Consider Example $13\mathrm{.}18.$ Suppose in a second case, $1\mathrm{.}20$ L of saline solution, with a density of $1020$ kg$/$m$3$ and a viscosity of $1\mathrm{.}10$ x $10-3$ Pa$.$s$,$ is to be infused into a patient in $10\mathrm{.}5$ hr$.$ The catheter is $35\mathrm{.}0$ mm long and has an inner diameter of $0\mathrm{.}320$ mm$.$ The gauge pressure in the the patient's vein is $12$ mm Hg$.$

What is the gauge pressure in the patient's arm in Pa$?$