Pressure
Pressure is force per unit area, a scalar quantity.
Pressure (symbolized as p or P) describes the force applied perpendicularly to a surface, divided by the area over which that force is spread. It is a scalar quantity, meaning it has no inherent direction—only the force resulting from it does. Mathematically, pressure is expressed as p = F/A (or P = F/A), where F is the magnitude of the normal force and A is the contact area. A more formal relationship involves the vector area element: the normal force on a surface element is given by dFₙ = –p dA, with the minus sign reflecting the convention that force points inward while the normal vector points outward. For any surface in contact with a fluid, the total force exerted by the fluid is the surface integral of this expression.
In thermodynamics, pressure is a fundamental parameter conjugate to volume. It can be defined as the negative partial derivative of internal energy with respect to volume at constant entropy and particle number: p = –(∂U/∂V)ₛ,ₙ.
The SI unit of pressure is the pascal (Pa), equal to one newton per square metre (N/m²). This unit was adopted in 1971; previously, SI pressure was simply given in newtons per square metre. Other common units include the pound-force per square inch (psi, or lbf/in²) in imperial and US customary systems, and the bar. The CGS unit is the barye (Ba), which equals 0.1 Pa. Pressure is also expressed in terms of standard atmospheric pressure: the atmosphere (atm) is exactly that pressure, and the torr is 1/760 of an atmosphere. Manometric units—such as centimetres of water, millimetres of mercury, or inches of mercury—represent pressure via the height of a fluid column in a manometer. Gauge pressure refers to pressure measured relative to ambient pressure.
Pressure can also be viewed as energy density, with units like joules per cubic metre (J/m³), which is equivalent to the pascal. Some deprecated units include grams-force or kilograms-force per square centimetre; the technical atmosphere (at) is defined as 1 kgf/cm² (about 98.0665 kPa or 14.223 psi). The symbol for pressure varies by field: IUPAC recommends a lower-case p, but upper-case P is also widely used, depending on context and the need to avoid confusion with symbols for power or momentum.
- symbol
- p or P
- SI unit
- pascal (Pa), equal to one newton per square metre (N/m²)
- common units
- pound-force per square inch (psi), atmosphere (atm), torr, millimetre of mercury, centimetre of water
- gauge pressure
- pressure relative to ambient pressure
- CGS unit
- barye (Ba), equal to 0.1 Pa
Lore & Background
Pressure is mathematically defined as p = F/A, where F is the magnitude of the normal force and A is the area of the surface in contact. It is a scalar quantity, meaning it has no direction; the force resulting from pressure has direction, but pressure itself does not. The IUPAC recommends a lower-case p, but upper-case P is also widely used depending on the field and context. Pressure is a fundamental parameter in thermodynamics, conjugate to volume, and is defined as a derivative of internal energy with respect to volume at fixed entropy and particle number. It is distributed to solid boundaries or across arbitrary sections of fluid, acting normal to these boundaries or sections at every point. The SI unit is the pascal (Pa), equal to one newton per square metre, a name added in 1971; prior to that, pressure in SI was expressed in newtons per square metre. Other common units include pounds per square inch (psi) in imperial and US customary systems, the bar, and the standard atmosphere (atm), which is approximately equal to typical air pressure at Earth mean sea level. Manometric units, such as millimetres of mercury or centimetres of water, express pressure by the height of a fluid column in a manometer; these are still used for blood pressure and lung pressures. Underwater pressure is often measured in decibars, as pressure in the ocean increases by roughly one decibar per metre depth.
Reader's Guide
Pressure is a key concept in physics and engineering, measured in many units. The SI unit is the pascal (Pa), but other units like pounds per square inch (psi), atmosphere (atm), and manometric units such as millimetres of mercury remain common. Gauge pressure is measured relative to ambient pressure, often indicated by suffixes like 'g' (e.g., psig). Pressure is also related to energy density, expressed in joules per cubic metre. Its definition as a derivative of internal energy with respect to volume at fixed entropy and particle number underscores its role in thermodynamics. Manometric units, such as centimetres of water or millimetres of mercury, are based on the height of a fluid column in a manometer, though modern definitions may be expressed in SI terms.
Did You Know?
- Pressure is a scalar quantity and has no direction.
- Gauge pressure is often indicated by appending 'g' to the unit, such as 'psig'.
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