Incompressible fluid: Difference between revisions
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{{DISPLAYTITLE:incompressible fluid}} | |||
A fluid in which the [[density]] remains constant for [[isothermal]] pressure changes, that is, for which the [[coefficient of compressibility]] is zero.<br/> Expansion and contraction of an incompressible fluid under diabatic heating or cooling is thus allowed for. In the more usual problem of isothermal processes, the fluid may or may not be stratified (have density differences within it), but motion of a [[parcel]] from higher to lower [[pressure]] or vice versa will not change the density of that parcel. Stated mathematically, the density gradient '''∇'''ρ and the [[local derivative]] ∂ρ/∂''t'' may not be zero, but the [[individual derivative]] ''D''ρ/''Dt'' vanishes. By the [[equation of continuity]], it follows that the total [[divergence]] vanishes: <blockquote>[[File:ams2001glos-Ie3.gif|link=|center|ams2001glos-Ie3]]</blockquote> where '''u''' is the [[velocity]] with components ''u'', ''v'', and ''w''. For many purposes in meteorology, the [[atmosphere]] is treated as a [[heterogeneous fluid]] in which only vertical motions show [[compressibility]]. Together with the assumption of [[hydrostatic equilibrium]], this has the effect of eliminating compression waves (including [[sound waves]]).<br/> | A fluid in which the [[density]] remains constant for [[isothermal]] pressure changes, that is, for which the [[coefficient of compressibility]] is zero.<br/> Expansion and contraction of an incompressible fluid under diabatic heating or cooling is thus allowed for. In the more usual problem of isothermal processes, the fluid may or may not be stratified (have density differences within it), but motion of a [[parcel]] from higher to lower [[pressure]] or vice versa will not change the density of that parcel. Stated mathematically, the density gradient '''∇'''ρ and the [[local derivative]] ∂ρ/∂''t'' may not be zero, but the [[individual derivative]] ''D''ρ/''Dt'' vanishes. By the [[equation of continuity]], it follows that the total [[divergence]] vanishes: <blockquote>[[File:ams2001glos-Ie3.gif|link=|center|ams2001glos-Ie3]]</blockquote> where '''u''' is the [[velocity]] with components ''u'', ''v'', and ''w''. For many purposes in meteorology, the [[atmosphere]] is treated as a [[heterogeneous fluid]] in which only vertical motions show [[compressibility]]. Together with the assumption of [[hydrostatic equilibrium]], this has the effect of eliminating compression waves (including [[sound waves]]).<br/> | ||
Latest revision as of 10:31, 19 April 2024
A fluid in which the density remains constant for isothermal pressure changes, that is, for which the coefficient of compressibility is zero.
Expansion and contraction of an incompressible fluid under diabatic heating or cooling is thus allowed for. In the more usual problem of isothermal processes, the fluid may or may not be stratified (have density differences within it), but motion of a parcel from higher to lower pressure or vice versa will not change the density of that parcel. Stated mathematically, the density gradient ∇ρ and the local derivative ∂ρ/∂t may not be zero, but the individual derivative Dρ/Dt vanishes. By the equation of continuity, it follows that the total divergence vanishes:
where u is the velocity with components u, v, and w. For many purposes in meteorology, the atmosphere is treated as a heterogeneous fluid in which only vertical motions show compressibility. Together with the assumption of hydrostatic equilibrium, this has the effect of eliminating compression waves (including sound waves).
fluido incompresible
Es un fluido en el que la densidad permanece constante para los cambios de presión isotérmica, es decir, para el cual el coeficiente de compresibilidad es cero.
De este modo se permite la expansión y contracción de un fluido incompresible bajo calentamiento o enfriamiento diabático. En el problema más habitual de los procesos isotérmicos, el fluido puede o no estar estratificado (tener diferencias de densidad dentro de él), pero el movimiento de una parcela de presión más alta a más baja, o viceversa, no cambiará la densidad de dicha parcela. Dicho matemáticamente, el gradiente de densidad ∇ρ y la derivada local ∂ρ/∂t pueden no ser cero, pero la derivada individual Dρ/Dt desaparece. De la ecuación de continuidad, se deduce que la divergencia total desaparece:
donde u es la velocidad con los componentes u, v y w. Para muchos fines en meteorología, la atmósfera se trata como un fluido heterogéneo en el que solo los movimientos verticales muestran compresibilidad. Junto con la suposición de equilibrio hidrostático, esto tiene el efecto de eliminar las ondas de compresión (incluidas las ondas de sonido).