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[black friday]

Hi All,

I'm just looking for a second opinion on a calculation I'm doing. It's probably pretty trivial for some of you, but it's been a while since I've done this.

The scenario is this: I'm looking to size a relief valve for a case which involves thermal expansion of an enclosed section of pipe that may be carrying cryogenic gas.

 

The way I'm calculating this is by taking the derivative volume w.r.t in the ideal gas law which works something like this...

 

P.V=z.n.R.T

 

V=z.n.R.T/P     I then take the derivative of both sides w.r.t time.

 

dV/dt=z.n.R/P * dT/dt      Due to the scenario where gas is exhausting through a relief valve, isobaric expansion is assumed and hence P is constand and can be factored out of the derivative.

 

I take dT/dt=Q/(m.Cp) and substitute.

 

dV/dt=z.n.R/P * Q/(m.Cp) substituting n=m/mw to remove moles...

 

dV/dt=z.m.R/(P.mw) * Q/(m.Cp) cancelling mass (m) leads to

 

dV/dt=z.R/(p.mw)*Q/Cp=z.R.Q/(mw.Cp.P) which should give me a result in m3/s if I am correct? I will calculate the heat duty by using Q=L.2.pi().k.deltaT/(ln(Ro/Ri)) to get the heat transfer through the pipewalls.

 

Is this correct? I am slightly bemused to see that the mass or volume of gas that the heat transfer is affecting is not a factor in the mass flow rate I get as a result, but nonetheless I think I have this right. I would love confirmation however.

 

Any help would be greatly appreciated.

 

Cheers!