I'm looking at classifying air flow characteristic of pneumatic components and I've decided to follow an ISO standard (ISO:6358). It states that the flow rate is a related to the inlet and outlet pressure \(\displaystyle \frac{p_{2}}{p_{1}}\), which would make since for compressible flow. For a component the conductance \(\displaystyle Ce=\frac{q_{v}}{p_{1}} \sqrt{\frac{T_{1}}{T_{0}}} =\frac{q_{m}}{\rho_{0} p_{1}} \sqrt{\frac{T_{1}}{T_{0}}}\) where \(\displaystyle q_{v}\) is volume flow rate at standard conditions, \(\displaystyle q_{m}\) is mass flow rate at actual conditions, and the subscripts denote \(\displaystyle 1\) are inlet conditions, and \(\displaystyle 0\) are standard conditions.

I was wondering if anyone knew where this relationship is derived?

The experimental setup is basically a pressure drop experimental system that has the capabilities to record standard condition flow rate, temperature and pressure at inlet and outlet locations of the component under test.