Pressure (symbol: $p$ or sometimes $P$) is the force per unit area applied to an object in a direction perpendicular to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.

Definition

Formula

Mathematically:

p = \frac{F}{A}\ \mbox{or}\ p = \frac{dF}{dA}

where:

$p$ is the pressure,

$F$ is the normal force,

$A$ is the area.

Pressure is a scalar quantity, and has SI units of pascals; 1 Pa = 1 N/m², and has EES units of psi; 1 psi = 1 lb/in².

Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume.

Units

The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N·m² or kg/m·s²). This special name for the unit was added in 1971; before that, pressure in SI was expressed simply as N/m².

Non-SI measures such as pound per square inch (psi) and bar are used in parts of the world. The cgs unit of pressure is the barye (ba), equal to 1 dyn·cm^-2. Pressure is sometimes expressed in grams-force/cm², or as kg/cm²

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, where the hecto prefix is rarely used. The unit inch of mercury (inHg, see below) is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because an increase in pressure of 1 dbar is approximately equal to an increase in depth of 1 meter. Scuba divers often use a manometric rule of thumb: the pressure exerted by ten metres depth of water is approximately equal to one atmosphere.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows:

standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., inches of water). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows for a shorter column (and so a smaller manometer) to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimeters of mercury or inches of mercury are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimeters of mercury in most of the world, and lung pressures in centimeters of water are still common.