Thanks for that height-depth note, I was getting a bit tangled in this.
As for the pressure difference, the bigger the difference between in and outside the tube, the bigger the fountain would be.
And it can be expressed ΔP = h3ρg-(h2-h1)ρg - h1ρg = (h3-h2-2h1)ρg??
This looks so wrong... so...
Wow, I can't get my head around it now... I will go get some sleep and respond tommorow.
But let me try at least, since the height A is smaller than height B I guess the pressure in the tube d at A must be smaller than at B.
Then the pressure at A in the tube would be:
P = h3ρg-(h2-h1)ρg ?
The tube is full of water, so I think the pressure in tube d at A would be
P = h1ρg+h3ρg ?
Of course the pressure changes there, but the initial pressure from the air in bottle B remains the same in the whole liquid no?
Well the bottles are connected with a tube full of air, so I guess the pascal law comes in, saying that pressure applied on the air must be same in every point in the given connected medium.
Oh I'm very sorry! I thought replied, and was wondering why you aren't writing back.
The pressures at B and C can't differ because that would mean the water would be pushed into the tube (with lower pressure).
Hence the pressure at B and C must be the same, that is P=h3ρg+Pa.
That is all, or no?
Of course that's not right, sorry, I have no idea how I got to that.
The bottles are connected with a tube (full of air)
The problem is that I really don't know what is the pressure force applied on the air.
I have literally no idea.
It's equal to the pressure force of air over the area of the water surface, but how big is that force... I really don't have clue how to calculate that
I was going over this and couldn't work it out.
It seems to me that if we made the surface height at the bottom bottle lower, the pressure would actually increase, and if we made the surface height lower in the middle bottle, the pressure would drop.
What to do now?
Yes of course, I was tired and my brain was working slowly yesterday.
So the parameters that matter are the differences between the heights of water surfaces. Is that right?
I think that is a similar problem, If we made the bottom lower it wouldn't really change anything since the gradient would stay the same.
Same applies to your second question.
Uh, this must imply that the only height that matters is the height of the top surface of the water relative to the tube d?