Question $4[20$ Marks in Total$]$

$($a$)$ Working from the Perfect Gas Law; derive an expression to determine the mass flow rate for Nitrogen drawn from a rigid container using macro$-$scale Pressure and Temperature transducers. Include a term to ensure the level of isothermality required.

$[10$ Marks$]$

$($b$)$ Define a list of specifications $($ie$.$ pressures required and temperature stability$)$ for a test rig that can measure a flow of Nitrogen in a $18$ cm long stainless steel tube with an internal diameter of $100$ microns, for a Knudsen number range of $0\mathrm{.}01$ to $0\mathrm{.}2.$

$[8$ Marks$]$

$($c$)$ If the fluid was a liquid $($eg$.$ water$),$ how would your approach differ?

$[2$ Marks$]$

Question $4[20$ Marks in Total$]$

$($a$)$ Working from the Perfect Gas Law; derive an expression to determine the mass flow rate for Nitrogen drawn from a rigid container using macro$-$scale Pressure and Temperature transducers. Include a term to ensure the level of isothermality required.

$[10$ Marks$]$

$($b$)$ Define a list of specifications $($ie$.$ pressures required and temperature stability$)$ for a test rig that can measure a flow of Nitrogen in a $18$ cm long stainless steel tube with an internal diameter of $100$ microns, for a Knudsen number range of $0\mathrm{.}01$ to $0\mathrm{.}2.$

$[8$ Marks$]$