Question $3(35$ points$).$ Larsen Pharmaceutical company has designed a batch process to create a crystalline API. On the benchtop, the reactor $($also known as a crystallizer$)$ used in successful production has the following properties: an overall tank diameter of $1\mathrm{.}0m,$ a liquid height of $2\mathrm{.}0m,$ and an impeller diameter of $0\mathrm{.}4m.$ You are tasked with scaling the reactor up to a volume of $100m^3.$ The fluid in the crystallizer has the following properties: viscosity of $0\mathrm{.}001P{a}^{**}s$ and density of $1000k\frac{g}{m^3}.($Recall that $Pa=kg{m}^{-1}{s}^{-2})$ The reactor uses a pitched blade turbine to maintain the appropriate suspension of catalysts, which moves at a speed of $18$ revolutions per second.

a$.(5$ points$)$ Determine if we can use the reported $N_P$ for a pitched blade turbine.

b$.(15$ points$)$ Calculate your new, scaled up tank diameter, liquid height, and impeller diameter.

c$.(15$ points$)$ Calculate the speed of the new impeller needed to maintain the turbulent energy dissipation.