$5\mathrm{.}4$ If the capillary pressure data given in Problem $5\mathrm{.}3$ was obtained from oil$-$displacing water in a centrifuge $($where $P_c$ is the core inlet pressure and $\frac{?}{\text{b}\text{a}\text{r}}(S{)}_w$ is the average water saturation$),$ calculate the following:

$($a$)$ The core inlet saturation versus the inlet capillary pressure, using Equation $(5\mathrm{.}5\mathrm{.}19).$

$($b$)$ Plot $P_{ci}$ versus $S_i$ and determine the threshold pressure.

$($c$)$ Compute the vertical saturation profile if the water$-$oil contact occurred at $2000m)=(0\mathrm{.}820.$