The pump shown in Fig. $4$ adds a $15-$ft head to the water $($p$=1\mathrm{.}94$ slugs$/$ft$3,\backslash$mu $=2\mathrm{.}34\backslash$times $10-5$ Ibf.s$/$ft$2$ and y$=62\mathrm{.}4$ lbf$/$ft$3)$ being pumped from the upper tank to the lower tank. If the pipe has a roughness $=0\mathrm{.}003$ ft$,$ determine the flow rate Q$.$ Use f $=0\mathrm{.}03$ as the initial guess then the following equation for the remaining iterations until f converges to the thousandth decimal place. $($Note: $1$ psi $=144$ lbf$/$ft$2$ and g $=32\mathrm{.}2$ ft$/$s$2)$