- #1
pisgirl
- 1
- 0
Hi all!
I have the following slide, and whilst I understand that the original point is "the rate of density, ρ, in each volume element is equal to the mass flux"...i am totally lost on the mathematics! (And I am meant to be teaching this tomorrow). I do not have any information on what the indivudual symbols refer to, I guess A is area and t is time etc. Can anyone understand this:
-∇(ρv)=[itex]\frac{\partial}{\partial t}[/itex](ρd[itex]\tau[/itex]) where d[itex]\tau[/itex]=Adx
-∇.v = [itex]\frac{\partial}{\partial t}[/itex] (Adx)
-[itex]\frac{\partial v}{\partial x}[/itex] Adx = [itex]\frac{\partial}{\partial t}[/itex](Adx)
-[itex]\frac{\partial v}{\partial x}[/itex]=[itex]\frac{1}{A}[/itex] [itex]\frac{\partial A}{\partial T}[/itex]
Unfortunately I am not sure how to even get from line 1 to 2
and how t combine partial with full!
Argh! Thank you in advance!
I have the following slide, and whilst I understand that the original point is "the rate of density, ρ, in each volume element is equal to the mass flux"...i am totally lost on the mathematics! (And I am meant to be teaching this tomorrow). I do not have any information on what the indivudual symbols refer to, I guess A is area and t is time etc. Can anyone understand this:
-∇(ρv)=[itex]\frac{\partial}{\partial t}[/itex](ρd[itex]\tau[/itex]) where d[itex]\tau[/itex]=Adx
-∇.v = [itex]\frac{\partial}{\partial t}[/itex] (Adx)
-[itex]\frac{\partial v}{\partial x}[/itex] Adx = [itex]\frac{\partial}{\partial t}[/itex](Adx)
-[itex]\frac{\partial v}{\partial x}[/itex]=[itex]\frac{1}{A}[/itex] [itex]\frac{\partial A}{\partial T}[/itex]
Unfortunately I am not sure how to even get from line 1 to 2
and how t combine partial with full!
Argh! Thank you in advance!