Problem $3$

Water flows through a horizontal pipe at a rate of $\backslash (10\backslash$mathrm$\{$gal$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The pipe consists of two sections of diameter $4$ in and $2$ in with a smooth reducing section. The pressure difference between the two pipe sections is measured by a mercury manometer. Neglecting frictional effects, determine the differential height of mercury between the two pipe sections. $(25$ points$)$

Figure $2$: Schematic for problem $3.$