A rotary vacuum filter with 20% submergence and 250-ft area is used to concentrate a fermentation broth from 5% solids in the feed to 25% solids in the cake. Determine the rotational speed required to produce a 50 gpm (3.15 L/sec) of filtrate under a vacuum of 500 mm Hg (66.7 kN/m2). The resistance of the filter cake is 1.3 x 1011 m/kg and the resistance of the filter medium is negligible. Assume that the specific gravity of the feed is 1.03 g/cm, the filtrate is essentially made of water, and the solids capture by the filter approaches 100%.