else could perform all necessary calculauons

$34.$ Pumping into a filter$-$E$.$ Fig. P$4\mathrm{.}34$ shows a centrifugal pump with pressure increase $p_2-p_1=a-b{Q}^2$atm, where a and $b$ are known constants, pumping a slurry into a plate$-$and$-$frame filter. The filter has a cross$-$sectional area $Ac{m}^2,$ cake permeability $$ darcies $(c\frac{m}{s})c\frac{P}{at\frac{m}{c}m},$ filtrate viscosity $cP,$ and cake$-$to$-$filtrate volumetric ratio $.$ A total volume $Vc{m}^3$ of filtrate has been passed. The pumn inlet and filter exit pressures are equal.

If $a=0\mathrm{.}2,b={10}^{-5},A=100,=100,=1,=0\mathrm{.}1,$ and $V={10}^4,$ all in units consistent with the above definitions, calculate the current volumetric flow rate $Qc\frac{m^3}{s}.$ Ignore the slight difference between slurry and filtrate volumes.

Answer is $100$cc$/$s