Specific Gas Constant: What is R/MW?

[Bystander]

This came up in the barometric pressure thread in college HW help, and I asserted that R/MW was "new" to me --- "no excuse, sir --- tell me when you're tired, sir --- one, sir --- two, sir --- ... one thousand and one, sir ..."

Okay, rummage around in Eshbach and there it is, in the context of flow through a jet engine --- makes sense in that instance, no fixed average MW for the process stream --- the chemist in me would have run just "bar" MW as a variable rather than R/MW, but, no big deal.

enigma states that R is seldom used without division by MW in the aero curriculum --- who, what, where, when, how did that get started? An rms v²/K might be useful for analyses of air flow, I suppose, but MW isn't changing that much, or is there actually dissociation going on in shockwaves around airfoils?

 

[jamesrc]

For me, the specific gas constant has routinely come up, mainly in the context thermodynamics and fluid dynamics. In choosing the most convenient form of the ideal gas law to use, those using \overline{R}=\frac{R_u}{\overline{M}}, e.g.:

P = \rho \overline{R}T

Pv = \overline{R}T

PV = m \overline{R}T

depending on what you choose as a state variable. I can't recall if I used these formulations in my physics curriculum, but they have been common in mechanical engineering.

P.S. In case it's not clear, in above equations:

P = pressure, T = temperature ρ = mass density, R_u = universal gas constant, \overline{R} = specific gas constant, V = volume, v = specific volume, m = mass, and \overline{M} = molecular weight.

 

[enigma]

Originally posted by Bystander
"no excuse, sir --- tell me when you're tired, sir --- one, sir --- two, sir --- ... one thousand and one, sir ..."

You know, when you first stated that, I thought it was so odd, that I really wasn't sure if you were making fun of me or not...

Okay, rummage around in Eshbach and there it is, in the context of flow through a jet engine --- makes sense in that instance, no fixed average MW for the process stream --- the chemist in me would have run just "bar" MW as a variable rather than R/MW, but, no big deal.

I'm curious how you would solve the problem without using a specific gas constant. I'm getting the feeling that you think it's 'cheating'. I can't see why you would want to deal with a >=1kg/sec mixed flow on a per mole basis.

enigma states that R is seldom used without division by MW in the aero curriculum --- who, what, where, when, how did that get started? An rms v²/K might be useful for analyses of air flow, I suppose, but MW isn't changing that much, or is there actually dissociation going on in shockwaves around airfoils? [/B]

What do you mean by the v and K?

There can be dissociation in shockwaves, depending on mach number. There is definitely dissociation in rocket engines.

 

[Bystander]

"Cheating?" No, the first thought that went through my mind was, "Why the hell are they taking extra laps around Robin Hood's barn?" It looks something akin to defining πr (insert editing) that really is a lower case "pi" in front of the 'r' it just looks like an 'n' --- by the by, the preview wasn't working for me on this post) (end editing) as "specific pi" for calculating circumference or area of a circle --- the actual number of operations doesn't change, the inputs don't change, and the results don't change --- we've just inserted an extra definition in things. Hence, my question --- .

However, the interests of chemists and aeros differ in the sense that the results are going to be expressed differently, placing emphasis on slightly different end products --- the aero to move some great thumping mass of sheet metal, plastic, and the fools contained within through a variety of fluids by throwing unidentified reaction mass out the back end --- the chemist to poison every living thing on the planet, foul the earth, the air, and the waters so nothing can ever live again. The uses of the gas constant in achieving these two goals are different --- the aero emphasizes mass, the chemist moles.

I am somewhat curious how long "specific gas constants" have been used --- since WW II and jet engine development programs, or since before W & O started souping up bicycles?

R/MW boils down to velocity squared per unit temperature --- I guess we leave a chemical species subscript on the temperature to identify what we're looking at, but since this suggestion evoked the "Huh?" response, rms velocities are obviously not of particular interest in the calculation method --- .

 

[enigma]

Ah, OK.

Yeah, that was what I thought the case may have been. There is no reason for a chemist to need to deal with many kg's per second of flow, and there is no reason a jet engine would care how many moles of gas went through.

I do know that it's more than just the aero's who use it: It was done the same way in my (mechie) thermodynamics class as well.

 

[russ_watters]

Originally posted by Bystander
..."no excuse, sir --- tell me when you're tired, sir --- one, sir --- two, sir --- ... one thousand and one, sir ..."

Naval Academy?

 

[Bystander]

Ft. Sill.