$3\mathrm{.}55.$ Three different liquids are used in the manometer shown here.

a$.$ Derive an expression for $P_1-P_2$ in terms of ${}_A,{}_B,{}_C,h_1,$ and $h_2.$

b$.$ Suppose fluid A is methanol, B is water, and $C$ is a manometer fluid with a specific gravity of $1\mathrm{.}37$ ; pressure $P_2=121\mathrm{.}0$kPa; $h_1=30\mathrm{.}0cm$; and $h_2=24\mathrm{.}0cm.$ Calculate $P_1(kPa).$