A sludge is clarified in a thickener, which is $50 \mathrm{ft}$ in diameter. The sludge contains $35 %$ solids by volume $(S G=1.8)$ in water, with an average particle size of $25 \mu \mathrm{m}$. The sludge is pumped into the center of the tank, where the solids are allowed to settle and the clarified liquid overflows the top. Estimate the maximum flow rate of the sludge (in gpm) that this thickener can handle. Assume that the solids are uniformly distributed across the tank and that all particle motion is vertical.