A slurry containing 5 g of solids per liter is passed through a filter at a constant flow rate of 50 L/min. The filter has an area of 400 cm^2. The liquid is water with a viscosity of 1 cP and density of 1 kg/L. The solids can be considered spheres with an average diameter of 0.1 mm and density 1.25 kg/Land the cake accumulated on the filter has a void fraction of 0.35.
(a) Assuming that the Blake-Kozeny equation applies, derive an expression to calculate the pressure drop through the cake as a function of time.
(b) If the maximum pressure drop allowed through the filter is 500 kPa, how long can the filter run before it needs cleaning?
(c) What is the thickness of the cake at the end of the cycle?