Equations and boiler pressure

 Posts: 537
 Joined: 13 years ago
Hi!
I'm building a homebrew PID controller with an old arduino for fun, and am getting schooled in math and physics I'd like to double check I'm on the right track here, and hopefully someone can offer a little help.
1. Assume sea level (indeed, I am at sea level).
2. At sea level, is the following approximately correct?
1 bar atmospheric pressure, 0 bar gauge pressure, and 1 bar absolute pressure
3. Is it correct that typical temperature range for 4L espresso boilers will be 212270F ? For my specific case, I have read a 5060F difference in boiler temp vs brew temp, which would mean, if I want to brew with 198F water, I need boiler temp between 248 and 258F.
4. Looking up saturated steam tables, this translates to roughly 2 bar gauge pressure at the upper end, and a 3 bar absolute pressure gauge
5. The pressure transducers I am looking at are 030psi and 050psi, and apparently measured in absolute  according to the data sheet. 30 psi converts to just under 2 bar.
6. If all the above is correct, I would want the 050psi measuring device? If the above is incorrect, please help me figure out which measurement range would best suite a 4L boiler with a 5060F water temp offset.
What extra confuses me: the mater xp110 pstat I have, has the labels, 0,51,2 bar. Huh?
Next, I'm also trying to find some kind of approximate formula for calculating temperature from pressure. Can someone provide a rough formula that could work?
In searching for this online, all I've found are calculators to do so, or the actual saturated steam pressure tables! That's not really helpful when trying to code the math. I did find some forum post where is was suggested to take the square root of the absolute pressure in bar twice, then multiple by 100. So for 3 bar, that would be:
(sqrt ( sqrt 3 )) * 100 = 131.6 C, which is 269F.... steam tables tell me this is 133C / 272F. I checked the formula at other pressures, and I think I just need to add about 2C to it (I'll do the actual math later) so.. hmmm.
Close enough, or is there something a little better?
Thanks for help
I'm building a homebrew PID controller with an old arduino for fun, and am getting schooled in math and physics I'd like to double check I'm on the right track here, and hopefully someone can offer a little help.
1. Assume sea level (indeed, I am at sea level).
2. At sea level, is the following approximately correct?
1 bar atmospheric pressure, 0 bar gauge pressure, and 1 bar absolute pressure
3. Is it correct that typical temperature range for 4L espresso boilers will be 212270F ? For my specific case, I have read a 5060F difference in boiler temp vs brew temp, which would mean, if I want to brew with 198F water, I need boiler temp between 248 and 258F.
4. Looking up saturated steam tables, this translates to roughly 2 bar gauge pressure at the upper end, and a 3 bar absolute pressure gauge
5. The pressure transducers I am looking at are 030psi and 050psi, and apparently measured in absolute  according to the data sheet. 30 psi converts to just under 2 bar.
6. If all the above is correct, I would want the 050psi measuring device? If the above is incorrect, please help me figure out which measurement range would best suite a 4L boiler with a 5060F water temp offset.
What extra confuses me: the mater xp110 pstat I have, has the labels, 0,51,2 bar. Huh?
Next, I'm also trying to find some kind of approximate formula for calculating temperature from pressure. Can someone provide a rough formula that could work?
In searching for this online, all I've found are calculators to do so, or the actual saturated steam pressure tables! That's not really helpful when trying to code the math. I did find some forum post where is was suggested to take the square root of the absolute pressure in bar twice, then multiple by 100. So for 3 bar, that would be:
(sqrt ( sqrt 3 )) * 100 = 131.6 C, which is 269F.... steam tables tell me this is 133C / 272F. I checked the formula at other pressures, and I think I just need to add about 2C to it (I'll do the actual math later) so.. hmmm.
Close enough, or is there something a little better?
Thanks for help

 Posts: 3917
 Joined: 12 years ago
I haven't looked at this closely but it might work for you:jedovaty wrote:Next, I'm also trying to find some kind of approximate formula for calculating temperature from pressure. Can someone provide a rough formula that could work?
Simplified Equations for Saturated Steam Properties for Simulation Purpose

 Posts: 33
 Joined: 4 months ago
You're looking for the ClausiusClapeyron Equation. See the link for a more detailed explanation.
https://chem.libretexts.org/Bookshelves ... n_Equation
https://chem.libretexts.org/Bookshelves ... n_Equation

 Posts: 537
 Joined: 13 years ago
Thanks for the response. I came across this in my search and the first word "Simplified" is a tiny little understatement. Actually, it's a gross understatement. I did give it multiple goes, and it seems like I need to include other kinds of pressure (e.g. critical and reduced pressures), and it's all assuming a third unit of measurement so I would need to do a three way calculation and that's.. no.jpender wrote:I haven't looked at this closely but it might work for you:
Simplified Equations for Saturated Steam Properties for Simulation Purpose
Hmm, this is new. I took a few minutes and looks like that needs more than just basic bath, including derivates and such.. that's too much beyond my abilities. UNCLE.kirby wrote:You're looking for the ClausiusClapeyron Equation. See the link for a more detailed explanation.
I like the double sqrt equation better so far, adding 2C to it seems to get me close. Any other thoughts?
Think about pi. You can use symbols and such, or you can use 22/7 or 3.14 to approximate. That's what I'm looking for here.
Also, the correct device measurement. Oi, this is way harder than expected

 Posts: 3917
 Joined: 12 years ago
Ignore my response. The ClausiusClapeyron equation isn't as exact but it's close enough at the relatively low temperature range you are interested in.
Simplified:
P = exp(4898 * (1/373  1/(T+273)))
where T is in °C and P is in bar
Simplified:
P = exp(4898 * (1/373  1/(T+273)))
where T is in °C and P is in bar
 Jeff
 Team HB
 Posts: 6913
 Joined: 19 years ago
You could also just do a table lookup with interpolation.

 Posts: 537
 Joined: 13 years ago

 Posts: 3917
 Joined: 12 years ago
Oh, you wanted T. Yeah, that looks good.
I like the coffee filter as scratch paper.
Also I agree with Jeff. You could just do a look up table with an entry for each 0.1bar or whatever pretty easily. You can generate a table here:
https://webbook.nist.gov/chemistry/fluid/
I like the coffee filter as scratch paper.
Also I agree with Jeff. You could just do a look up table with an entry for each 0.1bar or whatever pretty easily. You can generate a table here:
https://webbook.nist.gov/chemistry/fluid/

 Posts: 537
 Joined: 13 years ago
Hmmm, I guess that's another way to do it, sure. A lookup table means something called arrays/matrices, right? Eitherway more research, whether to look up how to do arrays, or how to do log base e math in arduino code. Just mumbling now.
I think we have the second question addressed then, yay!
Back to the first question then: ultimately would like to know whether to get a 030PSI or 050PSI (absolute) measuring device for a 4L espresso boiler? I can provide datasheet for the device if anyone is interested to read the specs.
I bought the 030psi last week, before I knew that pressure is measured different ways. So after reading up on it, I think the 050 is the correct one. But the mater pstat details are throwing a monkey wrench in this. I would test the whole thing, but the mater died a couple weeks ago, I didn't head the warnings and didn't use an intermediary relay between it and the heating element..
I think we have the second question addressed then, yay!
Back to the first question then: ultimately would like to know whether to get a 030PSI or 050PSI (absolute) measuring device for a 4L espresso boiler? I can provide datasheet for the device if anyone is interested to read the specs.
I bought the 030psi last week, before I knew that pressure is measured different ways. So after reading up on it, I think the 050 is the correct one. But the mater pstat details are throwing a monkey wrench in this. I would test the whole thing, but the mater died a couple weeks ago, I didn't head the warnings and didn't use an intermediary relay between it and the heating element..

 Posts: 33
 Joined: 4 months ago
First, I love that this conversation ended up with some equations written on a coffee filter.
Yeah if you could send some details on the measurement devices, that would be great. Most manometers measure difference relative to atmosphere. In that case, your 30 psi one would be close, but likely fine. However, if its reading is absolute, meaning relative to vacuum, you'll be out of its range.
Yeah if you could send some details on the measurement devices, that would be great. Most manometers measure difference relative to atmosphere. In that case, your 30 psi one would be close, but likely fine. However, if its reading is absolute, meaning relative to vacuum, you'll be out of its range.