Mph jet engine reaches 2 atmosphere 29.4 psi

[gary350]

As a jet engine travels through the sky and picks up speed ram air increases the air pressure at the air intalk of the engine. How many mph does the engine have to be going for ram air to 2 atmospheres = 29.4 psi?

At what speed in mph = 3 atmospheres?

4 atmospheres?

Is this a linear or nonlinear increase in air pressure vs mph?

 

[russ_watters]

Read the wiki link on Bernoulli's principle.

 

[boneh3ad]

Read the wiki link on Bernoulli's principle.

Bernoulli's equation would predict a velocity faster than the speed of sound, it's safe to assume any such situation is compressible and therefore not subject to Bernoulli's equation. The real issue here is that there isn't nearly enough information to answer such a question without making some major assumptions.

If the compression is isentropic, then the flow would have to be moving at something like Mach 1.04 to achieve double the atmospheric pressure, Mach 1.37 to triple the pressure, and 1.56 to quadruple it. That's just form isentropic stagnation, though, and discounts the formation of shocks, which are quite likely to occur here.

 

[russ_watters]

Bernoulli's equation would predict a velocity faster than the speed of sound, it's safe to assume any such situation is compressible and therefore not subject to Bernoulli's equation.

Bernoulli's equation can include a term for compressibility and that's discussed in the wiki.

But yes, the bigger problem is what the highest pressure you see is before reaching supersonic or choked flow.

Either way though, IMO one should start at zero and work their way up on this issue. That at least partially answers the last question.

 

[boneh3ad]

Bernoulli's equation can include a term for compressibility and that's discussed in the wiki.

The bigger problem is what the highest pressure you see is before reaching supersonic or choked flow.

Using the compressible version of the Bernoulli equation requires you to know how the density evolves, which requires all the same assumptions I mentioned before. Also, it seems pretty obvious that the OP doesn't know what he/she is doing here is would probably jump straight to the normal Bernoulli equation if all you do is tell him to read the wiki link on the Bernoulli equation, so I don't think that's the right approach. At any rate, assuming something like an isentropic compression or a normal shock let's you relate the Mach number directly to the pressure ratio, so that approach is going to be substantially easier anyway.

I edited my previous post to include the Mach numbers required to achieve those compressions assuming the flow is isentropic, and they are pretty clearly supersonic. The compression ratio to achieve sonic flow in air is $p/p_0 \leq 0.528$, and the OP is asking about 0.5, 0.33, and 0.25.

 

[rcgldr]

A side issue here is the speed of the intake flow into the jet engine. Relative to the jet, the intake air isn't stopped, it's just slowed down, so the speed decrease from free stream to intake speed needs to match the numbers posted by boneh3ad. In the case of most supersonic (not hypersonic) jets, the flow is slowed to subsonic, sometimes via the use of shockwaves.