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Jatzan
Mycophile



Registered: 07/21/20
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PC Water Requirement Calculation
#26884022 - 08/16/20 09:42 PM (3 years, 5 months ago) |
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I have never used a pressure cooker before, so I wasn't sure how much water to place in it. How much water would steam out of the PC for 60 or 120 minutes?
So I did some basic math to help me out with this. There are few questions I wanted to answer: 1. How much steam does water produce, under these conditions. 2. How much steam can exit the PC. 3. And finally, how much water will exit the pressure cooker for a certain duration.
I am trying to go for a ballpark estimate, so some vales could be rounded up or down a bit. This should not drastically change the result. I will also try to include imperial units for our non SI friends overseas. Here goes my thinking at 3am xD
1. How much steam does water produce, under these conditions?
To calculate this we will follow the ideal gas law PV=nRT. P= 2 bars (or atms or 15psi relative to normal atmospheric pressure) T= 395 K (or 122 C or 250 F) V= 1 litre (bit more than a quart of steam) R= 0.083 L*bar/(K*mol) this is the ideal gas constant
So plugging this into the equation results in n= 0.06 mol of water
The molar mass of water is 18 g/mol (1+1+16), so this results in 1.08 grams of water.
So 1.08 grams of water is enough to produce 1 litre of steam, under these conditions.
2. How much steam can exit the PC?
This calculation will be based on the area of the release valve and the speed at which steam is released from it. To calculate the area of the release valve, we simply use a weight for 1 bar relative pressure which weighs 90 grams (3.2 ounces). Note that different PC models may have slightly bigger or smaller opening area and consequently require heavier/lighter weight. As a reference for this calculation I used this article.
The force that this weight puts on the valve is measured by F=m*g, where g=9,81m/s^2. This amounts to 0.09 * 9.81 = 0.883 Newtons. Since 1N/m^2 = 1 Pascal and we have a relative pressure of 1 bar or 100 kilo Pascals, that means that 0.883N/AREA IN METERS^2 = 100000Pa. That means that the opening area is 8.83*10^-6 m^2 (or about 0.0137 square inches)
Now for the velocity of the steam when exiting the valve, I read a bunch of stuff about it and did a bunch of calculations. These things are rather complex to calculate accurately depending on the system so I will spare you the math and will give an estimate that the speed is 10 m/s (33 ft/s).
So in each second 8.83*10^-5 cubic meters of steam are released. This amounts to 0.0883 litres of steam. For 60 minutes, 318 litres of steam are released. For 120 minutes, 636 litres of steam.
3. How much water will exit the pressure cooker for 60 and 120 mins?
I will calculate the water required for different Average Steam Exit Velocities (ASEV) and different Time duration (T):
ASEV = 10m/s ; T = 60 mins; Water expended = 294.5g (0.31 quarts) ASEV = 10m/s ; T = 120 mins; Water expended = 589g (0.62 quarts) ASEV = 20m/s ; T = 60 mins; Water expended = 589g (0.62 quarts) ASEV = 20m/s ; T = 120 mins; Water expended = 1178g (1.24 quarts) ASEV = 30m/s ; T = 60 mins; Water expended = 883.5g (0.93 quarts) ASEV = 30m/s ; T = 120 mins; Water expended = 1767g (1.86 quarts) ASEV = 40m/s ; T = 60 mins; Water expended = 1178g (1.24 quarts) ASEV = 40m/s ; T = 120 mins; Water expended = 2356g (2.48 quarts)
Conclusions From the calculations one can easily see that keeping the ASEV as low as possible can lead to drastic savings in water and energy as well as preventing disasters by always having enough water in the PC. This illustrates how important it is to fine-tune the stove heat to keep the PC jiggle as stable as possible, barely jumping. Remember that for 294.5g (0.31 quarts) of water for 60 minutes, 318 litres of steam are released. For 120 minutes and 589g (0.62 quarts) of water, 636 litres of steam are released. Let those numbers sink in!
Moved the poll here because I couldn't edit this one.
Edited by Jatzan (08/20/20 12:04 PM)
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Tight Lunchbox
Drunk cat


Registered: 11/06/16
Posts: 2,116
Last seen: 4 months, 7 days
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Re: PC Water Requirement Calculation [Re: Jatzan]
#26884039 - 08/16/20 10:03 PM (3 years, 5 months ago) |
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idk man, a lot of the people on here just tape quarters to the weight so it doesn't jiggle. hope that helps.
-------------------- "it's all a joke between mom contractions and coffin fittings" The most useful tool for noobs
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Jatzan
Mycophile



Registered: 07/21/20
Posts: 148
Last seen: 2 years, 4 months
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Yeah, I also though of increasing the weight - it is definitely the way to achieve the needed pressure. The guys from the article I quoted went as far to increase the weight for 30 grams, which is quite a bit. It is kinda risky though, not all PCs are designed to handle larger pressure. Most probably the PC will not explode, but I have seen several posts when the PC buckled (usually on the bottom side)
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Jatzan
Mycophile



Registered: 07/21/20
Posts: 148
Last seen: 2 years, 4 months
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Re: PC Water Requirement Calculation [Re: Jatzan]
#26889977 - 08/20/20 11:57 AM (3 years, 5 months ago) |
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The results from the poll here, indicate that my estimation for the Average Steam Exit Velocity of 10m/s is near the experimental values from the poll 0-20m/s.
Physics
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Smartattack
C'mon man



Registered: 12/21/18
Posts: 3,775
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Re: PC Water Requirement Calculation [Re: Jatzan]
#26890031 - 08/20/20 12:44 PM (3 years, 5 months ago) |
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This is ridiculously simple shit. Put in 2 qts. 3 if you want to for some reason. Ive done 2 runs safely on 2 qts without adding more in a presto 23 at 15 psi for 2.5 hours each run.
-------------------- * Smarts videos * Planet of the APES   I'm a fungal white supremacist.
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Jatzan
Mycophile



Registered: 07/21/20
Posts: 148
Last seen: 2 years, 4 months
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Re: PC Water Requirement Calculation [Re: Smartattack]
#26890113 - 08/20/20 01:36 PM (3 years, 5 months ago) |
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If you have the presto 23qt pressure cooker, sure its ridiculously simple. I, on the other hand, have some vintage crappy soviet PC which only has 6 quarts of space inside (or so it claims). In that space i can barely put a total of 2 quarts of minijars and a quart of water so that it is not touching the jars.
Unfortunately, where I live, the max PC I can get is 9 quarts and its SUPER EXPENSIVE, so that is out of the question. I also just renovated my kitchen and repainted the walls so I would not like to ruin that.
So I think you see my predicament and why I need to completely understand the process, so that I can operate the PC with minimal risk and squeeze every bit of available space to make this work. 
This was a feasibility study
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Tight Lunchbox
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Re: PC Water Requirement Calculation [Re: Smartattack]
#26890838 - 08/20/20 09:54 PM (3 years, 5 months ago) |
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werd.
-------------------- "it's all a joke between mom contractions and coffin fittings" The most useful tool for noobs
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