Problem $2(5$ points$)$: An inverted U$-$tube manometer can be used to measure the

differential pressure between two reservoirs as shown in Figure $1$ below. Derive an

expression for the difference in pressure between the two reservoirs. Assuming that the

fluid in both arms is water and the fluid in the upper part is air, determine the pressure

difference $($in units of Pa$)$ between the two reservoirs if $z_1=10\mathrm{.}0in,z_2=5\mathrm{.}0$ in and $z_3=$

$3\mathrm{.}0$ in$.$

Figure $1$: Diagram of a U$-$tube differential pressure manometer.