# 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

here is how to get started on this.

for an ESTIMATE: we imagine the scramjet operating at steady-state cruise conditions with velocity V and an optimally-designed air inlet of area A.

Optimal design of the air inlet means that a streamline in the flow right at the edge of the air inlet will terminate at the edge- this is the "no-spillage" condition. This means that all the air coming straight at the inlet will enter it and the primary shock wave at the inlet will reside somewhere inside the lip.

With these simplifications, the mass flow rate of air entering the inlet (and therefore traveling through the engine) will be (air density x air velocity x inlet area).

This is a perhaps gross simplification of reality but it will put you in the ballpark. The experts here can furnish you with better approximations.