EngArc - L - Pressure

Pressure

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Pressure is defined as force per unit area. Pressure applies to fluids whereas stress, of the same units, applies to solids.

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The pressure in a fluid at rest at a given point is the same in all directions. Pressure is defined as the normal component of force per unit area. The pressure P at a point in a fluid in equilibrium is the same in all directions. For a viscous fluid in motion, the variation in the state of stress with orientation becomes an important consideration. The unit for pressure in the International System is the force of one newton acting on a square meter area, which is called the pascal (Pa). The pascal is a derived unit:

1 Pa = 1 N/m² = 1 kg/(ms²)

One pascal is the pressure exerted by a layer of water that is 0.1 mm thick at sea level. For high pressures, the standard atmosphere (atm), which is defined as exactly 1.01325 × 10⁵ Pa, is frequently used. By definition, 1 atm = 760 torr (exactly), which is the average barometric pressure at sea level.

Two other units, not part of the International System, continue to be widely used. These are the bar:

1 bar = 10⁵ Pa = 0.1 MPa

and the standard atmosphere, where:

1 atm = 101325 Pa = 14.696 lbf/in²

which is slightly larger than the bar.

Consider a gas contained in a cylinder fitted with a movable piston, as shown. The pressure exerted by the gas on all its boundaries is the same, assuming that the gas is in an equilibrium state. This pressure is fixed by the external force acting on the piston, since there must be a balance of forces for the piston to remain stationary. Thus, the product of the pressure and the movable piston area must be equal to the external force. If the external force is now changed, in either direction, the gas pressure inside must accordingly adjust, with appropriate movement of the piston, to establish a force balance at a new equilibrium state. As another example, if the gas in cylinder is heated by an outside body, which tends to increase the gas pressure, the piston will move insttead, such that the pressure remains equal to whatever value is required by the external force.

The air in Earth's atmosphere is attracted to Earth by gravity and pushes against every surface it touches. The pressure of the atmosphere can crush a metal can if the air is pumped out of the can. The pressure of the atmosphere changes from day to day, usually increasing when the weather is clearing and decreasing when a storm is coming. The pressure of the atmosphere also changes from place to place. It is highest below sea level and lowest on mountaintops for two reasons. The major reason is that the height of the column of air pushing down on an area below sea level is greater than the height of the column of air pushing down on an equal area on a mountaintop. The decrease in the force of gravity as distance from the center of Earth increases is much less important. A barometer may be used to measure the pressure of the atmosphere.

Pressure is the (compression) stress at a point in a static fluid. Next to velocity, its the pressure is the most dynamic variable in fluid mechanics. Differences or gradients in pressure often drive a fluid flow, especially in ducts. In low-speed flows, the actual magnitude of the pressure is often not important, unless it drops so low as to cause vapor bubbles to form in a liquid.

Pressure is defined as a normal force exerted by a fluid per unit area. Pressure is spoken of only when dealing with a gas or liquid. The counterpart of pressure in solids is normal stress. Since pressure is defined as force per unit area, it has the unit of newtons per square meter (N/m²), which is called a pascal (Pa). That is:

1 Pa = 1 N/m²

The pressure unit pascal is too small for pressure encountered in practice. Therefore, its multiples kilopascal (1 kPa = 10³3 Pa) and megapascal (1 MPa = 10⁶ Pa) are commonly used. Three other pressure units commonly used in practice, especially in Europe, are bar, standard atmosphere, and kilogram-force per square centimeter.

Note the pressure units bar, atm, and kgf/cm² are almost equivalent to each other. In the English system, the pressure unit is pound-force per square inch (lbf/in², or psi), and 1 atm = 14.696 psi. The pressure units kgf/cm² and lbf/in² are also denoted by kg/cm² and lb/in², respectively, and they are commonly used in tire gages. It can be shown that 1 kgf/cm² = 14.223 psi.

Pressure is also used for solids as synonymous to normal stress. For example, a 150-pound person with a total foot imprint area of 50 in² exerts a pressure of 150 lbf/50 in² = 3.0 psi on the floor. If the person stands on one foot, the pressure doubles.

Pressure has the same units as stress; commonly used units include 1 Pa (1 N/m²) and 1 lb/in² (1 psi). Also in common use is the atmosphere, abbreviated atm. One atmosphere is the approximate average pressure of the earth's atmosphere at sea level: 1 atmosphere = 1 atm = 1.013×10⁵ Pa = 14.7 lb/in². Pressure is a scalar quantity, not a vector quantity; it has no direction.