Determine the maximum flow rate of water through the horizontal $1-cm$ diameter system shown below, if a maximum pressure drop of $2-$atm is allowable between oulet and inlet. The $0\mathrm{.}5-m$ packed bed has a permeability of $1{10}^{-12}{m}^2.$

a$.$ Neglect viscous losses associated with the wall of the pipe or fittings. $(15$ pts$)$

b$.$ Consider the viscous dissipation due to the $2-m$ plastic tubing walls. Neglect the losses in fittings. $(25$ pts$)$

Additional information: ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1{10}^{-3}$Pas