- #1
tirrel
- 50
- 0
In the book about fluid-mechanics Landau in the first pages in the isentropic case from
[tex] dw=\frac{dp}{\rho}[/tex]
deduces
[tex] \nabla w=\frac{\nabla p}{\rho}[/tex]
but I can't understand... in its derivation dw and dp are material differential ([tex]dw=w(x+vdt,t+dt)-w(x,t)[/tex]) in my view) so writing it explicitely I was only able to deduce:
[tex](\nabla w-\frac{\nabla p}{\rho})\vec{v}=\partial_t(w-\frac{p}{\rho})[/tex]
but nothing more...
what am I missing?
[tex] dw=\frac{dp}{\rho}[/tex]
deduces
[tex] \nabla w=\frac{\nabla p}{\rho}[/tex]
but I can't understand... in its derivation dw and dp are material differential ([tex]dw=w(x+vdt,t+dt)-w(x,t)[/tex]) in my view) so writing it explicitely I was only able to deduce:
[tex](\nabla w-\frac{\nabla p}{\rho})\vec{v}=\partial_t(w-\frac{p}{\rho})[/tex]
but nothing more...
what am I missing?