A fireman is soaking a home that is dangerously close to a burning building. To prevent water damage to the inside of the neighboring home, he throttles down his flow rate so that it will not break windows. Assuming the typical window should be able to withstand a force up to $32lbf,$ what is the largest volumetric flow rate $(f\frac{t^3}{s})$ he should allow $($gal$/$min$.),$ given an $10-$ inch diameter $(D_1)$ firehose discharging through a nozzle with $4-$inch diameter $(d_2)$ outlet. The free jet from the nozzle is deflected by $90$ when it hits the window as shown.

$1\mathrm{.}20$

$12\mathrm{.}0$

$0\mathrm{.}12$

$2\mathrm{.}31$