In a batch thickener, an aqueous sludge containing $35 %$ by volume of solids $(S G=1.6)$ with an average particle size of $50 \mu \mathrm{m}$ is allowed to settle. The sludge is fed to the settler at a rate of $1000 \mathrm{gpm}$, and the clear liquid overflows the top. Estimate the minimum tank diameter required for this separation.