Calculating mass flow rate of a scramjet engine?

First post here.

I'm an undergraduate ME interested in fluid mechanics. I came across scramjets and I was interested about the engine. I want to calculate the mass flow rate of the engine and I made an attempt because it doesn't seem right and I can't find any resource explaining how to calculate the mass flow rate of a scramjet.

I arrived at this using standard definitions: $$\dot m = (\frac {P}{RT}AM\sqrt{\gamma RT})$$

where $$P$$ is the absolute pressure of free stream (air, in this case)

$$R$$ is the gas constant for air

$$A$$ is cross sectional area

$$M$$ is the Mach number

$$T$$ is absolute temperature

$$\gamma$$ is ratio of specific heats

I'll be honest, I have no strong intuition about this since I'm only a junior undergrad who only has taken Thermo and Fluids (no heat transfer yet, compressible flow not in curriculum) but if you guys can steer me in the right direction I would be very happy. I sense that it should be more geometry dependent, maybe angle of attack should be considered as well?

Thank you everyone!

• This may help : sciencedirect.com/science/article/abs/pii/S245190491630018X Aug 12 '19 at 6:29
• "(no heat transfer yet, compressible flow not in curriculum) " - Trying to calculate anything about a scramjet before you understand how a basic con-di nozzle works for compressible flow is going to be, well, "challenging". First crawl, then walk, then run is a good strategy here. Aug 12 '19 at 16:09
• to echo the sentiment of @alephzero, you should check to make sure that your equation gives the correct units for mass flow rate (e.g. $\frac{kg}{s}$). I'm getting $\frac{N}{\sqrt{\frac{J}{kg}}}$ from your equation, which doesn't make much sense as units of mass flowrate. Aug 12 '19 at 17:15