Question $2(20$ points$)$

Glycerin at $20C$ flows upward in a $10$ m length $(L)$ and $75$ mm diameter $(D)$ pipe with a centerline velocity $(V_c)$ of $1\mathrm{.}0\frac{m}{s}.$ The pipe is inclined $=60.$

a$)$ Prove that the flow is laminar $(2$ points$)$

b$)$ Determine the pressure drop, $p$ in kPa $(9$ points$)[$Give your answer with one $(1)$ decimal place$]$

c$)$ Determine the head loss, $h_L(9$ points$)[$Give your answer with two $(2)$ decimal places$]$

Note: for Glycerin use $=1,260k\frac{g}{m^3}$ and $=1\mathrm{.}50N*\frac{s}{m^2}$