Consider a U$-$tube manometer containing mercury which is attached to a pressurized tank containing air, oil, and water. The headspace is $1$ meter thick and contains air at a pressure of $30$ kilopascals $($kPa$).$ The oil layer is $3$ meters thick and the specific gravity of the oil is s$.$g$.$oil $=0\mathrm{.}82.$ The water layer is $2$ meters thick.

a$)$ Determine the pressure at the oil$-$water interface in kilopascals $($ kPa. Be sure to consider the effect of the air pressure in the headspace.

b$)$ Determine the pressure at the bottom of the tank in kPa. Be sure to consider the effects of the air pressure in the headspace and the oil layer.

c$)$ If the dimensions of the bottom of the tank are $4$ meters wide and $4$ meters long, determine the force acting on the bottom of the tank in kilonewtons $($kN$).$

d$)$ Determine the pressure at location $A$ in the manometer in kPa.

e$)$ Find the depth of mercury $y$ in meters in the U$-$tube manometer above location $B($i$.$e$.,$ height $y$ in the U$-$tube manometer$).$ The specific gravity of the mercury is $s.g*Hg=13\mathrm{.}6.$