31 |
$$ |
$$ |
32 |
\phi' = \int^{r_{surf}}_r b~ dr - \int^{R_o}_r b_o dr |
\phi' = \int^{r_{surf}}_r b~ dr - \int^{R_o}_r b_o dr |
33 |
$$ |
$$ |
34 |
\begin{eqnarray} |
and re-write as: |
35 |
\mathrm{and~re~write:}\hspace{10mm} |
\begin{equation} |
36 |
\phi' = \int^{r_{surf}}_{R_o} b~ dr & + & \int^{R_o}_r (b - b_o) dr |
\phi' = \int^{r_{surf}}_{R_o} b~ dr + \int^{R_o}_r (b - b_o) dr |
37 |
\label{eq:split-phi-Ro} \\ |
\label{eq:split-phi-Ro} |
38 |
\mathrm{or:}\hspace{10mm} |
\end{equation} |
39 |
\phi' = \int^{r_{surf}}_{R_o} b_o dr & + & \int^{r_{surf}}_r (b - b_o) dr |
or: |
40 |
|
\begin{equation} |
41 |
|
\phi' = \int^{r_{surf}}_{R_o} b_o dr + \int^{r_{surf}}_r (b - b_o) dr |
42 |
\label{eq:split-phi-bo} |
\label{eq:split-phi-bo} |
43 |
\end{eqnarray} |
\end{equation} |
44 |
|
|
45 |
In section \ref{sec:finding_the_pressure_field}, following eq.\ref{eq:split-phi-Ro}, |
In section \ref{sec:finding_the_pressure_field}, following eq.\ref{eq:split-phi-Ro}, |
46 |
the pressure/geo-potential $\phi'$ has been separated into surface ($\phi_s$), |
the pressure/geo-potential $\phi'$ has been separated into surface ($\phi_s$), |