A pilot$-$plant reactor, a scale model of a production unit, is of such size that $1g$ charged to the pilot$-$plant reactor is equivalent to $500g$ of the same material charged to the production unit. The production unit is $2m$ in diameter and $2m$ deep and contains a six$-$blade turbine agitator $0\mathrm{.}6m$ in diameter. The optimum agitator speed in the pilotplant reactor is found by experiment to be $330\frac{r}{m}in.$

$10\mathrm{.}1$ What are the significant dimensions of the pilot$-$plant reactor?

$10\mathrm{.}2$ With the same power per unit volume, what speed should the impeller turn in the production unit reactor?

$10\mathrm{.}3$ Estimate the blending times of the pilot$-$plant reactor and production unit reactor.