Problem $3(30$ points$).$ You need to scale up a batch crystallization of a biologic based on experiments made in a $1L$ crystallizer. The use of a $3cm$ diameter impeller at a speed of $800rpm$ yields good crystallization results. You want to maintain constant the power dissipated per unit volume in a $300L$ crystallizer. Find the impeller diameter and speed needed in the large scale. Assume that the liquid has the properties of water. Also, assume that geometric similarity is achieved when the volume of the vessel is proportional to the cube of the impeller diameter.