You must determine the maximum feed rate that a thickener can handle to concentrate a waste suspension from $5 %$ solids by volume to $40 %$ solids by volume. The thickener has a diameter of $40 \mathrm{ft}$. A batch flux test in the laboratory for the settled height versus time was analyzed to give the following data for the solids flux versus solids volume fraction. Determine (a) the proper feed rate of liquid in gpm, (b) the overflow liquid rate in gpm, and (c) the underflow liquid rate in gpm.

$\boldsymbol{\varphi}$ (Solids Volume Fraction)	Solids Flux $\left(\mathbf{f t}^{3} / \mathbf{h} \mathbf{f t}^{2}\right)$
0.03	0.15
0.05	0.38
0.075	0.46
0.10	0.40
0.13	0.33
0.15	0.31
0.20	0.38
0.25	0.60
0.30	0.80