- #106

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$$(F_3V-F_4m)\frac{dT}{dt}=\frac{dm}{dt}-\frac{UA}{(h_v-F_2)}(T-T_s)$$where A is the surface area of the tank, U is the overall heat transfer coefficient, and ##T_s## is the temperature of the surroundings; t is time.

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- #106

- 23,514

- 5,785

$$(F_3V-F_4m)\frac{dT}{dt}=\frac{dm}{dt}-\frac{UA}{(h_v-F_2)}(T-T_s)$$where A is the surface area of the tank, U is the overall heat transfer coefficient, and ##T_s## is the temperature of the surroundings; t is time.

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- #107

Tom.G

Science Advisor

Gold Member

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Not at the moment, but if somebody knew what weight range you needed, they could likely do a Google search and find a few. As you are the only one here that would have such information, who do you think would be the most appropriate to do the search? (hint, hint)Leopold89 said:Can anybody recommend a proper scale? One which I can connect to a (Linux) computer, can recalibrate myself and is cheap?

- #108

Leopold89

- 59

- 5

I have now finally completed the computation with the new model by Chestermiller. As I could not find a clever substitution to seperate this differential equation into two seperate, I instead implemented this equation as minimization problem with the mass and temperature time serieses as optimization variables. This had the unfortunate consequence that I could not compute the change over a whole day in a timely fashion. Now I had to reduce the time series to the first 200 minutes. Over the next days I will also try to complete the rest of the day.

- #109

Juanda

Gold Member

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Leopold89 said:I have now finally completed the computation with the new model by Chestermiller. As I could not find a clever substitution to seperate this differential equation into two seperate, I instead implemented this equation as minimization problem with the mass and temperature time serieses as optimization variables. This had the unfortunate consequence that I could not compute the change over a whole day in a timely fashion. Now I had to reduce the time series to the first 200 minutes. Over the next days I will also try to complete the rest of the day.

But you're still seeing mass increments. Although the overall trend seems more realistic than previous results.

Maybe the sensors are not measuring correctly sometimes when things are happening too fast.

- #110

Leopold89

- 59

- 5

Maybe it is not that realistic, because the gas temperature is essentially constant compared to room temperature, but the gauge pressure still rises, likely even more than justified, if you look at the plot in post #71. But I also had to adapt Chestermiller's formula a bit, because I do not have liquid phase under these conditions. I started with ##U=mu_V \Rightarrow \mathrm{d} U = m\mathrm{d}u_V + u_V\mathrm{d}m## and inserted it into ##\mathrm{d}U=h_V\mathrm{d}m - \alpha A\Delta T## and got ##m(\frac{\mathrm{d}u}{\mathrm{d} p} \dot p + \frac{\mathrm{d}u}{\mathrm{d}T}\dot T) + \alpha A(\dot T - \dot T_s) = (h-u)\dot m##. Maybe my derivation is wrong.Juanda said:But you're still seeing mass increments. Although the overall trend seems more realistic than previous results.

Maybe the sensors are not measuring correctly sometimes when things are happening too fast.

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