Air at $25C($with a density $=1\mathrm{.}184k\frac{g}{m^3}$ and dynamic viscosity $=1\mathrm{.}84910-5k\frac{g}{m}$ is flowing through a $15$ m long pipe with an internal diameter of $0\mathrm{.}05$ m $.$ The flow velocity is $10\frac{m}{s}.$ The pipe has a relative roughness of $lo\frac{n}{D}=0\mathrm{.}002.$

$($a$)$ Calculate the Reynolds number for the flow.

$($b$)$ Using the Reynolds number and the relative roughness, find the Darcy$-$Weisbach friction factor f from Moody's Chart.

$($c$)$ Using the friction factor, calculate the pressure drop over the length of the pipe using the Darcy$-$Weisbach equation.