Pumping into a filter—E. Fig. P4.34 shows a centrifugal pump with pressure increase p2 − p1 = a − bQ2 atm, where a and b are known constants, pumping a slurry into a plate-and-frame filter. The filter...

Pumping into a filter—E. Fig. P4.34 shows a centrifugal pump with pressure increase p2 − p1 = a − bQ2 atm, where a and b are known constants, pumping a slurry into a plate-and-frame filter. The filter has a cross-sectional area A cm2, cake permeability κ darcies [(cm/s) cP/(atm/cm)], filtrate viscosity μ cP, and cake-to-filtrate volumetric ratio ε. A total volume V cm3 of filtrate has been passed. The pump inlet and filter exit pressures are equal.

filter. If a = 0.2, b = 10−5, A = 100, κ = 100, μ = 1, ε = 0.1, and V = 104, all in units consistent with the above definitions, calculate the current volumetric flow rate Q cm3/s. Ignore the slight difference between slurry and filtrate.