In an auxiliary ventilation system, a fan is installed inside a 100 m long and 600 mm diameter duct to ventilate a blind heading face. The frictional coefficient of the duct is 0.0066 $\text{Ns}^2\text{m}^{-4}$ and the static pressure characteristic of the fan is represented by:

where, $P_s$ is in Pa and Q is in $\text{m}^3/\text{s}$. The quantity of air delivered by the fan in $\text{m}^3/\text{s}$ is ______.