How to calculate mass flow rate through valve for non-choked flow? I have a valve with a $K_v$ value of 12 m$^3$/hr when fully opened. I know the pressures upstream and downstream of the valve, $p_\mathrm{up}$ and $p_\mathrm{dn}$, and I want to know the mass flow rate through the valve. The $K_v$ is defined as:
$K_v = Q\sqrt{\frac{S.G.}{\Delta P}}$ where S.G. is the specific gravity of the fluid, for me, air, and $\Delta P$ is in bar.
I can plug in my $K_v$, $S.G.$, and $\Delta P$ into that equation and solve for $Q$, and multiply by the [upstream?] density to get the mass flow rate. But, there are a whole series of different equations for calculating the flow rate, for example here has the following equation for non-choked flow:
$$Q = N_2 c_v p_1 \left(1-\frac{2 \Delta p}{3p_1} \right) \sqrt{\frac{\Delta P}{p_1 S.G.T_1}}$$
Where $C_v$ is the imperial equivalent of the $K_v$ and $N_2$ is some constant used according to what units you have information in.
So my question is, why the two formulae? Is one for how to calculate the $K_v$ when you're performing a test at standard conditions, and the second is how you apply that coefficient to get your actual flow rate?
 A: There are several different types of valves, and many types of valves have three possible types of valve trim that can be installed in them.  The standard types of valve trim are quick opening, linear, and equal percentage.  Each of those valve trims has a curve that establishes valve position vs. flow rate for a given pressure drop across the valve, and for a given valve size.
I also note that you are mentioning non-choked flow, which clearly indicates that you are dealing with a compressible fluid.  Compressible flow calculations are somewhat more difficult to deal with than incompressible flow calculations because as the compressible fluid experiences pressure drop, its density drops and its velocity increases, further increasing the pressure drop per unit length.  Because of these complications, you would be well advised to get all the data off the valve that you can (e.g., valve size, valve type, manufacturer, etc.) and contact an appropriate valve vendor for help in doing your flow calculations.
