A slurry containing 1 lb of filterable solids per 10 lb of liquid is being filtered with a plate-and-frame filter press having a total filtering area of 250 ft2. This unit delivers 10,000 lb of filtrate during the first 2 h of filtration, starting with a clean unit and maintaining a constant pressure drop of 10 psi. The resistance of the filter medium is negligible. The time required for washing and dumping is 3 h/cycle. The pressure drop cannot exceed 10 psi, and the unit is always operated at constant pressure drop.
The filter press is to be replaced by a rotary vacuum-drum filter with negligible filter-medium resistance. This rotary filter can deliver the filtrate at a rate of 1000 lb/h when the drum speed is 0.3 r/min. Assuming the fraction submerged and the pressure drop are unchanged, what drum speed in r/min is necessary to make the amount of filtrate delivered in 24 h from the rotary filter exactly equal to the maximum amount of filtrate obtainable per 24 h from the plate-and-frame filter?