A Loop $1($L$1)$ from a series$-$parallel piping system is shown in Figure $4.$ The pump $(P)$ adds $75ft$ of head to the fluid. The magnitudes of the flowrates are given as

$Q_{11}=1\mathrm{.}4cfs,Q_{12}=1\mathrm{.}0cfs$ and $Q_{13}=1\mathrm{.}8cfs.$ The directions of the flows are shown in the figure. Assume the head loss in each pipe can be calculated from the

following equation

$h_L=8\mathrm{.}2Q^{1\mathrm{.}8}$ where $Q$ is in units of cfs and $h_L$ is in units of $ft.$

In the question that follows, select the answer that is closest to the true value.

What is the sum of the head losses around the loop in units of $ft?$

$-41\mathrm{.}8$

$-91\mathrm{.}8$

$-116\mathrm{.}8$

$-66\mathrm{.}8$rigure $4$