# Need help on rocket nozzle equation

I saw this earlier post about a guy who needed help with his equation, but I was wondering about how they got one of his numbers. They said that their foot-pound/pound/degree Rankine (the gas constant R) was 64.388, but when I looked the number up it said it was 1,545.348. Do I have to do something to this number to make is specific for my equation, or did he just get his numbers wrong?

ORIGINAL POST - Help on Nozzle Throat Area Calculation

• post is now linked Apr 19, 2021 at 12:32

The form of the gas constant used in that equation is not the universal gas constant. It is the gas constant for the particular gas under consideration.

The value is obtained by dividing the universal gas constant by the molecular weight aka molar mass of the gas. From the original text

where R = gas constant, given by R = R_bar / M. R_bar is the universal gas constant equal to 1545.32 ft-lb/lb° R, and M is the molecular weight of the gas. The molecular weight of the hot gaseous products of combustion of gaseous oxygen and hydrocarbon fuel is about 24, so that R is about 65 ft-lb/lb° R.

Source: Krzycki, HOW to DESIGN, BUILD and TEST SMALL LIQUID-FUEL ROCKET ENGINES equation 7

The author of the text is sloppy with units. In English units, the universal gas constant is actually

$$1545.4 \frac {ft\ lbf} {lbm-mole\ ^oR }$$

so that when the division is carried out, the gas constant (with units) is

$$64.39 \frac {ft\ lbf} {lbm\ ^oR }$$

Source: Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, p. 41

• Yay! Now I don't have to continue my attempt at untangling US customary units! Apr 19, 2021 at 13:01
• @SE-stopfiringthegoodguys I get ya, but to be fair, it's the non-universal gas constant that should be used, regardless of the units. Apr 19, 2021 at 13:03