Pressure
Pressure is a scalar physical quantity that represents the force exerted perpendicular to a surface per unit area over which that force is distributed.[1] In the International System of Units (SI), the unit of pressure is the pascal (Pa), defined as one newton of force per square meter of area (1 Pa = 1 N/m²).[2] Pressure arises from the interactions of particles or fields and acts equally in all directions within a fluid, always normal to any confining surface.[3] In solids, pressure relates to compressive stress, influencing material deformation and strength under load.[4] In fluids and gases, it governs behaviors such as buoyancy, flow, and equilibrium, with hydrostatic pressure increasing linearly with depth due to the weight of the overlying fluid (P = ρgh, where ρ is density, g is gravitational acceleration, and h is depth).[3] Atmospheric pressure, approximately 101,325 Pa at sea level, results from the weight of the air column above and drives weather patterns, respiration, and aviation.[5] Pressure measurement distinguishes between absolute pressure (relative to a vacuum) and gauge pressure (relative to atmospheric pressure), with applications spanning hydraulic systems that amplify forces via Pascal's principle, blood pressure monitoring in medicine, and tire inflation for vehicle safety.[6] These concepts underpin fields from engineering to physiology, enabling technologies like scuba diving equipment and weather forecasting.[1]Definition and Fundamentals
Core Definition
Pressure derives from the Latin word pressura, meaning a pressing or pressing down.[7] In physics, force is defined as any influence that tends to change the motion of an object, often described as a push or pull with both magnitude and direction.[8] Area refers to the measure of the extent of a two-dimensional surface over which a force acts.[9] Pressure is the measure of how force is distributed over a surface, quantified as the force per unit area, and it applies to interactions in solids, liquids, and gases.[1] This concept originated from 17th-century studies by Blaise Pascal on the behavior of fluids, where he explored how pressure transmits through liquids and gases.[10] The SI unit of pressure is the pascal (Pa), named after Pascal.[1]Mathematical Formulation
Pressure is mathematically defined as the force exerted perpendicular to a surface divided by the area over which that force is distributed, expressed by the equation P = \frac{F_\perp}{A}, where P denotes pressure, F_\perp is the component of the force normal to the surface, and A is the area of the surface. This formulation arises directly from the macroscopic application of force in mechanics, where pressure quantifies the intensity of force distribution independent of the surface's orientation, provided the perpendicular component is considered. For oblique forces, only the normal component contributes, as tangential forces produce shear rather than pressure; thus, \vec{F}_\perp = \vec{F} \cdot \hat{n}, with \hat{n} as the unit normal vector to the surface.[11] The derivation of this formula traces back to Newton's laws of motion, particularly the second law (F = ma), which relates force to the rate of change of momentum. In macroscopic contexts, pressure emerges when a net force acts over an area, such as in the equilibrium of a piston confining a substance, where the applied force balances the internal resistance per unit area. Microscopically, for gases, pressure results from the cumulative effect of molecular collisions with the container walls. Consider a molecule of mass m with velocity component v_x perpendicular to a wall of area A; upon elastic collision, the change in momentum is \Delta p_x = 2mv_x (by Newton's third law, the wall exerts an equal and opposite impulse). The number of collisions per unit time on the wall is proportional to the molecular density and the average speed component. Averaging over all molecules and directions yields the standard kinetic theory result P = \frac{1}{3} \rho \langle v^2 \rangle, where \rho = \frac{Nm}{V} is the mass density and the core pressure-area relation holds as P = F/A.[12]/02%3A_Gases/2.03%3A_The_Kinetic_Molecular_Theory_of_Gases) This averaging over collisions renders pressure a scalar quantity.[13] In the International System of Units (SI), consistency is maintained with force in newtons (N, equivalent to kg·m/s² from Newton's second law) and area in square meters (m²), resulting in pressure measured in pascals (Pa = N/m²). This unit ensures dimensional homogeneity, as [P] = [F]/[A] = ML^{-1}T^{-2}, aligning with fundamental mechanical principles.[14]Units and Measurement
The SI unit of pressure is the pascal (Pa), defined as one newton per square meter (1 Pa = 1 N/m²), which corresponds to the force of one newton applied uniformly over an area of one square meter.[15] In terms of base SI units, pressure has the dimensional formula [M L⁻¹ T⁻²], reflecting its nature as force per unit area, where mass [M], length [L], and time [T] derive from the kilogram, meter, and second, respectively.[16] Other common units of pressure include the atmosphere (atm), bar, torr, and pound per square inch (psi), each defined with precise conversions to the pascal for standardization in scientific and engineering applications. The standard atmosphere is exactly 101 325 Pa, representing the average sea-level atmospheric pressure.[17] The bar is defined exactly as 100 000 Pa, often used in meteorology and engineering for pressures near atmospheric levels.[18] The torr, named after Evangelista Torricelli, is exactly 101 325 / 760 Pa (approximately 133.322 Pa), while one psi equals approximately 6 894.757 Pa. These conversions ensure compatibility across disciplines, with the following table summarizing key relations:| Unit | Symbol | Value in Pascals (Pa) |
|---|---|---|
| Atmosphere | atm | 101 325 (exact) |
| Bar | bar | 100 000 (exact) |
| Torr | Torr | 101 325 / 760 ≈ 133.322 |
| Pound per square inch | psi | 6 894.757 |
P_{\text{gauge}} = P_{\text{absolute}} - P_{\text{atm}}
where P_{\text{atm}} is typically around 101 325 Pa at sea level; this relation accounts for environmental variations in applications like tire inflation or hydraulic systems.[23]