quantity

pressure

The force applied perpendicular to a surface per unit area, capable of altering material states.
15 related articles · 6 formulas

Description

Pressure is the force applied perpendicular to a surface divided by the area over which it acts. It is a fundamental concept in physics, governing everything from the behavior of gases and liquids to the structural integrity of materials. Pressure can alter the state of matter, such as compressing gases into liquids or transforming graphite into diamond under extreme conditions.

History

Blaise Pascal formalized the concept in the 17th century, leading to Pascal's law, which states that pressure applied to an enclosed fluid is transmitted undiminished. Later, the SI unit of pressure, the pascal (Pa), was named in his honor.

How it works

Pressure arises from collisions of particles (in fluids) or from external forces distributed over an area. In a fluid, pressure acts equally in all directions and increases with depth due to the weight of the overlying material. In solids, pressure is the normal force per unit area, which can cause deformation or phase transitions when it exceeds material strength.

In practice

Pressure is used in hydraulic systems, weather forecasting (atmospheric pressure), and industrial processes like high-pressure food preservation and diamond synthesis.

Fun fact

At the bottom of the Mariana Trench, pressure is over 1,000 times atmospheric pressure, enough to crush most submarines unless specially designed.

Concept graph →

Formulas

$$\frac{P_c v_c}{T_c} = \text{const}$$
Critical pressure, volume, and temperature have a constant ratio.
What is in the formula
P_cvariableCritical pressure — pressure pascal
v_cvariableCritical molar volume — molar volume cubic metre per mole
T_cvariableCritical temperature — temperature kelvin
$$w = \frac{P}{\rho}$$
Relates pressure to energy density in cosmology.
What is in the formula
wvariableequation of state parameter — equation of state parameter
Pvariablepressure — pressure pascal
ρvariableenergy density — energy density joule per cubic metre
$$\frac{d\epsilon}{dn} = \frac{\epsilon + p}{n}$$
The energy gradient per particle equals enthalpy per particle.
What is in the formula
\epsilonvariableenergy density — energy density joule per cubic metre
nvariableparticle number density — number density per cubic metre
pvariablepressure — pressure pascal
\frac{d}{dn}operatorderivative with respect to particle number density — derivative with respect to number density
$$\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}(\rho + 3p)$$
Relates acceleration to energy density and pressure.
What is in the formula
\ddot{a}variablesecond time derivative of scale factor — scale factor acceleration per second squared
avariablescale factor — scale factor
\rhovariableenergy density — energy density joule per cubic metre
pvariablepressure — pressure pascal
GconstantConstant of gravitation in Einstein's field equations. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$c_s^2 = \frac{dP}{d\varepsilon}$$
Speed of sound squared is the derivative of pressure with respect to energy density.
What is in the formula
c_svariablespeed of sound — speed of sound metre per second
Pvariablepressure — pressure pascal
εvariableenergy density — energy density joule per cubic metre
d/dεoperatorderivative with respect to energy density — derivative
$$\beta = \frac{8\pi p}{B^2}$$
Ratio of plasma pressure to magnetic pressure.
What is in the formula
βvariablePlasma beta — plasma beta
pvariablePlasma pressure — pressure pascal
BvariableMagnetic field strength — magnetic field tesla
πconstantMathematical constant — pi = 3.14159

Related articles · 15

Fluid Dynamics2026-03-281 minarXiv:2603.27227express
How Slits Turn a Sheet into a Wing
A flat sheet with slits in a flow of water or air behaves like self-adjusting blinds. The pressure opens the gaps, and each strip of material tilts, turning into a miniature wing. Thus, even a sheet placed perpendicular to the flow generates not only drag but also significant lateral lift.
How Soap Changes the Shape of a Drop
A drop of oil in water, coated with soap molecules, behaves differently from a bare drop. Soap molecules are tiny rods: one end loves water, the other loves oil. In a quiescent fluid, they stand on the surface like a picket fence, lowering the surface tension — the force that pulls the drop into a sphere.
Fluid Dynamics2026-03-191 minarXiv:2603.18615express
A Drop Strikes Differently
A raindrop falling to the ground strikes with a certain force. But what if the drop isn't round but elongated like a cigar or flattened like a pancake? It turns out that shape is everything: the impact force can vary by more than a factor of ten just because of how the drop looks at the moment of impact.
The Coin That Refuses to Stop
A coin spinning on a table is a familiar sight. At first it rotates quickly, then it tilts, and its rattling becomes faster and faster. In the last seconds it seems to hover: the rotation slows, but the coin just won't finally lie flat. This final moment is a real puzzle for physicists.
q-bio.OT2026-03-011 minarXiv:2603.01054express
How a Bladder Turns into a Pear
The bladder is like a balloon: as it fills, the wall stretches and the shape changes. Doctors usually monitor the pressure inside and how much fluid has entered, but they rarely look at the geometry itself — how the surface curves. Yet irregularities can appear before the usual metrics deteriorate.
The Glass That Breaks by a Single Law
Glass is a material with attitude. It seems fragile, but powerful invisible forces can live inside it. In chemically strengthened glass, the surface is compressed like a stretched rubber band, while the interior is stretched. When a fast object hits such glass, that rubber band snaps in many places at once. Scientists fired projectiles at glass and watched how it shattered.
Materials2026-02-121 minarXiv:2602.12427express
Friction in Faults: How Sand Turns into an Earthquake
When two tectonic plates grind against each other, a layer of pulverized rock ends up between them, like sand between your palms. This layer, which geologists call fault gouge, behaves not like solid rock but like a thick paste: it can compact, dilate, and slide. Whether a fault ruptures in a devastating earthquake or creeps slowly and safely depends on its whims.
Medical Physics2026-02-101 minarXiv:2602.10011express
Why Blood Pressure Won't Drop: Loops in the Vessels
Water in a circular hose, pumped around by a pump, won't stop even if you pinch one section: the flow finds a detour and keeps going around. That's roughly how some parts of our circulatory system are arranged — not as single pipes but as closed loops. Scientists built a computer model of blood flow and compared two scenarios: an open vessel and a closed loop.
Fluid Dynamics2026-02-032 minarXiv:2602.03617express
Roughness That Decides a Flight's Fate
A blunt cylinder flying at six times the speed of sound isn't the most elegant object, but it's the star of a new simulation. The surface of such a vehicle is never perfectly smooth: during atmospheric entry, the heat shield ablates, leaving bumps and pits.
Fluid Dynamics2026-01-201 minarXiv:2601.13971express
A Falling Plate Without a Supercomputer
A sheet of paper released from a window flutters, tumbles, and sometimes pauses flat for a second. Until now, to honestly predict such behavior, you had to run millions of equations on supercomputers for every drop of air. That's like simulating every atom of a cash register to count change at a store. The new approach is smarter.
Superconductivity2026-01-031 minarXiv:2601.01100express
Stretching a carbon sheet turns it into a superconductor
A thin sheet of carbon, resembling an intricate mesh of triangles, hexagons, and octagons, lies on a substrate. By itself, it is not superconducting: electrons move through it haphazardly, bumping into atoms. But stretch the sheet evenly, like canvas on a frame, and the picture changes.
How a Sheet of Paper Decides to Wrinkle or Fold
A thin rubber film lies on a table. Someone grabs it by the middle and slowly pulls upward. The film doesn't just rise: it arches into a dome, then wrinkles run along the dome's edge, like pleats on a skirt. Pull higher — the wrinkles gather into large folds that cross the entire film. And if you start lowering it, the folds don't disappear but collapse into new shapes.
Quantum Physics2026-01-012 minarXiv:2601.00483express
Levitation on Quantum Glue: The Casimir Effect in Action
The space between two closely spaced surfaces is far from empty: it's a seething "quantum glue." Within it, quantum fluctuations continuously pop in and out of existence: microscopic bursts of energy in electromagnetic fields that, according to quantum theory, give the vacuum a dynamic structure.
Fluid Dynamics2025-12-021 minarXiv:2512.03240express
How Honey Flows Through a Sponge: New Equations
Drop honey onto a sponge. It lazily creeps, avoiding the voids. But if the honey becomes thinner under pressure, the flow gets trickier. Liquid with variable thickness in an uneven labyrinth of pores — a problem that had defied calculation. The authors of the new work averaged the chaos of microchannels into simple equations.
Materials2025-06-042 minarXiv:2506.09058
Diamond Grains Map Pressure Inside a Cell
Inside a diamond anvil cell, a device where two diamonds squeeze a sample to hundreds of gigapascals, pressure is distributed unevenly. Some regions are compressed more, others less. This affects experimental results: the material may behave differently than under perfectly uniform compression.