Mass Flow with Stagnation Pressure/Temperature

I saw in many papers and books that when a compressible gas flows through an orifice, the mass flow is calculated using the stagnation pressure and temperature. That is,

$\dot{m} = \frac{P_o \cdot A \cdot v}{RT_o}$

By definition, the stagnation point is the point where the velocity is 0, and yet for the mass flow calculation, we have the velocity (which makes sense). Although I can derive the formulas using Bernoulli equation, still I don't have a good understanding of the practicality of using the stagnation point. When doing the derivation, I assume that the velocity of a fluid is 0 at the inlet, because I saw it in many examples (e.g. Pitot tube). Still, it is somehow against my intuition to say that the velocity is 0 at the inlet of an orifice. I do understand that the velocity is 0 when the stream hits and object.

Can anyone please clarify why should I use the stagnation pressure for the mass flow equation and how can I have a practical understanding of these concepts? I appreciate very much any help!

Paul

• Can you please provide a reference? – Deep Sep 28 '16 at 8:48
• For instance here you have one: grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/… The formula looks a bit different, and for an isentropic compressible flow (from theory) $P_{stagnation} = P_{total}$. Again, I know this from theory, but I have no practical visualization of it. – Physther Sep 28 '16 at 9:19
• In the link you have provided first the usual $p/RT$ has been used, and then assuming isentropic flow, $p_t, T_t$ have been introduced. Nevertheless it is not in the form you have written above. – Deep Sep 28 '16 at 9:54
• No, the form is different, but if one replaces velocity with $v = M *\sqrt{k R T}$-, where $k = \frac{Cp}{Cv}$ and so on, one would end up having the form from above. Still, why using the stagnation points (or $P_t = P_o$ for incompressible flows) and not simpy PV = m R T. Why do they use $P$=\dfrac{P_t}{1 + \dfrac{k-1}{2} M^2}^{(k/(k-1))}\$. Here are the difinitions for Pt and Tt and others: grc.nasa.gov/www/k-12/airplane/isentrop.html – Physther Sep 28 '16 at 15:17