During the scaling$-$up of a batch crystallization for a biochemical factory it was observed that virtually identical properties achieved when the test were conducted either at the laboratory scale $(5$ liter$)$ or the plant scale $(8000$ liters$).$ The lab$-$scale crystallizer had an impeller of $6$ cm diameter operating at $800$ rpm$,$ while the plant$-$scale crystallizer had a $40$ cm impeller with a speed of $90$ rpm$.$ What scale$-$up equation can be used to approximately characterize the scale of this crystallization? State which property or properties are assumed to be constant during scale.

Note: You might want to consider water with a density of $1\mathrm{.}0$ g$/$cm$3$ and viscosity of $0\mathrm{.}01$ g$/($cm s$).$