sonic flow in nozzle 1

[siriusengineer]

Hi,

I am a new engineer working on a derivation for maximum flow of a gas in a nozzle.

API RP 520, Pt. I, Para. 4.3.2.1 gives the equation for max flow to be

W=C*A*P*sqrt(T/M)

I've left out the correction factors for back pressure, non-ideal flow, and compressibility of a non-ideal gas.
Now I've been able to start with a tank of initial pressure and temperature, Po and To, and get to the following equation on my own.

W=Po*A*[(M/Ru/To)(k(2/(k+1))^((k+1)/(k-1))]^1/2

M being molecular weight, and Ru the universal gas constant.
Now the term C in the first equation is given as

C=520*[(k(2/(k+1))^((k+1)/(k-1))]^1/2

which makes the first equation almost match up with mine except for the 520 term, and the universal gas constant in my equation.

My question is this. Where did this C term come from and what are its units?

After putting in 1545.35 ft*lbf/lbmol/R for Ru and converting all the units to make sure W came out in lbm/s my term for C instead of being 520 would be 0.1443

A big thank you for any help on this.

 

[moltonian]

If the API derivation was for lb/hr their constant would be 0.1443 * 3600 = 519.48 !!

 

[Haf]

The fastest flow velocity you can have in a converging nozzle is sonic (Mach 1). Once the flow becomes sonic, the mass flow rate scales linearly with pressure, according to Fliegner's formula (which is only good for Mach 1 flow). If you can't find Fliegner's formula in your fluids references, let me know, and I'll type it out.

If you have a converging-diverging nozzle, flow will become supersonic under sufficient stagnation pressure and the Mach number can be calculated according to the area ratio of the nozzle. Flow will still be sonic at the throat, however, and therefore mass flowrate can still be calculated using Fliegner's formula (using properties at the throat).

Haf

 

[siriusengineer]

Argh! Of course. I was doing lbm/s instead of the lbm/hr I should have been converting to. I think that I'd been staring at it too long, and I fried my brain.

Thanks a bunch for getting me back on track.

 

[poetix99]

A link to "Fliegner's formula" is:

http://www.ijee.dit.ie/articles/999982/experime.htm

You might also want to refer to Thread# 378-31540; it is specifically concerned with transient flow, but deals with the same subject, broadly speaking.