equations:continuity_equation
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
equations:continuity_equation [2018/04/19 10:07] jakobadmin [Concrete] |
equations:continuity_equation [2020/03/03 10:38] (current) 128.179.254.165 |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | <WRAP lag> $\color{blue}{\frac{\partial \rho}{\partial t}} + \color{magenta}{\rho \vec \nabla \vec v} = \color{red}{\sigma} $</WRAP> | + | <WRAP lag> $\color{blue}{\frac{\partial \rho}{\partial t}} = \color{red}{\sigma} - \color{magenta}{\rho \vec{\nabla} \cdot \vec{v}} $</WRAP> |
| ====== Continuity Equation ====== | ====== Continuity Equation ====== | ||
| Line 5: | Line 5: | ||
| <tabbox Intuitive> | <tabbox Intuitive> | ||
| - | The continuity equation states that the $\color{red}{\text{total amount of a quantity (like water) that is produced (or destroyed) inside some volume}}$ is proportional to the $\color{blue}{\text{change of the quantity}}$ plus the $\color{magenta}{\text{total amount that flows in minus the amount that flows out of the volume}}$. | + | The continuity equation states that the total $\color{blue}{\text{change of some quantity}}$ is equal to the $\color{red}{\text{amount that gets produced}}$ minus the amount that $\color{magenta}{\text{flows out of the volume}}$. |
| - | + | ||
| - | Or formulated differently, the total $\color{blue}{\text{change of some quantity}}$ is equal to the $\color{red}{\text{amount that gets produced}}$ plus the amount that $\color{magenta}{\text{flows in minus the amount that flows out of the volume}}$. | + | |
| [{{ :equations:venturi.gif?nolink |Image by Thierry Dugnolle}}] | [{{ :equations:venturi.gif?nolink |Image by Thierry Dugnolle}}] | ||
| Line 41: | Line 39: | ||
| $$ \nabla \cdot J + \frac { \partial ( \nabla \cdot D ) } { \partial t } = 0. | $$ \nabla \cdot J + \frac { \partial ( \nabla \cdot D ) } { \partial t } = 0. | ||
| $$ | $$ | ||
| - | Finally, we use another [[equations:maxwell_equations|Maxwell equation]], namely [[equations:yang_mills_equations:gauss_law|Gauss law]], | + | Finally, we use another [[equations:maxwell_equations|Maxwell equation]], namely [[formulas:gauss_law|Gauss law]], |
| $$\nabla \cdot D = \rho | $$\nabla \cdot D = \rho | ||
| $$ | $$ | ||
| Line 101: | Line 99: | ||
| where $S$ denotes the surface of our volume $V$. This is the integral form of the continuity equation. | where $S$ denotes the surface of our volume $V$. This is the integral form of the continuity equation. | ||
| - | * The first term simply describes the total amount of the quantity, e.g. electric charge or mass, inside our volume. The second term describes the amount that flows into the surface minus the amount that flows out of the surface. | + | * The first term simply describes the total amount of the quantity, e.g. electric charge or mass, inside our volume. |
| + | * The second term describes the amount that flows into the surface minus the amount that flows out of the surface. | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
equations/continuity_equation.1524125262.txt.gz · Last modified: 2018/04/19 08:07 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
