A $\frac{1}{2}-$in$.-$diameter hose is used to fille the reservoir with water. If the pressure at the supply $A$ is $38,$ determine the time needed to raise the depth of the reservoich $=4ft.$ The hose has a length of $100ft$ and $f=0\mathrm{.}018.$ The reservoir has a width of $8ft.$ Neglect elevation changes in the hose and minor losses. Use $=62\mathrm{.}4l\frac{b}{f}{t}^3$ and $g=32\mathrm{.}2f\frac{t}{s^2}.(20$ points$)$