How to Calculate Water Leakage in an Inverted Bottle Experiment?

[Lnewqban]

No, but neither have I seen much in them which addresses the question asked, namely, where has the OP gone wrong?

The first step should be to read where the OP got to and check whether there are any errors so far. In this case, the equation obtained was substantially correct and, if completely correct, should have been adequate for the OP's purposes. That being so, there does not appear to be any merit in going back to basics, as in post #26.

Of the 47 posts, including this one, I see 17 by the OP and less than 10 others that make a reasonable attempt to address that question. Sadly, this is not unusual.

I see.
Thank you for your honest opinion, haruspex.

Evidently, my good intentions, not being supported by the deep understanding of these matters that you and other prominent members enjoy, have miserabily failed to be of any help.

My sincere apologies to all who may have been confused or annoyed by my past posts and diagrams, in this and many other PF threads, during a few, indeed enjoyable for me, years of learning and sharing.

 

[erobz]

I see.
Thank you for your honest opinion, haruspex.

Evidently, my good intentions, not being supported by the deep understanding of these matters that you and other prominent members enjoy, have miserabily failed to be of any help.

My sincere apologies to all who may have been confused or annoyed by my past posts and diagrams, in this and many other PF threads, during a few, indeed enjoyable for me, years of learning and sharing.

Don’t be too hard on yourself. I had a hand in this by doing exactly what Haruspex said also. I was too eager to help that I skipped digesting whether or not the OP had it. In my mind I saw too many variables and I wanted to reduce them without really looking. That started the wild goose chase.

 

[Steve4Physics]

Hey @Lnewqban. Go easy on yourself. You’ve produced plenty of really helpful stuff. None of us are perfect so we get things wrong sometimes. (I speak with much experience of getting things wrong!)

 

[haruspex]

have miserabily failed to be of any help.

No, that is going too far. You have often been of real help on threads, and your diagrams are excellent.
Just try to follow my approach in post #50: take into account what exactly the OP is asking and where they appear stuck.

 

[haruspex]

I calculated with the following data and got the following:
hv,2=0,11m , Vc=11,65ml, S=5,215·10^-3m^2 , h=32cm, patm= 105880Pa

I can see some possible problems with accuracy.

For clarity, l'll rewrite your equation as $p_{atm}=h_{v,2}g\rho(Sh-V_{all}+V_c)/V_c$.
Your equation subtracts $V_{all}$ from Sh to get the original air volume then adds $V_c$ to get the final air volume.
You have used S and h as though the total volume of the bottle is their product, Sh. But your h is the entire bottle length, so includes narrower sections. With those numbers, Sh= 1.667L, about 10% too much.
But you do not say how you determined S, so maybe the bottle volume really is that large and you found S by dividing it by h?
And you don't state the value of $V_{all}$. Presumably $V_{all}=0.75L$, but how precisely? And is the total volume of the bottle really 1.5L, or is that just what it says on the label?

The nature of this experimental method is that it requires considerable accuracy in all these numbers to get a reasonable result.

 

[haruspex]

Vall=0,5L

Ok, but what about my other questions?

you do not say how you determined S

is the total volume of the bottle really 1.5L, or is that just what it says on the label?