curve. Two numbers describe it, the pressure at 50% loss (P50) and the slope there. Choat and 23 co-authors assembled these for 226 species at 81 sites in 2012 and compared each species' P50 to the lowest water potential it actually experiences in the field. The gap is the hydraulic safety margin. Their finding: 70% of species run on margins under 1 MPa, and those margins are largely independent of mean annual precipitation. Rainforests are as close to the edge as the driest forests and woodlands.
Conductivity lost at Ψmin
17.7 %
Pammenter sigmoid
Safety margin
0.77 MPa
Ψmin − P50
Where Choat 2012 puts it
inside the <1 MPa band
the band 70% of 226 species occupy
Default is Brachychiton australis from Choat 2003. Published P50 spans roughly –0.2 to –14 MPa across woody plants, and varies within a species and between methods.
Drag it past P50 and the margin goes negative: the plant spends its worst afternoons below the pressure at which half its plumbing is gone.
Layer two · the flagship, where a method makes a physiology
The artefact that invents a fragile tree
Everything above assumed the curve is real. Much of the world's vulnerability data is not measured by drying branches, which is slow, but by spinning stem segments in a centrifuge: the rotation puts the water under a known tension, and conductivity is read as it spins. It is fast, and it built the databases. It also has a contested problem, and this is a live dispute in the field rather than a settled one.
Some vessels are longer than the sample. In a rotor of diameter D, a vessel running from the cut end to the axis is open: an unbroken air path from the outside world to the point of lowest pressure. It does not need to air-seed through a pit membrane, because there is no pit membrane in the way. It empties at trivial tension. Species with short vessels are unaffected. Species with long ones, many ring-porous and tropical angiosperms, are not.
Below, the same underlying plant is measured twice. The true curve does not move. Only the vessel length and the rotor do. Watch a sigmoid become the shape the literature calls "r"-shaped, and watch the fitted P50 walk several megapascals.
Open-vessel fraction
0.763
f = exp(−(D/2)/λ)
P50 the centrifuge reports
–0.43 MPa
true P50 is –3.17, shift 2.74 MPa
Safety margin it implies
–1.97 MPa
true margin is +0.77 MPa
r-shaped: 55.3% loss at only −0.5 MPa, where the true curve loses 0.5%
Diffuse-porous temperate species are centimetres. Ring-porous oaks and many lianas run to metres. Drag from 50 cm to 5 cm and the open-vessel fraction falls from 0.763 to 0.067; it takes about 2 cm before the diagnostic below reads clean.
Lopez and colleagues (2019) find both centrifuge techniques prone to artefactual embolism when maximum vessel length is longer than or similar to rotor diameter, which is the ratio this model turns on. Their own mitigations are procedural rather than mechanical: measure flow in an excised central part of the segment, start Cavitron runs below the threshold at which open vessels embolise, or correct with their CAVITOPEN model. Drag the rotor and see why. It is a weak lever next to picking a short-vesselled species.
Now run the published test. Torres-Ruiz and Cochard proposed a diagnostic in 2017 that needs no extra equipment: dry the sample to some tension first, then spin it at a less negative pressure than it has already survived. A clean sample cannot lose anything new, because it has already been past that point. Anything above zero is the method talking about itself.
New conductivity lost on the spin
73.8 %
dried to −3.0 MPa, then spun at −1.0 MPa
Verdict
artefact present
a clean sample loses nothing; we pass anything under 0.5%
Walk λ down and watch the same diagnostic fall: 73.8% at 50 cm, 6.5% at 5 cm, and only at about 2 cm does it drop to 0.11% and the verdict flip to clean. That is the honest shape of the dispute: the centrifuge is not wrong, it is wrong for some species, and which species is an empirical question about vessel lengths rather than a matter of opinion. Sperry and colleagues argued in 2012 that not every "r"-shaped curve is invalid, and Venturas and colleagues in 2019 compared four methods directly and found the divergence tracks vessel network structure. The argument is not about whether sap is under tension. It is about how well we can measure the tension at which a given stem gives up.
The check
No readout on this page is a stored number. Every readout above is computed in your browser from the formulas printed here; the figures quoted in the prose are typed, and the same formulas, with those figures, are recomputed offline by research/water-under-tension/verify-water-under-tension.mjs (68 checks, exits 0).
What is being computed, right now, with your slider values
The round trip, and exactly how much it proves
The Young-Laplace table above takes four published P50 values, applies the equation, and lands on the pore diameters the same paper published, within 5.3%. Be clear about what that is worth. Choat and colleagues did not measure those diameters: they calculated them from these same P50 values with this same equation. The agreement is therefore close to arithmetically guaranteed, and it tests only that we implemented their formula with their rounding. It is not independent empirical confirmation that pore size predicts embolism resistance. The 2003 paper tried to see the predicted pores directly. Scanning electron microscopy could not resolve them (no pores were visible at a resolution of 20 nm), and colloidal gold perfusion indicated pores of only 5 to 20 nm in all four species, smaller than predicted. That column is a check, not a claim. And the 20 nm pore that Zhang and colleagues quote at 7.2 MPa (with their 0.5 pore-shape correction) recomputes here as 7.27 MPa.
Every free choice on this page, named
- Water density. The 10.33 m ceiling uses 1000 kg/m³. At 20 °C water is 998.2 and the ceiling is 10.35 m. The selector lets you move it. The whole choice is worth 1.9 cm.
- Vapour pressure. The 10.33 m is the ideal with nothing above the column. A real perfect pump leaves water vapour there, 2.34 kPa at 20 °C, which takes about 24 cm off: at 20 °C the lift is about 10.11 m. The page's ceiling leaves this out. These vapour-pressure figures are worked by hand; the verifier does not check them.
- Contact angle θ = 0. This is an assumption, universal in the pit-membrane literature, not a measurement. Nobody has measured the contact angle inside a pit pore. A non-zero angle makes every inferred pore smaller than we state, since D = 4γcosθ/|P50| and cosθ is below 1.
- Surface tension γ. We default to pure water at 20 °C, 72.75 mN/m. Xylem sap carries lipids and surfactants, and its effective γ at the pit membrane is not well constrained. Dropping γ to 50 mN/m shrinks every inferred pore by 31%. So the pore-to-pressure map is a range, not a point, and we say so with the slider rather than in a footnote.
- Ψmin = −2.40 MPa. The default field minimum is ours, not a measurement: Choat 2003 reports no field minimum for Brachychiton australis. So the 0.77 MPa margin, and the artefact panel's "true margin", are illustrations of the arithmetic, not that species' measured margin.
- Pore-shape correction. A pit pore is not a cylinder. Some authors apply a factor near 0.5. Our default is 1.0 (no correction); the Zhang cross-check above applies 0.5 so it is comparable to their published figure.
- The frictional gradient slider. Gravity's 0.0098 MPa/m is fixed by the weight of water. The friction term is not fixed, it depends on transpiration rate and path conductance, so its default here is zero and the slider is yours. The zero-crossing height is unaffected by it only when it is zero.
- The artefact model. Vessel lengths are treated as exponentially distributed with mean λ, so the fraction reaching the rotor axis is exp(−(D/2)/λ). Real distributions are not exactly exponential, and conductivity is weighted toward the wide, long vessels, so f is an order-of-magnitude estimate. The artefact component is modelled as a steep sigmoid centred at −0.3 MPa. What is not a modelling choice is the direction: open vessels lose conductivity at pressures far less negative than any pit-membrane threshold, so contamination always pushes the apparent P50 toward zero.
What we did not verify, and what is disputed
- Tree heights are remeasured. Hyperion was verified at 115.55 m by Stephen Sillett in 2006 using a tape drop; later listings give 116.07 m (2019) and 116.22 m (2026). We mark all of them and none as permanent. The spread is worth 0.0066 MPa, which is nothing next to the effect.
- Koch's 122 to 130 m is a regression extrapolation, from height gradients in leaf functional traits, not an observed limit and not a law. The tallest tree in that study was 112.7 m. We draw it as a hatched band and label it as extrapolated.
- Cohesion-tension is the accepted mechanism, and we do not call it proven. The pressure-probe challenge of the 1990s was largely resolved in its favour, notably by Wei, Tyree and Steudle's maize work. But the two instruments were compared only over a narrow band: probe and pressure chamber agreed over the entire measured range of 0 to −0.7 MPa. Their oil-filled cell pressure probe should, by their own tests, be safe to about −1 MPa (water-filled probes cavitated at −0.6 to −0.7 MPa). That is a small corner of the range plants actually occupy, and the range of agreement between two instruments is not the same quantity as the usable sensitivity of either. Where they overlap they agree. Outside it, one of them is the only witness.
- The top of the pore slider is not sourced. We can source mean pit-membrane pore diameters of 5 to 20 nm to Choat, Cobb and Jansen (2008). We could not pin the couple-of-hundred-nanometre maximum to a specific page of that review, so we do not present it as their number. The slider's range is a convenience for exploring the equation.
- Whether structure alone sets the threshold is contested. Zhang and colleagues (2020) set the 7.2 MPa a 20 nm pore should hold in pure water against the far weaker pressures at which plants actually fail. Surfactants known to occur in sap probably lower γ, but even with lipids (2.4 MPa) most species fail sooner, and they read that as a question for the classic air-seeding mechanism. We do not adjudicate that. We give you the γ slider.
- Measured tensions near −10 MPa come from pressure-chamber work on desert and chaparral species. They are not typical of plants in general and we do not generalise them.
- P50 varies within a species and between methods. The four values in our table are from bench-dehydration curves in one paper on four species at one site. Treat them as anchors for the arithmetic, not as species constants.
- The open-vessel artefact is contested, not settled. We represent it as a live methodological dispute, which is what it is. We have not independently measured any vessel length, rotor, or curve; the panel is a model of the mechanism, driven by your sliders, not a reproduction of anyone's data.
What "negative absolute pressure" actually means
Gauge pressure below zero is ordinary: it just means below atmospheric, which is what a straw does. Absolute pressure below zero is not ordinary. It means the liquid is being pulled outward, in tension, the way a steel rod is in tension. Liquids can do this because their molecules cohere; water does it unusually well because of hydrogen bonding. The state is thermodynamically metastable: the vapour phase has lower free energy, and only an energy barrier to forming a bubble keeps the liquid there. Spinning-capillary and Berthelot-tube experiments have taken pure water to tensions of tens of megapascals in the laboratory, well beyond anything a tree needs, which is why the objection from bulk physics does not land. The tree's problem was never water's strength. It was the holes in its own walls.
The unit convention here, which trips people: plant physiologists write water potential Ψ, which is zero for free pure water at atmospheric pressure and goes negative from there. Absolute pressure is Patm + Ψ when the only term is pressure. So Ψ = −0.05 MPa is a straw, and Ψ = −1.13 MPa, which is what gravity alone demands at the top of Hyperion, is an absolute pressure of −1.03 MPa, a physical state no pump can produce.
Why root pressure is not the answer either
Some plants do push. Root pressure, generated osmotically, is real and it is why a cut grapevine bleeds in spring and why guttation drops appear on leaf margins at dawn. But the pressures involved are typically a fraction of a megapascal, and that fraction buys metres, not hundreds of metres. It is also absent in many species during active transpiration, precisely when the demand is highest. It refills embolised conduits in some plants; it does not run the column.
Corrections.
Corrected 2026-10-18: the dek and the source note said the verifier runs 66 offline checks; it runs 68 (it printed "ALL 68 CHECKS PASSED" when the layer was written and now). Found by the assay line, 2026-10-18.
Corrected 2026-10-18: the check panel said a non-zero contact angle makes every inferred pore larger than stated; with D = 4γcosθ/|P50| it makes every inferred pore smaller. Found by the assay line, 2026-10-18.
Corrected 2026-10-18: the check panel said the pressure probe's apparatus in Wei, Tyree and Steudle (1999) could not record below about −0.65 MPa; the paper used an oil-filled cell pressure probe it reports should be safe to about −1 MPa, and −0.6 to −0.7 MPa is where its water-filled probes cavitated. Found by the assay line, 2026-10-18.
Corrected 2026-10-18: the note on negative absolute pressure gave Ψ = −1.03 MPa as what gravity alone demands at the top of Hyperion; that is the absolute pressure there, and the water potential is −1.13 MPa, as the page's own readouts show. Found by the assay line, 2026-10-18.
Corrected 2026-10-18: the sources credited the 2020 pit-membrane paper to "S. Zhang et al."; its first author is Ya Zhang (Y. Zhang et al.). Found by the assay line, 2026-10-18.