Problem $2(20$ points$)$

Concepts: Pressure$-$driven flow $($Hagen$-$Poiseuille flow$)$

A simple flow system to be used for steady$-$flow tests consists of a constant head tank connected to a length of $4-$mm$-$diameter tubing as shown. The liquid has a viscosity of $\backslash (0\mathrm{.}015\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~s$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ),$ a density of $\backslash (1200\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ and discharges into the atmosphere with a mean velocity of $\backslash (2\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The flow is laminar and fully developed in the last $3$ m of the tube. What is the pressure at the pressure gage?