$1-(20$ points$)$ A chemical plant is transferring a highly corrosive liquid from a holding tank to a

reaction vessel. The liquid has a density of $1020k\frac{g}{m^3}$ 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 $7\mathrm{.}62cm,$ 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 $6\mathrm{.}31li\frac{t}{s}.$ 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 $\frac{V_{\text{p}\text{i}\text{p}\text{e}}^2}{2}(1\mathrm{.}4+\frac{4fL}{d}),$ where $f=\frac{0\mathrm{.}0791}{R{e}^{\frac{1}{4}}}.$