Pressure

The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra.

Pressure (symbol: "p") is the force applied to a surface (in a direction perpendicular to that surface) per unit area of the surface. If the force is concentrated on a small area, it will exert higher pressure than if the same force is distributed over a larger surface area. For example, a force applied with a finger may be able to push a thumbtack into a wall, but the same finger pressing directly against the wall (with the same force) may not make any lasting impression. This is because the thumbtack concentrates the force into a smaller area. Our understanding of the concept of pressure has proven advantageous in many ways. For example, we have been able analyze weather patterns, move fluids using pumps, and sterilize medical equipment at temperatures above the boiling point of water.

Mathematical formula

The mathematical formula for pressure can be expressed as:

$p={\frac {F}{A}}\,$

where:

$p$ is the pressure

$F$ is the normal force

$A$ is the area.

Pressure is a scalar quantity, and its SI unit is called a pascal (Pa), where 1 Pa = 1 Newton per square meter (N/m²). [Also equivalent to 1 J·m⁻³ ≡ 1 kg·m⁻¹·s⁻²]

Pressure is transmitted to solid boundaries or across arbitrary sections of fluid perpendicular to these boundaries or sections at every point.

Conjugate variables of thermodynamics
Pressure	Volume
Temperature	Entropy
Chem. potential	Particle no.

Hydrostatic pressure (Head pressure)

Hydrostatic pressure is the pressure resulting from the weight of a fluid.

$p=\rho gh\,$

where:

• ρ (rho) is the density of the fluid (for example, the practical density of freshwater 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 (in meters or feet).

Kinetic nature of pressure

In 1738, Swiss physician and mathematician Daniel Bernoulli (1700-1782) published Hydrodynamica, which laid the basis for the kinetic theory of gases. In this work, Bernoulli made the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, and that their impact on a surface causes the gas pressure that we feel. In addition, he proposed that what we experience as heat is simply the kinetic energy of their motion.

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. For example, if the air pressure in an automobile tire is given as "220 kPa", it is actually 220 kPa above atmospheric pressure. Given that 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 as "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 (pounds per square inch gauge)", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.

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.

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.

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

The name for the unit of pressure, the (Pascal), was added in 1971; before that, pressure in SI was expressed only using its units (N·m^-2).

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).

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 = 101,325 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) (symbol: at) is 1 kgf/cm²..
  • 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).

See also

• Atmospheric pressure
• Blood pressure
• Kinetic theory Pressure
• Combined gas law
• Conversion of units
• Ideal gas law
• Partial pressure
• Vacuum
• Boyle's Law

References

ISBN links support NWE through referral fees

• Young, Hugh D, and Freedman, Roger A. 2003. Physics for Scientists and Engineers 11th ed. San Fransisco, CA: Pearson. ISBN 080538684X
• Nave, Carl R. 2007 "Pressure" Hyperphysics Retrieved April 1, 2007.

External links

• Link to Hyperphysics
• Pressure being a scalar quantity
• Atmospheric pressure
• An exercise in air pressure

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