Pascal
On 19 September 1648 Florin Périer climbed the Puy de Dôme with a glass tube full of mercury. The experiment was requested by his brother-in-law, Blaise Pascal. Below, in Clermont, the mercury stood at about 71 cm. At the summit it dropped by 8.5 cm.
This showed that the mercury holds up the weight of the air above it. The higher you climb, the less air is above you and the lower the column. More than three hundred years later the unit of pressure was named after Pascal. One pascal is a force of one newton per square metre. That is very little: a sheet of paper presses on a desk with about 0.8 Pa.
| Notation | Pa |
| Definition | one newton per square metre · N/m² · kg·m⁻¹·s⁻² |
| Reference values | standard atmosphere 101 325 Pa · 1 bar — 100 000 Pa · 1 Torr — 101 325/760 Pa |
| Introduced | 1971, 14th General Conference on Weights and Measures |
| Standards | ISO 80000-4 · SI Brochure 9th ed. · ISO 2533 (standard atmosphere) |
| Typical values | 31 kPa — summit of Everest · 101 kPa — sea level · 110 MPa — bottom of the Mariana Trench |
01 · Definition
Force divided by area
Pressure p is a force F acting perpendicular to a surface, divided by the area A of that surface. One pascal is a force of one newton on one square metre. In SI base units it is a kilogram per metre per second squared.
In a liquid or a gas, pressure acts equally in all directions. This is Pascal's law. That is why at depth water presses on a bathyscaphe not only from above but from every side. Every ten metres of seawater add roughly one atmosphere.
Why a snowshoe holds and a stiletto sinks
A person stands on snow. The blue load is their weight, set with the slider. Only the support underneath changes. The smaller the area, the higher the pressure and the deeper the print. The dashed line is the snow surface before they stepped on it.
A tyre gauge reads 2.2 bar. That is gauge pressure: how much harder the air in the tyre pushes than the air outside. The absolute pressure in the tyre is about 3.2 bar. If you do not say which pressure you mean, the error is a whole atmosphere. That is why documents spell it out: «gauge pressure 220 kPa».
What happens to a balloon, a cup and a crisp packet
On the left is a cross-section of the world: a mountain, sea level and the ocean down to the bottom of the Mariana Trench. Depth is plotted unevenly so that the first tens of metres are visible. Drag the object up or down, or pick a place with a button. In the middle the object is shown large. Blue arrows are the pressure of water or air: the longer they are, the harder it presses. The dashed outline is the size of the object at sea level. On the right is a gauge with a logarithmic scale. If you leave it alone, the object tours the places by itself.
At sea level the pressure is 101.3 kPa. Take the balloon under water or up into the mountains.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
A hectopascal equals a millibar. So weather services changed the unit without changing the numbers: 1013 mbar became 1013 hPa.
The torr and the millimetre of mercury differ by less than one part in a million.
Tyre figures in psi and bar are gauge pressure. You need to add an atmosphere to them.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
The standard atmosphere is not a measurement but a convention. In 1954 the 10th General Conference on Weights and Measures fixed it at exactly 101 325 Pa. The number comes from the old definition: a column of mercury 760 mm high at 0 °C and standard acceleration due to gravity.
So the torr, one seven-hundred-and-sixtieth of an atmosphere, is an exact number too. The millimetre of mercury is calculated from the density of mercury and differs from the torr by less than one part in a million. For a doctor or a meteorologist there is no difference; for a metrologist there is.
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