Pressure
Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface. Mathematically:
Pressure is transmitted to solid boundaries or across arbitrary sections of fluid perpendicular to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume.
| Conjugate variables of thermodynamics | |
|---|---|
| Pressure | Volume |
| Temperature | Entropy |
| Chem. potential | Particle no. |
Example
As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity.
The gradient of pressure is called the force density.
Relative or gauge pressure
For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are sometimes called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa", but is actually 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa, the absolute pressure in the tire is therefore about 320 kPa. In technical work, this is written "a gauge pressure of 220 kPa". Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted. In non-SI technical work, a gauge pressure is sometimes written as "32 psig", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred [1].
Scalar nature of pressure
In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.
A closely related quantity is the stress tensor σ which relates the vector force F to the vector area A via
This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.
Kinetic nature of pressure
In 1738, Swiss physician and mathematician Daniel Bernoulli published Hydrodynamica which laid the basis for the kinetic theory of gases. In this work, Bernoulli positioned the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, and that what we experience as heat is simply the kinetic energy of their motion.
Negative pressures
While pressures are generally positive, there are several situations in which a negative pressure may be encountered:
- When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of -21 kPa (i.e. 21 kPa below atmospheric pressure).
- When attractive forces (e.g. Van der Waals forces) between the particles of a fluid exceed repulsive forces. Such scenarios are generally unstable since the particles will move closer together until repulsive forces balance attractive forces. Negative pressure exists in the transpiration pull of plants.
- The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed 'vacuum pressure' (not to be confused with the negative gauge pressure of a vacuum).
- Depending on how the orientation of a surface is chosen, the same distribution of forces may be described either as a positive pressure along one surface normal, or as a negative pressure acting along the opposite surface normal.
Hydrostatic pressure (Head pressure)
Hydrostatic pressure is the pressure due to the weight of a fluid.
- where:
- ρ (rho) is the density of the fluid (i.e. the practical density of fresh water is 1000 kg/m3);
- g is the acceleration due to gravity (approx. 9.81 m/s2 on Earth's surface);
- h is the height of the fluid column (i.e. meters or feet).
See also Pascal's law.
Stagnation pressure
Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the Mach number of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's equation (note: Bernoulli's equation only applies for incompressible flow).
The pressure of a moving fluid can be measured using a Pitot probe, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressure.
Units
Pascal (Pa) |
Bar (bar) |
Technical atmosphere (at) |
Atmosphere (atm) |
Torr (mmHg) |
Pound per square inch (psi) | |
|---|---|---|---|---|---|---|
| 1 Pa | ≡ 1 N/m² | 10−5 | 10.197×10−6 | 9.8692×10−6 | 7.5006×10−3 | 145.04×10−6 |
| 1 bar | 100 000 | ≡ 106 dyn/cm² | 1.0197 | 0.98692 | 750.06 | 14.504 |
| 1 at | 98 066.5 | 0.980665 | ≡ 1 kgf/cm² | 0.96784 | 735.56 | 14.223 |
| 1 atm | 101 325 | 1.01325 | 1.0332 | ≡ 101 325 Pa | 760 | 14.696 |
| 1 Torr | 133.322 | 1.3332×10−3 | 1.3595×10−3 | 1.3158×10−3 | ≡ 1 mmHg | 19.337×10−3 |
| 1 psi | 6,894.76 | 68.948×10−3 | 70.307×10−3 | 68.046×10−3 | 51.715 | ≡ 1 lbf/in² |
Example reading: 1 Pa = 1 N/m² = 10−5 bar = 10.197×10−6 at = 9.8692×10−6 atm ....etc.
Note: mmHg is an abbreviation for millimeters of mercury.
where:
- is the pressure
- is the normal force
- is the area.
The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N·m-2 or kg·m-1·s-2). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N/m².
Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (psi) and the bar.
The cgs unit of pressure is the barye (ba). It is equal to 1 dyn·cm-2.
Pressure is still sometimes expressed in kgf/cm² or grams-force/cm² (sometimes as kg/cm² and g/cm² without properly identifying the force units). But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is expressly forbidden in SI; the unit of force in SI is the newton (N). The technical atmosphere (symbol: at) is 1 kgf/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 practically all other fields, where the hecto prefix is hardly ever used. In Canadian weather reports, the normal unit is kPa. The obsolete unit inch of mercury (inHg, see below) is still sometimes used in the United States.
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 density allows for a shorter column (and so a smaller manometer) to measure a given pressure. The press exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation as above: p = hgρ.
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.
Although no longer favoured in physics, 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. Natural gas pipeline pressures are measured in inches of water, expressed as '"WC' ('Water Column'). Scuba divers often use a manometric rule of thumb: the pressure exerted by ten meters depth of water is approximately equal to one atmosphere.
Non-SI units presently or formerly in use include the following:
- atmosphere.
- manometric units:
- centimeter, inch, and millimeter of mercury (Torr).
- millimeter, centimeter, meter, inch, and foot of water.
- imperial units:
- kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch.
- pound-force, ton-force (short), and ton-force (long) per square foot.
- non-SI metric units:
- bar, millibar.
- kilogram-force, or kilopond, per square centimeter (technical atmosphere).
- gram-force and tonne-force (metric ton-force) per square centimeter.
- barye (dyne per square centimeter).
- kilogram-force and tonne-force per square meter.
- sthene per square meter (pieze).
Biology
In the human body there are several types of pressure receptor. Baroreceptors monitor blood pressure in the carotid arteries, aortic arch and right atrium of the heart. Mechanoreceptors are part of the somatosensory system and are present in the dermis of the skin and in deeper tissues. They respond to different forms of touch and pressure; the main types of mechanoreceptor are Pacinian corpuscles, Meissner's corpuscles, Merkel cells and Ruffini endings.
See also
- Atmospheric pressure
- Blood pressure
- Combined gas law
- Conversion of units
- Units conversion by factor-label
- Ideal gas law
- Kinetic theory#Pressure
- Partial pressure
- Sound pressure (audio)
- Microphone
- Timeline of temperature and pressure measurement technology
- Vacuum
- Boyle's Law
External links
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