Pressure

• 1. Introduction

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  Pressure acts on every object and every body in the physical world, yet it is invisible. A finger pressed against a wall leaves no mark. That same finger pressing the point of a thumbtack into the same wall punches right through. The applied force is identical in both cases. What changes is the area over which that force is spread. That single principle, force divided by area, is the definition of pressure, and it governs blood flowing through arteries, air trapped in a car tyre, water rising through the tallest trees, and even the expansion of the universe itself. What exactly is pressure, how do scientists measure it across such radically different situations, and where does it appear in forms that contradict everyday intuition? Those are the questions this documentary sets out to answer.

• 2. Force Per Unit Area

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  Blaise Pascal and Daniel Bernoulli are the two names most credited with establishing the concepts of fluid pressure, and the SI unit, the pascal (Pa), honours the first of them. One pascal equals one newton per square metre. That name was formally added to the SI system in 1971; before that, pressure in the international system was simply written in newtons per square metre.

  The pascal is not the only unit in use. Meteorologists often prefer the hectopascal for atmospheric air pressure, a value equivalent to the older millibar. Oceanographers generally measure underwater pressure in decibars, because pressure in the ocean increases by roughly one decibar for every metre of depth. Blood pressure worldwide is reported in millimetres of mercury, and lung pressures in centimetres of water remain common in medicine. Divers work with metres sea water and feet sea water. Aviation still uses the hectopascal with the hecto- prefix where other technical fields would use kilopascals. This patchwork of units reflects the enormous range of pressures that different disciplines encounter daily.

  The pound-force per square inch, abbreviated psi, remains the conventional unit in US customary and imperial systems. A car tyre inflated to 220 kPa of gauge pressure actually holds air at roughly 320 kPa of absolute pressure, because atmospheric pressure at sea level adds about 100 kPa on top. Confusing the two figures leads to real errors: a gas at 200 kPa gauge pressure is 50 percent denser than the same gas at 100 kPa gauge, not twice as dense, because only the absolute values matter when calculating density.

• 3. Depth, Density, and Liquid Pressure

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  When a person swims under water, the pressure felt on the eardrums comes from the weight of all the water above. Doubling that depth doubles the pressure. Tripling it triples the pressure. The volume of water is irrelevant: a swimmer dunked one metre beneath the surface of a small pool feels the same pressure as a swimmer one metre below the surface of a large lake.

  A vivid demonstration of this principle involves four interconnected vases filled to the same depth but holding different volumes. A fish hovering just below the surface in any of the vases experiences the same pressure. If the fish swims deeper, pressure increases equally in all four vases regardless of their shape. The reason is that water seeks its own level: if pressure at the bottom of one vase were higher than at the bottom of a neighbour, water would flow sideways and rise in the neighbour until the bottoms were equalised.

  Liquids are nearly incompressible. Water's volume decreases by only fifty millionths of its original volume for each additional atmosphere of pressure applied. That near-rigidity means the density of a given liquid stays almost constant at all depths, which is why simple formulas relating pressure to depth and density work accurately across the range of conditions encountered in everyday engineering.

  Torricelli's law gives the speed at which liquid exits a hole in the side of a container: it is the same speed the liquid would reach if it fell freely through the same vertical distance. A container with three holes at the top, middle, and bottom will shoot water from the bottom hole the farthest, because the greater depth means greater pressure, which means higher exit velocity.

• 4. Gauge, Absolute, and Negative Pressure

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  Gauge pressure is always measured relative to the surrounding ambient pressure, not to a perfect vacuum. An absolute pressure of 80 kPa in a region where atmospheric pressure is 101 kPa is recorded as a gauge pressure of negative 21 kPa. That negative reading is not exotic: abdominal decompression, an obstetric procedure, deliberately applies negative gauge pressure to a pregnant woman's abdomen at intervals.

  Negative absolute pressure is more unusual. In that condition, a bulk material is effectively under tension rather than compression. Solids and liquids can sustain some tension because the attractive forces between their molecules can temporarily overpower the kinetic energy trying to pull them apart. But the state is metastable, meaning any disturbance can collapse it. In liquids, the result is cavitation, the sudden formation of bubbles. Liquid mercury has been observed holding a negative absolute pressure of -425 (in the appropriate units) inside clean glass containers without cavitating. Negative liquid pressure is also believed to be the mechanism that draws sap upward in trees taller than 10 metres, a height beyond which atmospheric pressure alone cannot push water.

  At cosmological scales, dark energy is thought to produce a small but significant negative pressure that drives the accelerating expansion of the universe, connecting the everyday physics of a thumb pressed on a thumbtack to the largest structures in existence.

• 5. Gas Pressure and the Ideal Gas Law

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  In an ideal gas, molecules are treated as having no volume and no interactions with one another. Under that simplification, pressure varies in direct proportion to temperature and to the amount of substance present, and in inverse proportion to volume. That relationship is the ideal gas law, written with the ideal gas constant R linking the four variables.

  Real gases depart from this clean behaviour. Their molecules do have volume and do interact, so the relationship between pressure, temperature, and volume grows more complex. Vapour pressure is one manifestation of that complexity: it is the pressure a vapour exerts when it sits in thermodynamic equilibrium with its liquid or solid form in a closed system. Every liquid has a normal boiling point defined as the temperature at which its vapour pressure equals ambient atmospheric pressure. Any small rise above that temperature gives the vapour enough pressure to overcome the atmosphere and form bubbles inside the bulk liquid. Bubble formation deeper in a liquid requires still higher pressure and therefore higher temperature, because the liquid's own weight adds to the pressure at depth.

  When a mixture of gases is present, each component contributes its own share, called the partial vapour pressure, to the total pressure of the system. The sum of all partial pressures equals the total.

• 6. Stagnation, Surface, and Generalized Pressure

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  Stagnation pressure is what a moving fluid exerts when it is brought to a complete stop. A fluid moving at higher speed carries a lower static pressure by Bernoulli's principle, but when that same fluid is forced to a standstill it may register a higher stagnation pressure. A Pitot tube, and related devices such as the Kiel probe and the Cobra probe, exploit this distinction to measure both static and stagnation pressures by positioning inlet holes at different locations on the probe.

  Surface pressure is a two-dimensional counterpart to ordinary pressure: the lateral force per unit length applied along a line perpendicular to that force. It is denoted by the Greek letter pi and shares mathematical properties with three-dimensional pressure. Surface tension is a closely related concept, but it carries the opposite sign because tension is the reverse of compression. Chemical properties of thin films and surface coatings can be probed by measuring how surface pressure changes with area at constant temperature, a technique analogous to Boyle's law applied to a two-dimensional layer.

  In 2022, a paper published in Physical Review B by the Lei Li group at Sichuan University proposed a concept called generalized pressure: a framework that treats different sources of volumetric strain, such as chemical pressure and mechanical pressure, as equivalent if they produce the same magnitude of volume change. The framework draws on the equivalence principle from Einstein's general relativity. Testing the idea on the ternary semiconductor alloy AlxGa1-xN, the researchers found that the alloy and its end-member materials reach the same phase-transition points when plotted in terms of generalized pressure.