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First post. Hopefully somebody might be able to help.

As per the attached picture, we have a diesel generator day tank which is gravity-fed from a larger, higher storage tank. We also have a vent extending upwards from the day tank, as shown. The day tank has all other bungs properly sealed. I would like to understand the physics involved on why the fuel does not spill out from the vent given the higher level/capacity of the storage tank, especially when filling the larger tank by pump. Hopefully, we can apply the same principles to various set-ups.

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ARCOLON is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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From your diagram it seems the the top of the vent pipe is always higher than the top of the storage tank so the fuel cannot spill out of the vent. In any connected system of tanks and pipes the fuel level will be the same otherwise there would be a pressure difference that would cause fuel to move horizontally and equalize the levels.

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Rod Bhar is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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    $\begingroup$ Rod, in order to be sure, the height difference between tanks and size difference have nothing to do with the system as long as the lower tank vent is above the higher tank maximum level? Thanks $\endgroup$
    – ARCOLON
    Sep 23 at 12:43
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    $\begingroup$ Right. But that assumes the tanks aren't under pressure. If one tank is under high pressure it could obviously push the fuel level up in a connected tank that is under a lower pressure. But it seems from your description that nothing like that is happening. $\endgroup$
    – Rod Bhar
    Sep 23 at 12:48
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    $\begingroup$ Correct. Both tanks are vented. Now, hopefully, somebody can help with the math involved, just out of curiosity. Thanks again! $\endgroup$
    – ARCOLON
    Sep 23 at 13:05

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