What variables affect the height of a Heron's fountain?

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Homework Help Overview

The discussion revolves around understanding the mechanics of a Heron's fountain, specifically focusing on the variables that influence the height of the fountain. The original poster has constructed a fountain and is exploring the relationship between pressure and height in the system, particularly in relation to the bottles and tubes involved.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the role of pressure in the fountain, questioning how it is affected by various heights and the properties of the liquid. There are attempts to define relevant heights and their impact on pressure, along with expressions for calculating these pressures.

Discussion Status

The discussion is ongoing, with participants providing guidance on defining heights and pressures. Some participants are exploring the implications of changing heights on the fountain's operation, while others are questioning their understanding of the relationships involved. There is a recognition of the complexity of the problem, and participants are encouraged to clarify their assumptions and reasoning.

Contextual Notes

Participants note the importance of specific heights in the setup, such as the top of the tube and the water surface levels in the bottles. There is an acknowledgment of potential confusion regarding which heights are relevant to the pressure calculations, as well as the impact of viscosity and tube width on the fountain's behavior.

  • #61
Physicist1011 said:
Oh the pressure at A is atmospheric pressure so the difference in pressure between B and A is PB=Patm
Atmospheric pressure is a background common to all points. We only need concern ourselves with gauge pressure, i.e. the excess above atmospheric.
But you still have not answered my question about A and B. What path is there between those two surfaces which either only passes through water or only passes through air?
 
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  • #62
Well the water in B passes through a tube of water and comes out into air. So neither of those things you mentioned above happen because the water passes through water (in B) and then air (coming out of the tube d).
 
  • #63
Physicist1011 said:
Well the water in B passes through a tube of water and comes out into air. So neither of those things you mentioned above happen because the water passes through water (in B) and then air (coming out of the tube d).
As I reminded you, we are considering a static arrangement. Your finger is stopping the fountain, so nothing is actually passing anywhere.
My questions are in relation to paths that exist within this static arrangement. Could you thread a path from the one surface to the other without changing medium?
 
  • #64
Yes, the water is flowing in the tube to the 2nd surface so the medium does not change since the path is the same medium on both surfaces.
 
  • #65
Physicist1011 said:
Yes, the water is flowing in the tube to the 2nd surface so the medium does not change since the path is the same medium on both surfaces.
Which tube? They are labelled.
 
  • #66
tube d
 
  • #67
Physicist1011 said:
tube d
As I wrote in post #59, tube d connects reservoir B to the base of the fountain. It does not connect with reservoir A. There is no water path from the surface of reservoir B to the surface of reservoir A.
 
  • #68
Oh, tube e - tube of air connecting to 2 air mediums.
 
  • #69
Physicist1011 said:
Oh, tube e - tube of air connecting to 2 air mediums.
That connects the airspaces at B and C, not A and B..
 
  • #70
ok. tube f is a tube full of water which connects a water medium to another water medium.
 
  • #71
Physicist1011 said:
ok. tube f is a tube full of water which connects a water medium to another water medium.
Yes, A and C, not A and B.
Have you lost track of where we are at?
You need to make a list of the pairs of surfaces which are connected by a water only path, and a list of pairs connected by an air only path.
In post #56 you claimed there was such a path connecting A and B. Are you ready to agree there is not one?
 
  • #72
oh sorry tube d definitely isn't one.
 
  • #73
Physicist1011 said:
oh sorry tube d definitely isn't one.
Ok.
In post #56, you correctly had A and C connected by water.
For B and C you wrote "same", but it is not clear whether you meant they are the same pressure or that the connection is the same type as AB. Please clarify.
Finally, you need to say what the base of the fountain (the point inside tube d that's at the same height as surface A) connects to, and through what medium.
 
  • #74
B and C are of the same pressure. The base of the fountain connects from b into the atmosphere - through both water and air.
 
  • #75
Physicist1011 said:
B and C are of the same pressure.
Right.
Physicist1011 said:
The base of the fountain connects from b into the atmosphere - through both water and air.
No, remember that we are supposing you have a finger on top of that tube, so the fountain base is isolated from the atmosphere.
Now, what equations can you write relating the four pressures?
 

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