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:

$K_v = Qsqrt{frac{S.G.}{Delta P}}$ 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?