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**Expansion 1D Euler Eq.??**

Trying to figure out an expansion step for 1D Euler Equations for unsteady gas flow.

Continuity:

[itex]\frac{\partial(\rho F)}{\partial t}[/itex]+[itex]\frac{\partial (\rho uF)}{\partial x}[/itex]=0

After Expansion:

[itex]\frac{\partial(\rho)}{\partial t}[/itex]+[itex]\frac{\partial (\rho u)}{\partial x}[/itex]+[itex]\frac{\rho u}{F}\frac{dF}{dx}[/itex]=0

I understand to go from step 1 to step 2, you divide by F; however, for Step 2 where is the third term coming from and what does it mean?

I have the same question for the momentum equation:

Momentum:

[itex]\frac{\partial (\rho uF)}{\partial t}[/itex]+[itex]\frac{\partial (\rho u^{2}+p)F}{\partial x}[/itex]-[itex]p\frac{dF}{dx}[/itex]+[itex]\frac{1}{2}\rho u^{2}f\pi[/itex] D=0

After Expansion:

[itex]\frac{\partial (\rho u)}{\partial t}[/itex]+[itex]\frac{\partial (\rho u^{2}+p)}{\partial x}[/itex]+[itex]\frac{\rho u^{2}}{F}\frac{dF}{dx}[/itex]+[itex]\frac{1}{2}\rho u^{2}f\pi[/itex] D=0

Again, where is the [itex]\frac{\rho u^{2}}{F}\frac{dF}{dx}[/itex] term coming from and what does it mean?