An aqueous slurry containing particles with the size distribution shown in the following table is fed to a $20 \mathrm{ft}$ diameter settling tank (see, e.g., McCabe et al. (1993) or Perry's Handbook for the definition of mesh sizes):

Tyler Mesh Size	% of Total Solids in Feed
$8 / 10$	5.0
$10 / 14$	12.0
$14 / 20$	26.0
$20 / 28$	32.0
$28 / 35$	21.0
$35 / 48$	4.0

The feed enters near the center of the tank, and the liquid flows upward and overflows at the top of the tank. The solids loading of the feed is $0.5 \mathrm{lb}_{\mathrm{m}}$ of solids per gallon of slurry, and the feed rate is $50,000 \mathrm{gpm}$. What is the total solids concentration and particle size distribution in the overflow? The density of solids is $100 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$. Assume (1) the particles are spherical, (2) the particles in the tank are unhindered, and (3) the feed and overflow have the same properties as water.