$(6$ points$)$ What power will be required to mix an aqueous solution of $50\%$NaOH in a baffled tank, $2$ m in diameter? The mixing will be performed in the vertical tank filled to a height of $2$ m by a disk turbine with six flat blades. The turbine is $0\mathrm{.}67$ m in diameter and positioned $0\mathrm{.}67$ m above the bottom of the tank. The turbine blades are $0\mathrm{.}134$ m wide and turn at $90\frac{r}{m}in.$ The solution has a viscosity of $0\mathrm{.}012$ Pa$.$s and a density of $1500k\frac{g}{m^3}.$