- #1
lostidentity
- 18
- 0
I'm trying to find the volume and surface area of a 1-D dimensional sphere, i.e. retaining only the radial dependence.
I know that the volume element for a 3-D sphere would be
[tex]dV = r^2\sin\theta{d}\theta{d}\phi{d}r[/tex]
If it's one-dimensional would it just be [tex] dV = r^2{d}r[/tex]? Or would it just be [tex]dr[/tex]?
With regards to the surface area vector in 3-D it is
[tex]d\boldsymbol{A} = r^2\sin\theta{d}\theta{d}\phi\hat{\boldsymbol{e}_r}[/tex]
so in 1-D would it be
[tex]d\boldsymbol{A} = r^2\hat{\boldsymbol{e}_r}[/tex] or would it just be [tex]\hat{\boldsymbol{e}_r}[/tex]?
Essentially what I'm trying to do is a Finite Volume Method for a 1-D sphere and I want to find the surface area vectors, and volume for my Finite Volume Cells.
I know that the volume element for a 3-D sphere would be
[tex]dV = r^2\sin\theta{d}\theta{d}\phi{d}r[/tex]
If it's one-dimensional would it just be [tex] dV = r^2{d}r[/tex]? Or would it just be [tex]dr[/tex]?
With regards to the surface area vector in 3-D it is
[tex]d\boldsymbol{A} = r^2\sin\theta{d}\theta{d}\phi\hat{\boldsymbol{e}_r}[/tex]
so in 1-D would it be
[tex]d\boldsymbol{A} = r^2\hat{\boldsymbol{e}_r}[/tex] or would it just be [tex]\hat{\boldsymbol{e}_r}[/tex]?
Essentially what I'm trying to do is a Finite Volume Method for a 1-D sphere and I want to find the surface area vectors, and volume for my Finite Volume Cells.