Chaining pressure vessels and outlet temperature

[bionic6manuel]

Say I have a boiler with,
pressure = 86 bars
temperature = 573.15 K
overall heat transfer = 96 w/m2K

And there will be a pipe connecting the boiler to a pressure vessel
pipe length = 0.05m
pipe overall heat transfer = 0.146 w/m2K

The pressure vessel,
volume = 231cm3
pressure = 85 bars
overall heat transfer = 10kw/m2K
inlet steam temperature 573.08

Is the a way to find out the outlet steam temperature from the first pressure vessel, because I would like to connect another pressure vessel with the same data as the first pressure vessel.

 

[AdrianMay]

To my taste, you are posing this question in a peculiar way. Perhaps I can rephrase it a way that I can think about, then you can fill in the data that hasn't been communicated yet.

You have an enclosure consisting of three chambers connected by two pipes which presumably resist the flow of gas otherwise you'd just have one enclosure.

In the first chamber, you have a source of heat which is boiling water at some rate. The heat flow and steam production rate are connected by the latent heat of water. To maintain a steady state, either the steam escapes from some chamber (the third I suppose), or the water condenses and gets pumped back to the boiler, perhaps via the nearest lake.

If you knew about the resitances of the pipes, then you'd be able to use something like Ohms law to figure out the pressure differences between the chambers. If you knew how much lagging the chambers and pipes had, and how much steam or water was exiting the system at what temperature, then you could also figure out the temperature drops. It would be a bunch of linear simultaneous equations.

Does that help?

 

[bionic6manuel]

I failed to mention that the steam mass flow is 1.4 kg/h and in each pressure vessel there would be a pressure drop of about 1.5 bars. The thing is i would like to find out the temperature drop in the last pressure vessel. what are the linear equations

 

[AdrianMay]

You might have more luck on the thermodynamics section of the forum. There is an equation for the case that gas escapes through a constriction from a high pressure to a low pressure, and you can get the temperature drop from the pressure drop. But there are four equations like that and I can never sort them out in my head. I hated thermo at school.

 

[bionic6manuel]

Could you tell me the names of these four equations

 

[AdrianMay]

Gibbs, Helmholz, something like that. They look like dU = TdS - pdV except with p and V swapped around, and/or T and S swapped around, and with signs changed. That gives four combinations. But you have to know which to use when.

 

[absurdist]

You should've posted this in the chemical engineering section!
Try using a process simulation software like ASPEN HYSIS/PROMAX