Physics Library
 An open source physics library
Encyclopedia | Forums | Docs | Random | Template Test |  
Login
create new user
Username:
Password:
forget your password?
Main Menu
Sections

Talkback

Downloads

Information
Reynolds' transport theorem (Theorem)

Let $F(\mathbf{r},t)$ represent the amount of some physical property of a continuous material medium per unit volume. The total amount of this property present in a finite region ${\cal V}$ of the material is obtained through the volume integral.

$\displaystyle \int_{\cal V} F(\mathbf{r},t) \;dV $

If this property is being transported by the action of the flow of the material with a velocity $\mathbf{u}(\mathbf{r},t)$, then Reynolds' transport theorem states that the rate of change of the total amount of $F$ within the material volume is equal to the volume integral of the instantaneous changes of $F$ occuring within the volume, plus the surface integral of the rate at which $F$ is being transported through the surface ${\cal S}$ (bounding ${\cal V}$) to and from the surrounding region.

$\displaystyle \frac{d}{d t} \int_{\cal V} F(\mathbf{r},t) \;dV = \int_{\cal V} ... ...\partial F}{\partial t} \;dV + \int_{\cal S} F\mathbf{u} \cdot \mathbf{n} \;dS $
Here, $\mathbf{n}$ is a unit vector indicating the normal direction of the surface (oriented to point out of the volume).



"Reynolds' transport theorem" is owned by PhysBrain.

View style:


Cross-references: unit vector, velocity, volume

This is version 4 of Reynolds' transport theorem, born on 2006-07-05, modified 2007-07-08.
Object id is 193, canonical name is ReynoldsTransportTheorem.
Accessed 3225 times total.

Classification:
Physics Classification: 51.10.+y (Kinetic and transport theory of gases )
 47.10.+g (General theory )
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:

No messages.

Testing some escape charachters for html category with a generator has an injective cogenerator" now escape ” with "