|
|
| Line 1: |
Line 1: |
| {{About|thermodynamics and fluid mechanics|other uses|Compression (disambiguation)}}
| | Eusebio Stanfill is what's indicated on my birth marriage certificate although it is not necessarily quite the name on several other birth certificate. Idaho is our birth fit. I work as an get clerk. As a man what I really like is behaving but I'm thinking through to starting something new. You can find my website here: http://prometeu.net<br><br>my webpage [http://prometeu.net clash of clans cheat] |
| {{Redirect|Incompressible|the property of vector fields|Solenoidal vector field|the topological property|Incompressible surface}}
| |
| {{Thermodynamics|cTopic='''[[Material properties (thermodynamics)|Material properties]]'''}}
| |
| | |
| In [[thermodynamics]] and [[fluid mechanics]], '''compressibility''' is a [[Measure (mathematics)|measure]] of the relative volume change of a [[fluid]] or [[solid]] as a response to a [[pressure]] (or mean [[stress (physics)|stress]]) change.
| |
| | |
| :<math>\beta=-\frac{1}{V}\frac{\partial V}{\partial p}</math>
| |
| | |
| where ''V'' is [[Volume (thermodynamics)|volume]] and ''p'' is [[pressure]].
| |
| | |
| ==Definition==
| |
| | |
| The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is [[adiabatic process|adiabatic]] or [[isothermal]]. Accordingly '''isothermal''' compressibility is defined:
| |
| | |
| :<math>\beta_T=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_T</math>
| |
| | |
| where the subscript ''T'' indicates that the partial differential is to be taken at constant temperature
| |
| | |
| '''Isentropic''' compressibility is defined:
| |
| | |
| :<math>\beta_S=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_S</math>
| |
| | |
| where ''S'' is entropy. For a solid, the distinction between the two is usually negligible.
| |
| | |
| ===Relation to speed of sound===
| |
| | |
| | |
| Because the [[speed of sound]] is defined in [[classical mechanics]] as:
| |
| | |
| :<math>c^2=\left(\frac{\partial p}{\partial\rho}\right)_S</math>
| |
| | |
| Where <math>\rho</math> is the density of the material. It is therefore found, through methods of replacing partial derivatives, that the isentropic compressibility can be expressed as:
| |
| | |
| :<math>\beta_S=\frac{1}{\rho c^2}</math>
| |
| | |
| ===Relation to bulk modulus===
| |
| | |
| | |
| 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 [[compressibility equation]] relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid.
| |
| | |
| ==Thermodynamics==
| |
| | |
| {{main|Compressibility factor}}
| |
| 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
| |
| | |
| : <math>Z=\frac{p \underline{V}}{R T}</math>
| |
| where ''p'' is the [[pressure]] of the gas, ''T'' is its [[temperature]], and <math>\underline{V}</math> 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:
| |
| | |
| : <math>p = {RT\over{\underline{V}}}</math>
| |
| | |
| ''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 (thermodynamics)|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.
| |
| | |
| A related situation occurs in hypersonic aerodynamics, where dissociation causes an increase in the “notational” molar volume, because a mole of oxygen, as O<sub>2</sub>, becomes 2 moles of monatomic oxygen and N<sub>2</sub> similarly dissociates to 2N. Since this occurs dynamically as air flows over the aerospace object, it is convenient to alter ''Z'', defined for an initial 30 gram mole of air, rather than track the varying mean molecular weight, millisecond by millisecond. This pressure dependent transition occurs for atmospheric oxygen in the 2500 K to 4000 K temperature range, and in the 5000 K to 10,000 K range for nitrogen.<ref>{{cite book|isbn=1-56347-048-9|last=Regan|first= Frank J.|title=Dynamics of Atmospheric Re-entry|page= 313}}</ref>
| |
| | |
| In transition regions, where this pressure dependent dissociation is incomplete, both beta (the volume/pressure differential ratio) and the differential, constant pressure heat capacity will greatly increase.
| |
| | |
| For moderate pressures, above 10,000 K the gas further dissociates into free electrons and ions. ''Z'' for the resulting plasma can similarly be computed for a mole of initial air, producing values between 2 and 4 for partially or singly ionized gas. Each dissociation absorbs a great deal of energy in a reversible process and this greatly reduces the thermodynamic temperature of hypersonic gas decelerated near the aerospace object. Ions or free radicals transported to the object surface by diffusion may release this extra (non-thermal) energy if the surface catalyzes the slower recombination process.
| |
| | |
| The [[isothermal]] compressibility is related to the [[isentropic]] (or [[adiabatic]]) compressibility by the relation,
| |
| | |
| : <math>\beta_S = \beta_T - \frac{\alpha^2 T}{\rho c_p} </math> | |
| | |
| via [[Maxwell's relations]]. More simply stated,
| |
| | |
| : <math>\frac{\beta_T}{\beta_S} = \gamma</math>
| |
| | |
| where,
| |
| | |
| : <math>\gamma \! </math> is the [[heat capacity ratio]]. [[Relations between specific heats|See here]] for a derivation. | |
| | |
| ==Earth science==
| |
| {| class="wikitable" align="right"
| |
| |+ Vertical, drained compressibilities<ref>{{cite journal |last1=Domenico|first1= P. A. |last2= Mifflin|first2 =M. D. |year=1965 |title=Water from low permeability sediments and land subsidence |journal=Water Resources Research |volume=1 |issue=4 |pages=563–576 |doi=10.1029/WR001i004p00563|bibcode = 1965WRR.....1..563D |osti=5917760 }}</ref>
| |
| |-
| |
| ! Material !! ''β'' (m²/N or Pa<sup>−1</sup>)
| |
| |-
| |
| | Plastic clay || 2{{e|–6}} – 2.6{{e|–7}}
| |
| |-
| |
| | Stiff clay || 2.6{{e|–7}} – 1.3{{e|–7}}
| |
| |-
| |
| | Medium-hard clay || 1.3{{e|–7}} – 6.9{{e|–8}}
| |
| |-
| |
| | Loose sand || 1{{e|–7}} – 5.2{{e|–8}}
| |
| |-
| |
| | Dense sand || 2{{e|–8}} – 1.3{{e|–8}}
| |
| |-
| |
| | Dense, sandy gravel || 1{{e|–8}} – 5.2{{e|–9}}
| |
| |-
| |
| | Rock, fissured || 6.9{{e|–10}} – 3.3{{e|–10}}
| |
| |-
| |
| | Rock, sound || <3.3{{e|–10}}
| |
| |-
| |
| | Water at 25 °C (undrained)<ref>{{cite journal |last1=Fine|first2= F. J. |last2= Millero |year=1973 |title=Compressibility of water as a function of temperature and pressure |volume=59 |issue=10 |pages=5529–5536 |journal=Journal of Chemical Physics |doi=10.1063/1.1679903 |bibcode = 1973JChPh..59.5529F |first1=Rana A. }}</ref> || 4.6{{e|–10}}
| |
| |}
| |
| '''Compressibility''' is used in the [[Earth science]]s 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 [[aquifer]]s. 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 [[subsidence|settlement]].
| |
| | |
| 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 [[Deep foundation|piles]] or other innovative techniques.
| |
| | |
| ==Fluid dynamics==
| |
| {{main|Navier-Stokes equations#Compressible flow of Newtonian fluids}}
| |
| The degree of compressibility of a fluid has strong implications for its dynamics. Most notably, the propagation of sound is dependent on the compressibility of the medium.
| |
| | |
| ===Aeronautical dynamics===
| |
| {{main|Aerodynamics#Design_issues_with_increasing_speed}}
| |
| 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 (500 mph).
| |
| | |
| Many effects are often mentioned in conjunction with the term "compressibility", but regularly have little to do with the compressible nature of air. 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]].
| |
| <!-- Please see the article discussion if you think terms incompressible and compressible should be swapped -->
| |
| | |
| ==Negative compressibility==
| |
| Under very specific conditions the compressibility can be negative.<ref>{{cite journal|doi=10.1002/pssb.200777708|title=Negative compressibility, negative Poisson's ratio, and stability|year=2008|last1=Lakes|first1=Rod|last2=Wojciechowski|first2=K. W.|journal=Physica Status Solidi (b)|volume=245|issue=3|pages=545|bibcode = 2008PSSBR.245..545L }}<br>{{cite journal|doi=10.1002/pssr.200802101|title=Negative compressibility|year=2008|last1=Gatt|first1=Ruben|last2=Grima|first2=Joseph N.|journal=Physica status solidi (RRL) - Rapid Research Letters|volume=2|issue=5|pages=236|bibcode = 2008PSSRR...2..236G }}<br>{{Cite journal|doi=10.1126/science.281.5374.143a|title=Materials with Negative Compressibilities|year=1998|last1=Kornblatt|first1=J. A.|journal=Science|volume=281|issue=5374|pages=143a|bibcode = 1998Sci...281..143K }}<br>{{Cite journal|doi=10.1080/09500830600957340|title=Negative incremental bulk modulus in foams|year=2006|last1=Moore|first1=B.|last2=Jaglinski|first2=T.|last3=Stone|first3=D. S.|last4=Lakes|first4=R. S.|journal=Philosophical Magazine Letters|volume=86|issue=10|pages=651|bibcode = 2006PMagL..86..651M }}</ref>
| |
| | |
| ==See also==
| |
| *[[Poisson ratio]]
| |
| *[[Mach number]]
| |
| *[[Prandtl-Glauert singularity]], associated with supersonic flight.
| |
| *[[Shear strength]]
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| [[Category:Thermodynamics]]
| |
| [[Category:Fluid dynamics]]
| |
| | |
| | |
| [[de:Kompressionsmodul#Kompressibilität]]
| |
Eusebio Stanfill is what's indicated on my birth marriage certificate although it is not necessarily quite the name on several other birth certificate. Idaho is our birth fit. I work as an get clerk. As a man what I really like is behaving but I'm thinking through to starting something new. You can find my website here: http://prometeu.net
my webpage clash of clans cheat