Q$\mathrm{.}1)(25$ p$)$ Two tanks containing fluids of A and $B$ are separate from each other by a weightless semi$-$cylindrical gate of radius $R$ and length $L.$ If the depths of the fluids in the tanks are as given in the figure, $H_A$ and $H_B$ determine:

a$)$ the required value of air pressure in tank A not to have fluid leakage from tank $B$ to tank $A,$ and

b$)$ plot the pressure distribution diagram on the vertical wall $(1)-(2)$ on the figure given below.