Need help figuring out velocity of a venting gas

[steves1080]

I have a compressible gas (nitrogen) venting from a pipe. What I am trying to figure out is how fast the gas is exiting the pipe. I know the volumetric flow rate and the area of the pipe, but I cannot use the standard Q=Av formula because that provides me with an exit velocity of Mach 3 (a little extreme). I am assuming compressibility comes into the equation but I don't know how exactly. Any guidance would be great; thank you in advance.

 

[boneh3ad]

Do you know any of the pressures?

 

[steves1080]

That's where it gets a little tricky. The process piping is pressurized to just under 3000 psig, but there is a relief valve that vents off gas once 3000 psig is attained. There is a long vent line that opens up to atmosphere, and I need the exhaust velocity at the exit. Wouldn't I just assume that the pressure is ambient at the end of the pipe? Otherwise, what do I set it as?

 

[SteamKing]

You need to know the characteristics of this 'long vent line' running from the relief valve. You are going to have flow with friction of the nitrogen gas as it escapes thru the vent. I also suspect that with the gas flowing through the relief valve and into this long duct, flow is going to be choked at some point in the vent ('choked' means that the nitrogen has reached Mach 1 and the mass flow at that point has reached its maximum value).

At the minimum, you should have a sketch of the vent starting at the relief valve and running to the outlet, along with pipe sizes and schedules and lengths, plus a list of any fittings which might also be present in the vent line (elbows, tees, valves, etc.) It would also help if ambient temp. can be provided, along with temp. of the N2, if it is different from ambient.

 

[steves1080]

I appreciate your level of detail, but I'm not trying to get that involved with the problem. Just trying to get a worst case force of the outlet to know what kind of torque will be experienced at the elbow bend when it vents at full pressure. That's a good point about choked flow, I might just assume a sonic velocity and call it a day.

But my primary question is still does Q=Av still apply to compressible fluids?

Thanks

 

[SteamKing]

You can't use Q because the pressure is changing as the N2 moves down the pipe. You have to use m-dot, the mass flow rate.

 

[steves1080]

actually i just need to know the force of the fluid exiting the pipe into the atmosphere (need to know what kind of stress is being put on the pipes at that point). so i guess my underlying question would just be can i use F = (1/2)*(density of GN2)*(exit velocity^2)*(area of pipe cross section) where exit velocity = the speed of sound?