pressure

pressure

[presh-er]
pressure, in mechanics, ratio of the force acting on a surface to the area of the surface; it is thus distinct from the total force acting on a surface. A force can be applied to and sustained by a single point on a solid. However, a force can only be sustained by the surface of an enclosed fluid, i.e., a liquid or a gas. Thus it is more convenient to describe the forces acting on and within fluids in terms of pressure. Units of pressure are frequently force units divided by area units, e.g., pounds per square inch, dynes per square centimeter, or newtons (N) per square meter.

Pressure of Fluids

A fluid exerts a pressure on all bodies immersed in it. For a fluid at rest the difference in pressure between two points in it depends only upon the density of the fluid and the difference in depth between the two points. For example, a swimmer diving down in a lake can easily observe an increase in pressure with depth. For each meter (foot) increase in depth, the swimmer is subjected to an increase in pressure of 9,810 N per sq m (62.4 lb per sq ft), because water weighs 9,810 N per cu m (62.4 lb per cu ft). Since a liquid is nearly incompressible, its density does not change significantly with increasing depth. Therefore, the increase in pressure is caused solely by the increase in depth.

The variations in pressure of a gas are more complicated. For example, since air has such a low density compared to a liquid, a change in its pressure is only measurable between points that have a great height difference. The air pressure in a typical room is the same everywhere, but it is noticeably lower at the top of a mountain than at sea level. Because air is a gas, it is compressible. Its density decreases with increasing altitude. Thus changes in air pressure depend upon both the variations in the density of air and changes in the altitude at which it is measured. These two factors combine to reduce the air pressure at an altitude of 5,500 m (18,000 ft) to one half its value at sea level. Atmospheric (air) pressure at sea level will support a column of mercury that is about 76 cm (30 in.) high. The exact height varies with the weather. A unit called a standard atmosphere exerts a pressure equivalent to a column of mercury 76 cm high at sea level when the temperature is 0°C;; it is equal to 101,300 N per sq m (14.7 lb per sq in.).

Influences on and Effects of Pressure

Different gas laws relate the pressure of a gas to its volume, its temperature, or both. A rise in pressure affects both the melting point and the boiling point of a substance, raising the melting and boiling points of most substances. In the case of water, however, an increase in pressure lowers its melting point so that the pressure of a skate blade on an ice surface causes the ice below it to be converted to the liquid state (see states of matter; expansion). Bernoulli's principle relates the effect of the velocity of a fluid on the pressure within the fluid.

Buoyancy

A body immersed in a fluid experiences a larger upward pressure on its lower surface than a downward pressure on its upper surface because of the difference in height or depth between the two surfaces; this difference in pressure results in a buoyant force that pushes the body upward (see Archimedes' principle). If the weight of the body is less than the buoyant force, the body will rise; if the weight is greater, the body will sink. The buoyant effect of this pressure may be noted in the rise of balloons or other objects filled with gases, such as hydrogen or helium, that are less dense than air.

Hydraulic Force

According to Pascal's law the pressure exerted on an enclosed fluid is transmitted undiminished throughout the fluid and acts equally in all directions. On the basis of this law, various hydraulic devices are used to multiply a force. For example, a force of 10 N exerted on a piston whose area is 1 sq m and which is inserted into an enclosed chamber filled with water or another fluid transmits a pressure of 10 N per sq m throughout the fluid. If a second piston, at another part of the chamber, has an area of 10 sq m, then this pressure results in a force of 10 N being exerted on each square meter of its area, or 100 N total force.

Tools for Measuring Pressure

The instrument for measuring atmospheric pressure, the barometer, is calibrated to read zero when there is a complete vacuum; the pressure indicated by the instrument is therefore called absolute pressure. The term "pressure gauge" is commonly applied to the other instruments used for measuring pressure. They are manufactured in a great variety of sizes and types and are employed for recording pressures exerted by substances other than air—water, oil, various gases—registering pressures as low as 13.8×103 N per sq m (2 lb per sq in.) or as high as 13.8×107 N per sq m (10 tons per sq in.) and over (as in hydraulic presses). Some pressure gauges are made to carry out special operations, such as the one used on a portable air compressor. In this case, the gauge acts automatically to stop further operation when the pressure has reached a certain point and to start it up again when compression has fallen off to a certain limit.

In general, a gauge consists of a metal tube or diaphragm that becomes distorted when pressure is applied and, by an arrangement of multiplying levers and gears, causes an indicator to register the pressure upon a graduated dial. The Bourdon gauge used to measure steam pressure and vacuum consists essentially of a hollow metal tube closed at one end and bent into a curve, generally elliptic in section. The open end is connected to the boiler. As the pressure inside the tube (from the boiler) increases, the tube tends to straighten out. The closed end is attached to an indicating needle, which registers the extent to which the tube straightens out. For pressure too small to be accurately measured by the Bourdon gauge, the manometer is used. The simplest type of manometer consists of a U tube partially filled with a liquid (i.e., mercury), leaving one end open to the atmosphere and the other end to the source of pressure. If the pressure being measured is greater or less than atmospheric pressure, the liquid in the tube moves accordingly. Pressures up to several million lb per sq in. have been produced in experiments to determine the effect of high pressure on various substances.

Pressure (symbol: '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

Pressure is an effect which occurs when a force is applied on a surface. The symbol of pressure is p (lower case). The upper case P is reserved for power.

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 metre (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 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 and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm2. In US Customary units, it is 14.696 psi.

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.

Presently or formerly popular pressure units include the following:

  • atmosphere
  • manometric units:
    • centimeter, inch, and millimeter of mercury (torr)
    • millimeter, centimeter, meter, inch, and foot of water
  • customary 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)
  • non-SI metric units:
    • bar, decibar, millibar
    • kilogram-force, or kilopond, per square centimetre (technical atmosphere)
    • gram-force and tonne-force (metric ton-force) per square centimetre
    • barye (dyne per square centimetre)
    • kilogram-force and tonne-force per square metre
    • sthene per square metre (pieze)

Examples

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.

Another example is of a common knife. If we try and cut a fruit with the flat side it obviously won't cut. But if we take the thin side, it will cut smoothly. The reason is, the flat side has a greater surface area(less pressure) and so it does not cut the fruit. When we take the thin side, the surface area is reduced and so it cuts the fruit easily and quickly. This is one example of a practical application of Pressure.

The gradient of pressure is called the force density. For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure (also sometimes spelled gage pressure). An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa/32psi", but is actually 220 kPa/32 psi above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa/14.7 psi, the absolute pressure in the tire is therefore about 320 kPa/46.7 psi. In technical work, this is written "a gauge pressure of 220 kPa/32 psi". 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 of 32 psi is sometimes written as "32 psig" and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa, a gas (such as helium) at 200 kPa (gauge) (300 kPa [absolute]) is 50 % more dense than the same gas at 100 kPa (gauge) (200 kPa [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature

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 magnitude but no direction sense 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 (at right angle) to the surface.

A closely related quantity is the stress tensor σ, which relates the vector force F to the vector area A via

mathbf{F}=mathbf{sigma A},

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.

Types

Explosion or deflagration pressures

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures

While pressures are generally positive, there are several situations in which negative pressures 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 an atmospheric pressure of 101 kPa).
  • 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.
  • In the cosmological constant.

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 tube, 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.

Surface pressure

There is a two-dimensional analog of pressure -- the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyle's law, πA = k, at constant temperature.

pi = frac{F}{l}.

Pressure of an ideal gas

In an ideal gas, molecules have no volume and do not interact. Pressure varies linearly with temperature, volume, and quantity according to the ideal gas law,
P=frac{nRT}{V}
where:
n is the number of moles of substance
T is the temperature (in kelvin)
V is the volume (in liters)
R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.

See also

Notes

External links

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