Designing a vertical cylindrical gravity settler involves accommodating a fluid mixture with a flow rate of $20$ m$3/$hr$,$ consisting of liquids with densities of $1050$ kg$/$m$3$ and $875$ kg$/$m$3.$ The design specification includes a settling time of $30$ minutes, considering equal fluid entry in the feed and allocating one$-$fifth of the settler for vapor space. For this setup, determine the tank volume, dimensions $($height and diameter$),$ and the height at which the heavy liquid overflows. Assume the tank$\text{'}$s height is $4/5$ of its diameter, and the vessel ends are approximately flat.