- #1
c0der
- 54
- 0
From the Eulerian form of the continuity equation, where x is the Eulerian coordinate:
[itex] \frac {\partial \rho}{ \partial t } + u \frac {\partial \rho}{\partial x} + \rho \frac { \partial u}{\partial x} = 0[/itex]
The incremental change in mass is, where m is the Lagrangian coordinate:
[itex] dm = \rho dx[/itex]
The specific volume is:
[itex] V = \frac{1}{\rho}[/itex]
How does one get the final form of the continuity equation in Lagrangian coordinates as follows:
[itex]\frac{\partial V}{\partial t} = \frac{\partial u}{\partial m} [/itex]
[itex] \frac {\partial \rho}{ \partial t } + u \frac {\partial \rho}{\partial x} + \rho \frac { \partial u}{\partial x} = 0[/itex]
The incremental change in mass is, where m is the Lagrangian coordinate:
[itex] dm = \rho dx[/itex]
The specific volume is:
[itex] V = \frac{1}{\rho}[/itex]
How does one get the final form of the continuity equation in Lagrangian coordinates as follows:
[itex]\frac{\partial V}{\partial t} = \frac{\partial u}{\partial m} [/itex]