Pressure is the normal force exerted per unit area and is a scalar quantity in a fluid at rest. It is commonly represented by P and has the SI unit pascal, equal to one newton per square metre. In continuum mechanics, pressure is associated with the isotropic part of the stress tensor and represents compressive normal stress under fluid equilibrium. Pressure can be absolute, gauge or differential depending on the reference used. It occurs in gases, liquids and solids, although its interpretation and role differ according to the material and mechanical state. In fluid systems, pressure is a fundamental state and field variable that can drive motion, support loads and exchange mechanical energy with surrounding systems.
Absolute pressure is measured relative to an ideal vacuum, while gauge pressure is measured relative to local atmospheric pressure. Thus gauge pressure equals absolute pressure minus atmospheric pressure. A pressure reading below atmospheric pressure is commonly described as negative gauge pressure but can still correspond to a positive absolute pressure. Differential pressure is the difference between pressures at two specified locations and is frequently used in flow measurement, filtration and industrial control. Confusing these reference systems can lead to major errors in calculations, particularly when equations require absolute pressure, such as many thermodynamic relationships and equations of state.
In a static fluid under gravity, pressure varies with vertical position according to the hydrostatic equation. For constant density, the pressure difference between two points is rho g times their vertical separation. Pressure therefore increases with depth in a liquid and generally decreases with altitude in the atmosphere. At a given point in a fluid at rest, pressure acts equally in all directions. This isotropic property allows pressure to transmit forces through hydraulic systems. Pascal's principle describes how a pressure change applied to a confined fluid can be transmitted throughout the fluid, forming the basis of hydraulic presses, brakes, actuators and other systems.
Pressure gradients are central to Fluid Dynamics because they can accelerate fluids. A fluid element experiences a net pressure force when pressure differs across its spatial extent. In many flows, pressure gradients balance or compete with inertial, viscous and body forces. A pressure drop along a pipe is commonly associated with frictional resistance, although pumps, elevation changes and changes in velocity can also contribute to pressure differences. Pressure should therefore not be interpreted as simply the force that makes fluid flow; rather, spatial variation in pressure is one of several mechanisms governing fluid acceleration and momentum transport.
Pressure is also related to thermodynamic state. For gases, pressure, volume, temperature and amount of substance are connected through equations of state such as the Ideal Gas Law under appropriate conditions. Compressing a gas can increase pressure, but the resulting temperature also depends on whether heat is transferred and on the thermodynamic process. In liquids, pressure changes can produce relatively small density changes under ordinary conditions, which is why incompressibility is often a useful approximation. At very high pressures, however, liquid compressibility becomes significant and must be included in appropriate models.
Pressure measurement uses instruments such as barometers, manometers, Bourdon tube gauges, diaphragm sensors, piezoresistive transducers and other electronic pressure sensors. Measurement systems may require calibration against known standards and compensation for temperature or other environmental effects. Pressure sensors can measure static pressure, stagnation pressure or differential pressure depending on their configuration. In fluid systems, a pressure measurement can also be influenced by sensor location, flow disturbance, tubing geometry and dynamic response. Correct interpretation therefore requires knowing precisely what physical quantity the instrument measures and what reference pressure is being used.
Pressure forces are important in engineering structures and natural systems. Dams experience increasing hydrostatic pressure with depth, aircraft wings experience pressure distributions associated with airflow, pipelines require pressure ratings, and atmospheric pressure affects weather and gas systems. Pressure differences can cause leakage through seals, drive filtration, move fluids through pipes and produce forces on submerged bodies. In rotating fluids, pressure can vary radially as well as vertically because centripetal acceleration must be balanced by a corresponding pressure gradient. Pressure is therefore a field quantity whose spatial distribution often contains more physical information than a single pressure value.
Pressure is sometimes confused with force, but they are not interchangeable. A force depends on the total interaction over an area, while pressure describes force per unit area and can vary across that area. The same total force can correspond to very different pressures if applied over different areas. Likewise, high pressure does not automatically imply high flow speed because the relationship between pressure and velocity depends on geometry, viscosity, elevation, compressibility and other conditions. Correct interpretation of pressure requires specifying its reference, location, spatial distribution and relationship to the governing physical processes.
