Crystallization is a process where solid particles of specified size and shape are formed from a homogeneous phase. It may also consider as a solid$-$liquid separation process in which mass transfer of a solute occurs from the liquid to the solid phase. It is desired to scale up a batch crystallization of an antibiotic based on experiments with a $1$ liter crystallizer. The use of a $3cm$ diameter impeller at a speed of $800rpm$ led to good crystallization results. For maintaining power per volume constant upon scale up to $300$ liters, calculate the value at large scale of:

i$.$ the impeller diameter

ii$.$ the speed

$*$The solvent has the same density and viscosity as water