'A Loop $1($L$1)$ from a series$-$parallel piping system is shown in Figure $4.$ The pump $($P$)$ adds $100$ ft of head to the fluid. The magnitudes of the flowrates are given as

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

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

$-91\mathrm{.}8$

$-66\mathrm{.}8$

$-116\mathrm{.}8$

$-41\mathrm{.}8$