How this instrument works
Surface tension is the energy needed to stretch a liquid's surface by one square metre, which is physically the same thing as a force pulling along every metre of a line drawn on that surface — hence the unit newtons per metre. It exists because molecules inside a liquid pull equally on their neighbours in every direction, while molecules at the surface only get pulled sideways and downward, so the surface behaves like a taut, slightly elastic skin resisting any increase in area.
Dip a narrow glass tube into that liquid and the same skin does something visible: water climbs the inside wall, curls into a bowl-shaped meniscus, and keeps rising until the tension pulling around the wetted rim exactly supports the weight of the column it has lifted. Balancing an upward pull of γ around a rim of length 2πr against the weight ρgh·πr² of the raised cylinder, then cancelling the shared πr, leaves γ = ρghr ⁄ 2 for a liquid that wets the glass completely — this instrument's formula, first worked out by James Jurin in 1718 and still called Jurin's law.
The formula assumes the contact angle between liquid and glass is zero, so the meniscus forms a full hemisphere and cosθ drops out of the general γ = ρghr ⁄ (2cosθ) relation. Clean water in clean glass gets close to that ideal; oily glass, a liquid such as mercury that beads instead of wets, or a tube wide enough that gravity flattens the meniscus into something other than a spherical cap will all throw the reading off, which is why modern labs favour ring and plate tensiometers for anything beyond a teaching demonstration.
- Enter the liquid's density in the Liquid density field — water at room temperature is close to 1000 kg/m³.
- Measure how far the liquid climbed above the flat surface outside the tube and enter it in Capillary rise height.
- Enter the tube's inside bore radius, not its diameter, in Capillary tube radius.
- Read the result in Surface tension, given in newtons per metre.
- Compare the reading against a known value, such as water's roughly 0.0728 N/m at 20°C, to judge how clean and vertical the tube setup was.
Worked example — water rising 14 mm up a 0.5 mm capillary tube
Take a glass capillary tube with a 0.5 mm bore radius, so r = 0.0005 m, and dip it in water treated as exactly 1000 kg/m³ for this demonstration, so rho = 1000. The water climbs 14 mm up the inside wall before settling, so h = 0.014 m. Plugging into gamma = rho × g × h × r ÷ 2 with g = 9.80665 m/s² gives gamma = 1000 × 9.80665 × 0.014 × 0.0005 ÷ 2 = 0.034323275 N/m, which the instrument rounds for display to about 0.0343 N/m.
That figure sits below water's real textbook surface tension near 0.0728 N/m at room temperature, and the gap is expected: 1000 kg/m³ and 14 mm are round, illustrative numbers chosen to demonstrate the arithmetic, not a measurement taken from an actual rise in an actual tube. A genuine capillary-rise reading needs a scrupulously clean, perfectly vertical tube, a meniscus read at eye level, and a contact angle close enough to zero that the cosθ term stays negligible — which is exactly why laboratories doing precision work now reach for a Du Noüy ring or Wilhelmy plate tensiometer instead, keeping the capillary tube for teaching the underlying physics.
Questions
What exactly does surface tension measure?
Either of two equivalent things: the energy needed to increase a liquid's surface area by one square metre, in joules per square metre, or the force pulling along a one-metre line drawn on that surface, in newtons per metre — the two units are dimensionally identical. Water's value near 0.0728 N/m at 20°C is high for a common liquid, which is why insects can stand on it and why capillary rise in a narrow tube reaches centimetres rather than millimetres.
Why does the liquid rise instead of staying level with the reservoir?
Adhesion between the liquid and the glass wall is stronger than the liquid's own cohesion at that boundary, so the edge of the liquid climbs the wall, dragging a curved meniscus upward. The climb continues until the weight of the lifted column exactly balances the upward pull of surface tension acting around the wetted circumference — the point this formula solves for.
Why does the worked example give a lower number than water's known 0.0728 N/m?
Because the worked example uses round, illustrative inputs — a density of exactly 1000 kg/m³ and a rise of 14 mm — chosen to keep the arithmetic easy to follow, not a live measurement of real water in a real tube. Feed the instrument a rise closer to 30 mm for the same 0.5 mm tube and the result lands much nearer water's textbook figure; the formula itself is exact for a fully wetting liquid.
Does the tube's diameter matter, or just the radius?
Only the radius enters the formula directly, but diameter matters indirectly: a wider tube holds a heavier column of liquid for the same rise, which is exactly why wide tubes show barely any capillary rise while hair-thin ones can lift water several centimetres. Very wide tubes also break the model's spherical-meniscus assumption, since gravity flattens the curve before it can form a full hemispherical cap.
What if the liquid doesn't wet the tube, like mercury in glass?
Then the formula as written overstates the effect, because it assumes a contact angle of zero. Mercury beads against glass with a contact angle near 140°, cosθ is negative, and mercury is actually pushed down below the reservoir level rather than pulled up — the general relation h = 2γcosθ ⁄ (ρgr) still applies, it just returns a negative height for a non-wetting liquid.
How does this compare to a Du Noüy ring or Wilhelmy plate tensiometer?
Those instruments measure the force needed to pull a ring or plate free of the surface directly with a balance, so they don't depend on knowing a tube's exact bore radius or achieving perfect wetting — both hard to guarantee outside a controlled lab. Capillary rise is older, simpler, and needs no special apparatus, which is why it remains a standard teaching method even though ring and plate methods now dominate precision measurement.