Pressure

Distribution of pressures on a cylinder that moves at constant speed within an ideal fluid

Scheme; each "element" is represented with a dP force and a dS area

Animation: effect of pressure on the volume of a gas

The pressure (symbol: p or P) is a physical quantity that measures the projection of force in the perpendicular direction by unit area, and serves to characterize how a certain resultant force is applied on a line.

In the International System of Units, pressure is measured in a derived unit called pascal (Pa), which is equivalent to a total force of one newton (N) acting uniformly over an area of one square meter (m²). In the Anglo-Saxon system, pressure is measured in pounds per square inch (pound per square inch or psi), which is equivalent to a total force of one pound acting on an area of one square inch.

Definition

Pressure is the magnitude that relates the force to the surface on which it acts; that is, it is equivalent to the force acting on the surface. When a normal force F is applied uniformly on a flat surface of area A, the pressure P is given as follows:

p=FA{displaystyle p={frac {F}{F}{A}}{,}

In a general case where the force can have any direction and not be uniformly distributed at each point, the pressure is defined as

p=dF→ → AdA⋅ ⋅ n→ → {displaystyle p={frac {d{vec {F}}_{A}}}{da}}}{cdot {vec {n}}}}}}

where n→ → {displaystyle {vec {n}}} is a unitary and normal vector to the surface at the point where the pressure is intended to be measured. The previous definition can also be written as

p=ddA∫ ∫ Sf→ → ⋅ ⋅ n→ → dS{displaystyle p={frac {d}{dA}}{int _{S}{vec {f}}}{cdot {vec {n}}}dS}

Symbol	Name
f→ → {displaystyle {vec {f}}}	Force per surface unit
n→ → {displaystyle {vec {n}}}	Normal vector to surface
A{displaystyle A}	Total area of the surface S

Absolute and relative pressure

In certain applications, pressure is measured not as absolute pressure, but as pressure above atmospheric pressure, called relative pressure, normal pressure, gauge pressure or gauge pressure.

Consequently, absolute pressure is atmospheric pressure (P_a) plus the handmetric pressure (P_m) (press measured with the gauge) Pab=Pa+Pm{displaystyle P_{ab}=P_{a}+P_{m}}}.

Hydrostatic and hydrodynamic pressure

In a moving fluid, the hydrostatic pressure can differ from the so-called hydrodynamic pressure, so it must be specified which of the two is referring to a certain measure of the same hydrostatic pressure.

Pressure of a gas

In the framework of the kinetic theory, the pressure of a gas is explained as the macroscopic result of the forces implied by the collisions of the gas molecules with the walls of the container. Pressure can therefore be defined by referring to the microscopic properties of the gas:

For an ideal gas with (N) molecules, each of mass (m) and moving with an average random velocity (u_rms) contained in a cubic volume (V), the gas particles impact the walls of the container in a manner that can be calculated statistically by exchanging momentum with the walls at each impact and exerting a net force per unit area which is the pressure exerted by the gas on the solid surface.

The pressure can then be calculated as

p=Nmurms23V{displaystyle p={N,m{u_{rms}}{2} over 3V}}}(ideal gas)

This result is interesting and significant, not only because it offers a way to calculate the pressure of a gas, but also because it relates an observable macroscopic variable, the pressure, with the average kinetic energy per molecule, 1/2 mu_rms², which is a microscopic quantity not directly observable. Note that the product of the pressure times the volume of the container is two-thirds of the total kinetic energy of the gas molecules contained.

Properties of pressure in a fluid medium

Memometer

1. The pressure-associated force in an ordinary fluid at rest is always directed towards the outside of the fluid, so because of the principle of action and reaction, it results in a compression for the fluid, never a traction.
2. The free surface of a resting liquid (and located in a constant gravitational field) is always horizontal. That is true only on the surface of the Earth and at first sight, due to the action of constant gravity. If there are no gravitational actions, the surface of a fluid is spherical and therefore not horizontal.
3. In the fluids at rest, any point of a liquid mass is subject to pressure that is function only of the depth to which the point is found. Another point at the same depth will have the same pressure. To the imaginary surface that passes through both points is called a surface of pressure or isopathic surface.

Applications

Hydraulic brakes

Many cars have anti-lock braking systems (ABS) to prevent the frictional force of the brakes from locking up the wheels, causing the car to skid. In an anti-lock braking system, a sensor monitors the rotation of the car's wheels when the brakes come on. If a wheel is about to lock up, the sensors detect that the rotation speed is dropping sharply, and they decrease the brake pressure for an instant to prevent it from locking up. Compared to traditional braking systems, anti-lock braking systems allow the driver to control the car more effectively in these situations, especially if the road is wet or covered with snow.

Cooling

Refrigeration is based on the alternate application of high and low pressure, making a fluid circulate at times of pressure through a pipe. When the fluid goes from high to low pressure in the evaporator, the fluid cools and removes heat within the cooler.

The fluid is in a closed circuit, the one that begins in the compressor. It is there where the refrigerant fluid, in a gaseous state, is compressed at high pressure and high temperature; then, through a pipe, it is sent to the condenser where, maintaining the pressure, it will be cooled in such a way that it will pass from a gaseous state to a liquid one. Once this process is finished, the liquid fluid will be directed through another pipe to the evaporator, where through a throttling valve —which can be a capillary pipe, a thermostatic expansion valve (TEV) or another— after which it is "releases" the liquid to a low pressure environment (such as the evaporator), producing the violent evaporation of the liquid for which the necessary heat is transferred, generating the "cooling" of the environment located around the pipe and consequently of the products to be refrigerated. The gas then returns to the compressor through the return line (piping), completing the compression refrigeration circuit.

Car tires

Inflates to a pressure of 206,842 Pa, which is equivalent to 30 psi (using psi as the unit of pressure relative to atmospheric pressure). This is done so that the tires have elasticity in the face of strong blows (very frequent when driving in the car). The air is locked at higher pressure than atmospheric inside the chambers (approximately 2 times higher), and in the most modern tires between the flexible rubber cover and the rim, which is made of rigid metal.

Pressure exerted by liquids

The pressure that originates in the free surface of the liquids contained in capillary tubes, or in liquid drops is called capillary pressure of these

It occurs due to surface tension. In a drop it is inversely proportional to its radius, reaching considerable values.

For example, in a drop of mercury one ten thousandth of a millimeter in diameter there is a capillary pressure of 100 atmospheres. The hydrostatic pressure corresponds to the quotient between the normal force (F) that acts, within a fluid, on a face of a body and that is independent of its orientation.

It depends solely on the depth at which the considered element is located. That of a vapor, which is in dynamic equilibrium with a solid or liquid at any temperature and which depends solely on said temperature and not on the volume, is designated by the name of vapor pressure or saturation.

Units of measurement, pressure and their conversion factors

The mean atmospheric pressure is 101,325 pascals (101.3 kPa) at sea level, where 1 atm = 1.01325 bar = 101,325 Pa = 1.033 kgf/cm² and 1 mca = 9.81 kPa.

The obsolete gauge units of pressure, such as the millimeter of mercury (still used in medicine), are based on the pressure exerted by the weight of some reference fluid under a certain standard gravity. Millimeters of water column are also used.