The filter of Prob. 29.7 is washed at 70F and 70 lb /in. 2 with a

The filter of Prob. 29.7 is washed at 70°F and 70 lb_ƒ/in.² with a volume of wash water equal to one-third that of the filtrate. The washing rate is 85 percent of the theoretical value. How long should it take to wash the cake?

Prob. 29.7

The following relation between α and Δp for superlight CaCO₃ has been determined to be 

a = 8.8 x 10¹⁰ [1 + 3.36 x 10^-4 (Δp)^0.86]

where Δp is in pounds force per square foot. This relation is followed over a pressure range from 0 to 1,000 lb_ƒ/in.². A slurry of this material giving 3.0 lb of cake solid per cubic foot of filtrate is to be filtered at a constant pressure drop of 70 lb_ƒ/in.² and a temperature of 70°F. Experiments on this sludge and the filter cloth to be used gave a value of R_∞ = 1.2 x 10¹⁰ ft^-1. A pressure filter of the tank type is to be used. How many square feet of filter surface are needed to give 1,400 gal of filtrate in a 1-h filtration? The viscosity is that of water at 70°F.