## Pressure

Glossary Definition for 16-19

## Description

Pressure is a bulk property of fluids (liquids and gases). A fluid exerts a force normal to any surface with which it is in contact. The magnitude of the force on a surface depends on the area of the surface and not on its orientation; at any given position, the magnitude of the force per unit area is constant. Pressure has no defined direction; it is a scalar quantity.

Pressure is usually represented by the symbol *p*.

For a plane surface of area *A*, pressure is defined as

*p* = *F**A*

where *F* is the magnitude of the force the fluid exerts on the surface.

## Discussion

For a body of liquid in which gravity and temperature variations can be ignored, the pressure is nearly the same in all parts of the liquid. This allows a modest force applied over a small area to the liquid to be translated into a much larger force acting over a larger area, which forms the basis for hydraulic systems, for example in the brakes of motor vehicles.

In a gas, the microscopic origin of pressure can be understood in terms of the motion of its molecules. The molecules of the gas move freely, colliding with each other and the walls of the container. When a molecule collides with a wall and bounces off at the same speed, there is a momentum transfer to the wall. To determine the total force on the wall due to the gas, the effect of all the molecules of the gas colliding with the wall is added up. The equivalent pressure depends on the mass of each molecule, m, the number of them per unit volume, *n*, and the average squared speed of the molecules, <*v*^{ 2}> , via the formula p= = 13*n**m*<*v*^{ 2}>.

Note that it is incorrect to use the concept of pressure in describing the forces between two solids; pressure should be strictly reserved for fluids and fluids in contact with solids. When dealing with solids, stress is the relevant quantity.

## SI unit

pascal, Pa

## Expressed in SI base units

kg m^{-1} s^{-2}

## Other commonly used unit(s)

N m^{-2}, (1 N m^{-2} = 1 Pa), bar (1 bar = 10^{5}Pa), mmHg (1 mmHg = 133 Pa), atm (1 atm = 1.103 × 10^{5} Pa), torr (1 torr = 133 Pa), psi (1 psi = 6.9 × 10^{3} Ps)

## Mathematical expressions

*p*=*F**A*

where*F*is the magnitude of the force a fluid exerts on an area*A*
For an ideal gas
*p**V*=*n**R**T*

where*V*is the volume,*n*is the number of moles of gas molecules,*R*is the molar gas constant and*T*is the temperature measured in kelvin

and*p**V*=*N**k**T*where*N*is the number of molecules (numper per unit volume) and*k*is the Boltzmann constant

and*p*= 13*n**m*<*v*^{ 2}>

where*n*is the number of molecules per unit volume,*m*is the average mass of each molecule and <*v*^{ 2}> is the mean speed squared of the molecules- In a column of fluid, the change of pressure Δ
*p*due to an increase of height Δ*h*is

Δ*p*= ρ*g*Δ*h*

where ρ is the density of the fluid and*g*is the gravitational field.

## Related entries

- Stress

## In Context

Close to sea level, the pressure exerted by the Earth’s atmosphere is about 1.01 × 10^{5} Pa.

The world record for free deep-sea diving (without breathing apparatus) is currently (February 2017) held by Herbert Nitsch, who in 2012 reached a depth of 253.2 m, where the pressure is 2.6 × 10^{6} Pa(26 atm).

In the Sun’s interior, where the number density is about 2 × 10^{57} m^{-3} and the temperature about 10^{7}K, the pressure is about 2 × 10^{14} Pa.

In interstellar space, where number densities range from about 10^{5} to about 10^{10} m^{-3}, and temperatures range from about 3 K to 10^{6}K, the pressure varies by only about two orders of magnitude and most regions have pressures of the order 10^{-13}Pa.

## Reference

- www.deeperblue.com/herbert-nitsch-the-deepest-man-on-earth/