An agitated vessel $($diameter $=2\mathrm{.}5m)$ is filled with an aqueous solution of $70\%$NaOH at

$80C($viscosity $=0\mathrm{.}12N*\frac{s}{m^2}$ and density $=1500k\frac{g}{m^3})$ at a depth of $2m.$ To agitate the

solution an impeller with rotation speed of $200rpm$ is installed in the middle of the vessel.

There are two options of impeller to be considered and the details are presented in Table $1.$

Table $1$ Impeller type and details.

a$)$ Determine the power required to run this agitated vessel using each impeller.