Water flows from P to Q through two soil samples, Soil $1$, Soil $2$, having cross sectional area of $80 \: cm^2$ as shown in the figure. Over a period of $15$ minutes, $200$ ml of water was observed to pass through any cross-section. The flow-conditions can be assumed to be steady state. If the coefficient of permeability of Soil $1$ is $0.02$ mm/s, the coefficient of permeability of Soil $2$ (expressed in mm/s) would be _________