$($b$)$ In laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are $0\mathrm{.}05\frac{m^3}{s}$ and $0\mathrm{.}25\frac{m}{s}$ respectively. If the full$-$scale structure $(30$ times bigger$)$ is subjected to a discharge of $270\frac{m^3}{s},$ then find the time scale $($model to full scale$).$

$7+7$