Show me the steps to solve $4($a$)$ Consider a water tank as shown in Figure $5.$ The width $($the direction into the paper$)$ of the tank is $5$ m $.$ Initially the tank is half full. Then the circular pipe on the top starts to feed in the water with a volume flow rate of $\backslash (15\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ At the same time, the tank starts to discharge the water from the bottom with a trapezoid$-$shaped velocity distribution shown in the figure. The maximum velocity around the central region of the $\backslash (\backslash$operatorname$\{$tank$\}\backslash )$ is $\backslash ($ v$\_\{\backslash$max $\}=0\mathrm{.}3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The leaking is estimated to be $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Is the water inside the tank increasing or decreasing? If it is increasing, how long will the tank get filled; and if it is decreasing, how long will the tank become empty?