Speed of Sound in Compressed C02 Tank

[MattRob]

Hey,
I've built a Cold Gas Rocket using a Co2 tank that stores liquid C02 at room temperature around 850 psi. (A Cold Gas Rocket is a rocket that uses a pressurized tank to propel the reaction mass instead of combustion, essentially just open a scuba tank and that's a very dangerous (not the one I built) cold gas rocket.)
I suspect the exhaust velocity of the rocket is the speed of sound in the tank (850 +/- 200 psi) minus the speed of sound in the air (14.7 psi).
C02 is at room temperature, tank is half full of liquid, other half is high-pressure C02 at just below liquid pressure (still around ~850 psi).

So,
1) Is the exhaust/exit velocity the speed of sound in the higher pressure area minus the speed of sound in the lower pressure area?
2) What is the speed of sound in the C02 tank?

Information:
Tank Pressure: (800 psi +/- 200 for range of temperatures)
Tank temperature: ~72*F, Room temperature.
Tank state: half liquid, half gas. I'm more concerned with the liquid, calculate for liquid, please. (Since the liquid is forced to the exit when the valve is opened, it's the one that counts.)
Tank density: ? Liquid C02 at room temperature and 850 psi.

Thanks in advance.

 

[omoplata]

I found this http://www.google.com/url?sa=t&sour...uRmPLVkA&sig2=owumVzMLC129DqRicyovfA&cad=rja". It has equations for exhaust velocities. As far as I can tell, they are not related to the speed of sound of anything.

They also refer to a book, "Understanding Space" by Jerry Jon Sellers. That book probably has all the equations you need. You can check http://www.worldcat.org" to find if that book is available in any libraries near you. In not, you might be able to ask your local public library to borrow that book from a library that has it.

 

[SteamKing]

Contrary to what Omoplata writes, the maximum flow of a pressurized gas from a tank is directly proportional to the speed of sound in that gas. The condition is called "choked flow", and more details can be found here: http://en.wikipedia.org/wiki/Choked_flow

 

[omoplata]

Thanks for correcting. I didn't know that.

 

[PJC01]

I would first like to commend you on your Cold Gas Rocket project. It is always exciting to see individuals exploring and experimenting with scientific concepts.

To answer your first question, the exhaust velocity of the rocket would indeed be the difference between the speed of sound in the higher pressure area (850 psi) and the lower pressure area (14.7 psi). This is because the speed of sound is directly proportional to the pressure of the medium it is traveling through.

To calculate the speed of sound in the C02 tank, we would need to know the temperature and density of the C02 in the tank. Since you have provided the tank temperature (72°F) and pressure (800 psi), we can use the ideal gas law to calculate the density of the C02 in the tank.

Using the ideal gas law, we can calculate the density of the C02 in the tank as follows:

PV = nRT
where:
P = pressure (in Pa)
V = volume (in m^3)
n = number of moles
R = gas constant (8.314 J/mol K)
T = temperature (in K)

Rearranging the equation to solve for density (ρ), we get:

ρ = (P * M) / (RT)
where:
M = molar mass of C02 (44.01 g/mol)

Plugging in the values we have, we get a density of approximately 14.6 kg/m^3 for liquid C02 at 72°F and 800 psi.

To calculate the speed of sound in this medium, we can use the following formula:

v = √(γ * R * T)
where:
v = speed of sound (in m/s)
γ = adiabatic index (1.3 for C02)
R = gas constant (8.314 J/mol K)
T = temperature (in K)

Plugging in the values, we get a speed of sound of approximately 259 m/s for liquid C02 at 72°F and 800 psi.

I hope this helps answer your questions. Keep up the great work with your Cold Gas Rocket project!