$1.$ Mechanical design of a cylindrical storage tank You are required to design a cylindrical storage tank with inner diameter $30$ m$,$ height $15$ m to contain a liquid of density $1000$ kg$/$m$.$ The tank is made out of carbon steel whose density is $7850$ kg$/$m$.$ The allowable stress is $165$ N$/$mm$,$ modulus of elasticity is $2$ x $105$ N$/$mm and the corrosion allowance is $1\mathrm{.}5$ mm$.$ Take the joint efficiency as $0\mathrm{.}85$ in your calculations. A$)$ Design the vessel shell considering the hydrostatic forces to act at different heights of the shell. Assume $15$ plates to be arranged in a circle to make the shell cross$-$section with $2$ mm gap between each plate for welding. Choose the appropriate length of the plate from IS$-1370($Refer to Tables $1$ and $2)$ given the plate width to be $2500$ mm$.$ Do not go below a thickness of $8$ mm for the top course. The answers are to be presented as in the following tabulation. Level or height $($m$)$ Plate thickness $($mm$)$ No$.$ of plate layers $(8$ marks$)$ B$)$ The bottom of the storage vessel rests on a uniformly levelled surface. Find the thickness of the bottom plate, sketch plate and the annular plate. $(2$ marks