$2.(35$ Points$)$ The gage pressure in a sealed water storage tank $\backslash (\backslash$left$(\backslash$mathrm$\{$p$\}\_\{0\}\backslash$right$)\backslash )$ is $15$ kPa and has an exit orifice at the bottom of the tank for the water to discharge. The water level in the tank $\backslash (\backslash$left$(\backslash$mathrm$\{$h$\}\_\{1\}\backslash$right$)\backslash )$ is $2\mathrm{.}5$ m above the outlet. The water discharges into a pipe of diameter $6$ cm that flows horizontally and then rises to a new height, labeled point $2$ in the figure below. The flow is then converged to a new pipe diameter of $4$ cm and then the flow is discharged to the atmosphere at a height $\backslash (\backslash$left$(\backslash$mathrm$\{$h$\}\_\{4\}\backslash$right$)\backslash )$ of $0\mathrm{.}4$ m above the tank exit orifice. The height ratio between $\backslash (\backslash$mathrm$\{$h$\}\_\{2\}\backslash )$ and $\backslash ($ h$\_\{3\}\backslash )$ is $\backslash (1$: $2\backslash$left$($h$\_\{3\}=2$ h$\_\{2\}\backslash$right$)\backslash )$ A mercury manometer is connected across the diverging section that records a differential height $\backslash (\backslash$left$(\backslash$mathrm$\{$h$\}\_\{\backslash$mathrm$\{$m$\}\}\backslash$right$)\backslash )$ of $0\mathrm{.}2$ m $.$ Neglect frictional effects throughout the system and note that the density of water is $\backslash (998\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and the specific gravity of mercury is $13\mathrm{.}6.$

a$)$ What is the discharge rate out of the system to the atmosphere in $\backslash ($ L $/\backslash$mathrm$\{$s$\}\backslash )?$

b$)$ What is the dynamic pressure at state $1?$

c$)$ What is the gage pressure at state $2?$

d$)$ Sketch in box below the energy grade line $($EGL$)$ and hydraulic grade line $($HGL$)$ between the water surface in the tank through the discharge location at point $4.$