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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℃; it is equal to 101,300 N per sq m (14.7 lb per sq in.).
Influences on and Effects of Pressure
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.
The ratio of force to area. Atmospheric pressure at the surface of Earth is in the vicinity of 15 lbf/in.2 (1.0 × 105 Pa). Pressures in enclosed containers less than this value are spoken of as vacuum pressures; for example, the vacuum pressure inside a cathode-ray tube is 10-8 mmHg, meaning that the pressure is equal to the pressure that would be produced by a column of mercury, with no force acting above it, that is 10-8 mm high. This is absolute pressure measured above zero pressure as a reference level. Inside a steam boiler, the pressure may be 800 lbf/in.2 (5.5 × 106 Pa) or higher. Such pressure, measured above atmospheric pressure as a reference level, is gage pressure, designated psig. See Pressure measurement
pressureThe force per unit surface area at any point in a gas or liquid. The pressure of a gas is proportional to temperature and density: at constant temperature, as the density is increased the pressure increases accordingly. This law of classical physics does not apply to degenerate matter.
a physical quantity characterizing the intensity of normal forces (perpendicular to the surface) with which one body acts on another’s surface (for example, the foundations of a building acting on the ground, a liquid acting on the walls of a vessel, and gas in the cylinder of a motor acting on the piston). If the forces are distributed uniformly over the surface, then the pressure ρ on any part of the surface i s p = F/S, where 5 is the area of the part and F is the sum of the forces applied perpendicular to it. If the distribution of forces is nonuniform, this equality gives the mean pressure on the given small area, whereas at the limit, with S tending toward zero, it gives the pressure at a given point. If the distribution of forces is uniform, the pressure at all points of the surface is the same; if the distribution is nonuniform, the pressure varies from point to point.
For a continuous medium, the concept of pressure at each point in the medium is similarly introduced; it plays an important part in the mechanics of liquids and gases. At any point in a quiescent liquid the pressure in all directions is the same;
|Table 1. Conversion of units of pressure|
|Nlm2||bar||kgflcm2||atm||mm Hg||mm H20|
|1 N/m2(Pascal).................||1||10-5||1.01972 x 10-5;||0.98692 x 10-5||750.06 x 10-5||0.101972|
|1 bar = 106dynes/cm2.................||105||1||1.01972||0.98692||750.06||1.01972 x 104|
|1 kgf/cm2 = 1 at.................||0.980665 x 105||0.980665||1||0.96784||735.56||104|
|1 atm.................||1.01325 x 105||1.01325||1.0332||1||760||1.0332 x 104|
|1 mm Hg (torr).................||133.322||1.33322 x 10-3||1.35951 x 10-3||1.31579 x10--3||1||13.5951|
|1 mm H20.................||9.80665||9.80665 x 10-5;||10-4||9.67841 x 10-5||7.3556 x 10-4||1|
this is true also of moving liquids or gases, if they may be considered ideal (frictionless). In a viscous liquid the value of the mean pressure for three mutually perpendicular directions is taken to be the pressure at a given point.
Pressure plays an important part in physical, chemical, mechanical, and biological phenomena.
S. M. TARG
In a gaseous medium pressure is associated with the transfer of momentum during collisions of thermally moving gas molecules with each other or with the surface of bodies adjacent to the gas. The pressure in gases, which may be called thermal, is proportional to the temperature (the kinetic energy of the particles). In condensed mediums (liquids and solids), unlike gases, in which the mean distances between randomly moving particles are much greater than the size of the particles themselves, interatomic distances are comparable to atomic dimensions and are determined by the equilibrium of interatomic (intermolecular) forces of repulsion and attraction. When atoms approach one another repulsion forces increase, bringing about so-called cold pressure. In condensed mediums the pressure also has a “thermal” component, which is associated with the thermal vibrations of the atoms (nuclei). Given a steady or diminishing volume of a condensed medium, the thermal pressure rises as the temperature increases. At temperatures of about 104 ° K or more, thermal excitation of electrons makes an appreciable contribution to the thermal pressure.
Pressure is measured with manometers, barometers, and vacuometers, as well as with various pressure sensors.
Units of pressure have the dimensions of force divided by area. In the International System of Units, the unit of pressure is the newton per sq m (N/m2); in the Mks system, it is the kilogram-force per sq cm (kgf/cm2). Subsidiary units of pressure also exist—for example, the physical atmosphere (atm), the technical atmosphere (at), the bar, and mm of water and mercury columns (torr), by means of which the pressure measured is compared with the pressure of a column of liquid (water or mercury). (See Table 1.)
In the USA and Great Britain pressure is expressed in pounds-force per square inch (lbf/in.2), poundals per square foot (pdl/ft2), inches of water (in. H20), feet of water (ft H20), and inches of mercury (in. Hg); 1 lbf/in.2 = 6,894.76 N/m2; 1 pdl/ft2 = 1.48816 N/m2; 1 in. H20 = 249.089 N/m2; 1 ft H20 =2,989.07 N/m2; 1 in. Hg = 3,386.39 N/m2.
L. D. LIVSHITS