A chemical plant is transferring a highly corrosive liquid from a holding tank to a

reaction vessel. The liquid has a density of $1020$ kg$/$m$3$ and a viscosity of $1\mathrm{.}8$ mPa$$s$.$ The liquid is

being pumped from the holding tank into the bottom of the reaction vessel, which is located $6\mathrm{.}1$

meters above the surface of the liquid in the holding tank. The pressure in the holding tank is

maintained at $101\mathrm{.}3$ kPa $($abs$),$ while the pressure in the reaction vessel is maintained at $608$ kPa

$($abs$)$ to ensure optimal reaction conditions. The pipe connecting the holding tank and the reaction

vessel is equivalent to L $=22\mathrm{.}9$ meters of pipe with an inside diameter, d$,$ of $7\mathrm{.}62$ cm$,$ which

includes the additional resistance of any valves and pipe fittings. The desired flow rate of the

liquid as it is pumped to the reaction vessel is $6\mathrm{.}31$ lit$/$s$.$ Estimate the amount of pumping power

$($kilowatts$)$ required for the transfer of liquid from the holding tank to the reaction vessel?

The head loss is known to be equal to

vpipe$^2/2$g $*(1\mathrm{.}4+(4$fL$/$d$)),$ where f$=0\mathrm{.}0791/($Re$^(1/4))$