In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. The thermodynamic properties of materials are intensive thermodynamic parameters which are specific to a given material. ... Specific heat capacity, also known simply as specific heat (Symbol: C or c) is the measure of the heat energy required to raise the temperature of a given amount of a substance by one degree. ... In physics, thermal expansion is the tendency of matter to increase in volume or pressure when heated. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ... In mathematics, a measure is a function that assigns a number, e. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... For other uses, see Solid (disambiguation). ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ...

where V is volume and p is pressure. The above statement is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal. Accordingly we define the isothermal compressibility as: The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... In thermodynamics, an adiabatic process or an isocaloric process is a process in which no heat is transferred to or from the working fluid. ... An isothermal process is a thermodynamic process in which the temperature of the system stays constant; ΔT = 0. ...

where the subscript T indicates that the partial differential is to be taken at constant temperature. The adiabatic compressibility as:

where S is entropy. For a solid, the distinction between the two is usually negligible.

The inverse of the compressibility is called the bulk modulus, often denoted K (sometimes B). That page also contains some examples for different materials. The bulk modulus (K) of a substance essentially measures the substances resistance to uniform compression. ...

Fluid Dynamics

Compressibility is an important factor in aerodynamics. At low speeds, the compressibility of air is not significant in relation to aircraft design, but as the airflow nears and exceeds the speed of sound, a host of new aerodynamic effects become important in the design of aircraft. These effects, often several of them at a time, made it very difficult for World War II era aircraft to reach speeds much beyond 800 km/h (500mph). This article does not cite any references or sources. ... Look up aircraft in Wiktionary, the free dictionary. ... The speed of sound is a term used to describe the speed of sound waves passing through an elastic medium. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000...

Some of the minor effects include changes to the airflow that lead to problems in control. For instance, the P-38 Lightning had a particular problem in high-speed dives that led to a nose-heavy condition. Pilots would enter dives, and then find that they could no longer control the plane, which continued to nose over until it crashed. Adding a "dive flap" beneath the wing to upset the airflow (and so increasing drag and restraining the terminal velocity) fixed the problem. The Lockheed P-38 Lightning was a World War II American fighter aircraft. ...

A similar problem affected some models of the Supermarine Spitfire. At high speeds the ailerons could apply more torque than the Spitfire's thin wings could handle, and the entire wing would twist in the opposite direction. This meant that the plane would roll in the direction opposite to that which the pilot intended, and led to a number of accidents. Earlier models weren't fast enough for this to be a problem, and so it wasn't noticed until later model Spitfires like the Mk.IX started to appear. This was mitigated by adding considerable torsional rigidity to the wings, and was wholly cured when the Mk.XIV was introduced. The Supermarine Spitfire was an iconic British single-seat fighter used primarily by the RAF and many Allied countries through the Second World War and into the 1950s. ... For the band with a similar name, see The Ailerons Ailerons are hinged control surfaces attached to the trailing edge of the wing of a fixed-wing aircraft. ...

The Messerschmitt Bf 109 and Mitsubishi Zero had the exact opposite problem in which the controls became ineffective. At higher speeds the pilot simply couldn't move the controls because there was too much airflow over the control surfaces. The planes would become difficult to manoeuvre, and at high enough speeds even less manoeuvrable aircraft could out-turn them. German Airfield, France, 1941 propaganda photo of the Luftwaffe, Bf 109 fighters on the tarmac The Messerschmitt Bf 109 was a German World War II fighter aircraft designed by Willy Messerschmitt in the early 1930s. ... Mitsubishi A6M3 Zero wreck abandoned at Munda Airfield, Central Solomons, 1943. ...

Finally, another common problem that fits into this category is flutter. At some speeds the airflow over the control surfaces will become turbulent, and the controls will start to flutter. If the speed of the fluttering is close to a harmonic of the control's movement, the resonance could break the control off completely. This was a serious problem on the Zero. When problems with poor control at high speed were first encountered, they were addressed by designing a new style of control surface with more power. However this introduced a new resonant mode, and a number of planes were lost before this was discovered. Aeroelasticity is the science which studies the interaction among inertial, elastic, and aerodynamic forces. ... In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. ... This article is about resonance in physics. ...

All of these effects are often mentioned in conjunction with the term "compressibility", but in a manner of speaking, they are incorrectly used. From a strictly aerodynamic point of view, the term should refer only to those side-effects arising as a result of the changes in airflow from an incompressible fluid (similar in effect to water) to a compressible fluid (acting as a gas) as the speed of sound is approached. There are two effects in particular, wave drag and critical mach. Wave drag is an aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft flying at high-subsonic speeds. ... Critical mach is a aeronautics term that refers to the speed at which some of the airflow on a wing becomes supersonic. ...

Wave drag is a sudden rise in drag on the aircraft, caused by air building up in front of it. At lower speeds this air has time to "get out of the way", guided by the air in front of it that is in contact with the aircraft. But at the speed of sound this can no longer happen, and the air which was previously following the streamline around the aircraft now hits it directly. The amount of power needed to overcome this effect is considerable. The critical mach is the speed at which some of the air passing over the aircraft's wing becomes supersonic. Solid blue lines and broken grey lines represent the streamlines. ...

At the speed of sound the way that lift is generated changes dramatically, from being dominated by Bernoulli's principle to forces generated by shock waves. Since the air on the top of the wing is traveling faster than on the bottom, due to Bernoulli effect, at speeds close to the speed of sound the air on the top of the wing will be accelerated to supersonic. When this happens the distribution of lift changes dramatically, typically causing a powerful nose-down trim. Since the aircraft normally approached these speeds only in a dive, pilots would report the aircraft attempting to nose over into the ground. Bernoullis Principle states that in an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or gravitational energy. ... Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ...

All of these effects have adverse effects on the control or performance of the plane. For this reason it's common to see references to aircraft that suffer from compressibility. The P-38 and Zero are particularly common examples, although in fact they are both bad ones.

Thermodynamics

The term "compressibility" is also used in thermodynamics to describe the deviance in the thermodynamic properties of a real gas from those expected from an ideal gas. The compressibility factor is defined as Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Here is a partial list of thermodynamic properties of fluids: temperature [K] density [kg/m3] specific heat at constant pressure [J/kg·K] specific heat at constant volume [J/kg·K] dynamic viscosity [N/m²s] kinematic viscosity [m²/s] thermal conductivity [W/m·K] thermal diffusivity [m²/s] volumetric... An ideal gas (also called a perfect gas) is a hypothetical fluid consisting of particles that are identical to each other, occupy negligible volume and undergo perfect elastic collisions with each other, with no intermolecular forces and no intramolecular storage of energy, as opposed to a real gas, a gas... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ...

where p is the pressure of the gas, T is its temperature, and is its molar volume. In the case of an ideal gas, the compressibility factor Z is equal to unity, and the familiar ideal gas law is recovered: The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... Fig. ... In chemistry, the molar volume of a substance is the ratio of the volume of a sample of that substance to the amount of substance (usually in mole) in the sample. ... Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834. ...

Z can, in general, be either greater or less than unity for a real gas.

The deviation from ideal gas behavior tends to become particularly significant (or, equivalently, the compressibility factor strays far from unity) near the critical point, or in the case of high pressure or low temperature. In these cases, a generalized Compressibility chart or an alternative equation of state better suited to the problem must be utilized to produce accurate results. The term critical point can mean any of: critical point (thermodynamics) critical point (mathematics) critical loops (topology) critical point (set theory) This is a disambiguation page: a list of articles associated with the same title. ... In physics and thermodynamics, an equation of state is a constitutive equation describing the state of matter under a given set of physical conditions. ...

Earth sciences

Compressibility is used in the Earth sciences to quantify the ability of a soil or rock to reduce in volume with applied pressure. This concept is important for specific storage, when estimating groundwater reserves in confined aquifers. Geologic materials are made up of two portions: solids and voids (or same as porosity). The void space can be full of liquid or gas. Geologic materials reduces in volume only when the void spaces are reduced, which expel the liquid or gas from the voids. This can happen over a period of time, resulting in settlement. Earth science (also known as geoscience, the geosciences or the Earth Sciences), is an all-embracing term for the sciences related to the planet Earth. ... Specific storage (Ss), storativity (S), specific yield (Sy) and specific capacity are aquifer properties; they are measures of the ability of an aquifer to release groundwater from storage, due to a unit decline in hydraulic head. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0–1, or as a percent between 0–100%. The term porosity is used in multiple fields including manufacturing, earth sciences and construction. ... Timber frame building showing considerable, but tolerable settlement Settlement in construction refers to the distortion or disruption of parts of a building due to either; unequal compression of its foundations, shrinkage such as that which occurs in timber framed buildings as the frame adjusts its moisture content, or by undue...

It is an important concept in geotechnical engineering in the design of certain structural foundations. For example, the construction of high-rise structures over underlying layers of highly compressible bay mud poses a considerable design constraint, and often leads to use of driven piles or other innovative techniques. Bostons Big Dig presented geotechnical challenges in an urban environment. ... High-rise is a 1975 novel by J. G. Ballard. ... Richardson Bay mudflats of are exposed layers of bay mud Bay mud consists of thick deposits of soft, unconsolidated silty clay, which is saturated with water; these soil layers are situated at the bottom of certain estuaries, which are normally in temperate regions that have experienced cyclical glacial cycles. ... Look up Pile in Wiktionary, the free dictionary. ...

References

1. ^ Domenico, P.A. and Mifflin, M.D. (1965). "Water from low permeability sediments and land subsidence". Water Resources Research 1 (4): 563–576. OSTI:5917760. 
2. ^ Fine, R.A. and Millero, F.J. (1973). "Compressibility of water as a function of temperature and pressure". Journal of Chemical Physics 59 (10). DOI:10.1063/1.1679903. 

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See also

• Avogadro's number
• Mach number
• Prandtl-Glauert singularity, associated with supersonic flight.
• Shear strength