Difference between revisions of "Velocity"

Latest revision as of 18:53, 28 December 2018

high-resolution terminology - matching measurements at high-resolution

Velocity

Description

Velocity, v [m·s^-1], is the speed in a defined spatial direction, and as such velocity is a vector. Velocity is the advancement in distance per unit time,

v ≡ dz ∙ dt^-1 [m·s^-1]

Abbreviation: v [m·s^-1]

Reference: Gnaiger 2018 MiPschool Tromso A2

Communicated by Gnaiger E 2018-10-20

Velocity in diffusion: from particle format to chemical format

When a force acts on a particle X in direction z, it causes an acceleration, thus increasing the velocity of the particle up to a stationary state, when the effect of the force is counteracted by the frictional resistance. At this stationary state, the potential for performing work (erg; exergy) is not any longer conserved in kinetic exergy (acceleration), but is dissipated such that the exergy driving the process is consumed only to maintain the particle at constant velocity. Then the motive particle has an average velocity v in the z direction, relative to any reference velocity, irrespective of its speed following the pattern of Brownian motion. Since v is a vector with information on magnitude and spatial direction, it is written in bold face,

v ≡ dz ∙ dt^-1 [m·s^-1]

Similarly, the motive force, d_mF_NX (units: newton per particle X [N∙x^-1]), is a vector or gradient, taken here as being oriented in the z direction only, interacting with the motive particle X. The velocity at stationary state is proportional to the motive force, with the mobility, u_NX, as the proportionality constant (in the particle or molecular format, N),

v = -u_NX ∙ d_mF_NX [m/s]

For a number of uncharged motive particles or molecules, N_X, diffusing at velocity v, the corresponding flow of diffusion, I_dNX, across a plane perpendicular to the gradient in direction z is,

I_dNX = N_X ∙ v [x∙m∙s^-1]

Subscripts m and d indicate the partial process of vectoral motion or specifically diffusion. Subscript N indicates the particle format, expressing X as a dimensionless number (unit [x]). In contrast, n_X = N_X∙N_A^-1 is the amount of X in motion expressed in the unit mole [mol] (N_A is the Avogadro constant). Then flow in the molar format, n_A, is amount times velocity, replacing particle number N [x] by amount of substance n,

I_dnX = n_X ∙ v [mol∙m∙s^-1]

To simplify symbols, we may drop the subscript n, I_dX ≡ I_dnX, which indicates a molar format, expressing X as amount [mol], compared to the particle format.

MitoPedia concepts: Ergodynamics

@@ Line 1: / Line 1: @@
 {{MitoPedia
-|abbr='''''v'''''
+|abbr='''''v''''' [m·s<sup>-1</sup>]
-|description='''Velocity''', '''''v''''' [m/s], is the [[speed]] in a defined spatial direction, and as such velocity is a vector. Velocity is the [[advancement]] of distance per unit time,
+|description='''Velocity''', '''''v''''' [m·s<sup>-1</sup>], is the [[speed]] in a defined spatial direction, and as such velocity is a [[vector]]. Velocity is the [[advancement]] in distance per unit time,
-  '''''v''''' ≡ d'''''z''''' ∙ d''t''-1 [m/s]
+  '''''v''''' ≡ d'''''z''''' ∙ d''t''<sup>-1</sup> [m·s<sup>-1</sup>]
 |info=[[Gnaiger 2018 MiPschool Tromso A2]]
 }}
+ Communicated by [[Gnaiger E]] 2018-10-20
+== Velocity in diffusion: from particle format to chemical format ==
+:::: When a [[force]] acts on a particle X in direction ''z'', it causes an [[acceleration]], thus increasing the velocity of the particle up to a stationary state, when the effect of the force is counteracted by the frictional resistance. At this stationary state, the potential for performing [[work]] (''erg''; exergy) is not any longer conserved in kinetic exergy (acceleration), but is dissipated such that the exergy driving the process is consumed only to maintain the particle at constant velocity. Then the motive particle has an average velocity '''''v''''' in the ''z'' direction, relative to any reference velocity, irrespective of its speed following the pattern of [[Brownian motion]]. Since '''''v''''' is a vector with information on magnitude and spatial direction, it is written in bold face,
+ '''''v''''' ≡ d'''''z''''' ∙ d''t''<sup>-1</sup> [m·s<sup>-1</sup>]
+:::: Similarly, the motive force, d<sub>'''m'''</sub>''F''<sub><u>''N''</u>X</sub> (units: newton per particle X [N∙x<sup>-1</sup>]), is a vector or gradient, taken here as being oriented in the ''z'' direction only, interacting with the motive particle X. The velocity at stationary state is proportional to the motive force, with the mobility, ''u''<sub><u>''N''</u>X</sub>, as the proportionality constant (in the [[Motive unit |particle or molecular format, <u>''N''</u>]]),
+ '''''v''''' = -''u''<sub><u>''N''</u>X</sub> ∙ d<sub>'''m'''</sub>''F''<sub><u>''N''</u>X</sub> [m/s]
+:::: For a number of uncharged motive particles or molecules, ''N''<sub>X</sub>, diffusing at velocity '''''v''''', the corresponding flow of diffusion, '''''I'''''<sub>'''d'''<u>''N''</u>X</sub>, across a plane perpendicular to the gradient in direction ''z'' is,
+ '''''I'''''<sub>'''d'''<u>''N''</u>X</sub> = ''N''<sub>X</sub> ∙ '''''v''''' [x∙m∙s<sup>-1</sup>]
+:::: Subscripts '''m''' and '''d''' indicate the partial process of vectoral motion or specifically diffusion. Subscript <u>''N''</u> indicates the particle format, expressing X as a dimensionless number (unit [x]). In contrast, ''n''<sub>X</sub> = ''N''<sub>X</sub>∙''N''<sub>A</sub><sup>-1</sup> is the amount of X in motion expressed in the unit mole [mol] (''N''<sub>A</sub> is the [[Avogadro constant]]). Then flow in the molar format, ''n''<sub>A</sub>, is amount times velocity, replacing particle number ''N'' [x] by [[amount of substance]] ''n'',
+ '''''I'''''<sub>'''d'''<u>''n''</u>X</sub> = ''n''<sub>X</sub> ∙ '''''v''''' [mol∙m∙s<sup>-1</sup>]
+:::: To simplify symbols, we may drop the subscript <u>''n''</u>, '''''I'''''<sub>'''d'''X</sub> ≡ '''''I'''''<sub>'''d'''<u>''n''</u>X</sub>, which indicates a molar format, expressing X as amount [mol], compared to the particle format.
 {{MitoPedia concepts
 |mitopedia concept=Ergodynamics
 }}
-{{MitoPedia methods}}
-{{MitoPedia O2k and high-resolution respirometry}}
-{{MitoPedia topics}}
- Communicated by [[Gnaiger E]] 2018-10-20
-== Velocity in diffusion ==
-:::: When a [[force]] acts on a particle X in direction ''z'', it causes an [[acceleration]], thus increasing the velocity of the particle up to a stationary state, when the effect of the force is counteracted by the frictional resistance. At this stationary state, the potential for performing work (erg; exergy) is not any longer conserved in kinetic exergy (acceleration), but is dissipated such that the exergy driving the process is consumed only to maintain the particle at constant velocity. Then the motive particle has an average velocity '''''v''''' in the ''z'' direction, relative to any reference velocity, irrespective of its speed following the pattern of [[Brownian motion]]. Since '''''v''''' is a vector with information on magnitude and spatial direction, it is written in bold face,
- '''''v''''' ≡ d'''''z''''' ∙ d''t''-1 [m/s]
-:::: The velocity at stationary state is proportional to the motive [[force]], with the mobility, ''u''''N''X, as the proportionality constant,
- '''''v''''' = -uNX ∙ dmFNX [m/s]
-:::: For a number of uncharged motive particles or molecules, ''N''X, diffusing at velocity '''''v''''', the corresponding flow of diffusion, '''''I'''''d''N''X, across a plane perpendicular to the gradient in direction ''z'' is,
- IdNX = NX ∙ v [x∙m∙s-1]