$[15$ points$]$ 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 in the figure below. The liquid has a viscosity of $=0\mathrm{.}025Pa*s,$ a density of $=800k\frac{g}{m^3},$ and discharges into the atmosphere with a mean velocity of $\frac{?}{\text{b}\text{a}\text{r}}(V)=5\frac{m}{s}.$

$($a$)$ Determine if the pipe flow is laminar or cuvuenv.

$($b$)$ The flow is fully developed in the last $3$ m of the tube. What is the pressure at the pressure gage? $($The pressure at the outlet is the atmosphere pressure.$)$

$($c$)$ What is the magnitude of the wall shearing stress, ${}_w,$ in the fully developed region?