Ouestion $1$: $(28$ points$)$

A $10$ cm diameter pipe feeds a cylindrical water storage tank with a constant water flow speed of $\backslash (1\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The tank has a diameter of $0\mathrm{.}5$ m and has a $5$ cm diameter circular outlet at $10$ cm above the tank bottom. Considering atmospheric conditions outside the tank and using the density of water, $\backslash (\backslash$rho$\_\{\backslash$text $\{$water $\}\}=1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ calculate the maximum water depth $($h$)$ in the tank? $[$The direction of gravity is in the negative $\backslash ($ z $\backslash )$ direction in the schematic. Hint: maximum water depth occurs when the water level in the tank stops changing$].$