In a polymerization operation, a liquid mixture $($density$,=165060$ kg$/$m$3,$ viscosity, $=8005$mPa.s$)$ is agitated in a tank by a propeller mixer with a diameter $($D$)$ of $0\mathrm{.}50\mathrm{.}05$ m$.$ You are provided data for the power number $($Np$)$ versus Reynolds number $($Re$)$ for the propeller below

in Figure Q$3.$ If the impeller rotation rate $($N$)$ is estimated at $151$ rpm$,$

$($i$)$ What is the expected value of the power $($P$)$ of the motor required to drive the impeller?

$[10$ marks$]$

$($ii$)$ What is the error in the estimate of the power? Show all steps.