One thousand liters of $95\mathrm{.}0wt\%$ glycerol$-5\mathrm{.}0\%$ water solution is to be diluted to $60\mathrm{.}0\%$ glycerol by adding a $35\mathrm{.}0\%$ solution pumped from a large storage tank through a $3\mathrm{.}0-cm$ ID pipe at a steady rate.

The pipe dischages at a point $5\mathrm{.}0m$ higher than the liquid surface in the storage tank.

The operation is carried out isothermally and takes $13\mathrm{.}0$ minutes to complete.

The friction loss $($ hat$(F)$ of Equation $7\mathrm{.}7-2)$ is $40\mathrm{.}0\frac{J}{k}g.$

Calculate the final solution volume and the shaft work in $kW$ that the pump must deliver, assuming that the surface of the stored solution and the pipe outlet are both at $1\mathrm{.}00$atm.

Data: ${}_{H_{2}O}=1\mathrm{.}00k\frac{g}{L}$;${}_{gly}=1\mathrm{.}26k\frac{g}{L}$

$V_{\text{f}\text{i}\text{n}\text{a}\text{l}}=\frac{L}{2}L$

$W_s^{}=$