Determine the surface area of a rotary-drum filter that processes 20 m³/hr of a calcium carbonate slurry at a pressure drop of 0.679 bar with 37.5% submergence, and a drum rotation rate of 0.2 rpm. Pertinent data are: T = 20°C, mass-fraction carbonate in the feed 0.15, mass fraction of water in the filter cake = 0.40, filtrate density 998.3 kg/m³, filtrate viscosity = 1 cP, and dry carbonate density 2,709 kg/m³. Assume the media resistance is negligible. Use Table 19.8 for cake compressibility.

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Table 19.9 Filter-Cake Compressibility Substance Calcium carbonate Kaolin, Hong Kong Solkofloc Talc Titanium dioxide Zinc sulfide a' x 10-¹0, m/kg 1.604 101 0.0024 8.66 32 14 Exponent s 0.2664 0.33 1.01 0.51 0.32 0.69