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

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SUMMARY

The height of a Heron's fountain is influenced primarily by the pressure in "bottle b," which is determined by the hydrostatic pressure of the water in the system. Key variables affecting this pressure include the volume of liquid (V), the density of the liquid (ρ), and the height difference (Δh) between the water levels in the connected bottles. The relevant heights to consider are the top of the tube (tube d), the top surface of the water, and the bottom of the container (bottle c). Understanding these relationships allows for accurate predictions of fountain height based on the principles of fluid dynamics.

PREREQUISITES
  • Hydrostatic pressure principles
  • Fluid dynamics concepts
  • Understanding of pressure equations (p=F/A, ph=mgh)
  • Basic knowledge of viscosity and its effects on fluid flow
NEXT STEPS
  • Research the Bernoulli's principle and its application in fluid dynamics.
  • Study the effects of viscosity on fluid flow in tubes.
  • Explore the relationship between pressure and height in hydrostatic systems.
  • Learn about the design and construction of fluid systems, including Heron's fountains.
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Students studying physics, engineers designing fluid systems, and hobbyists interested in constructing hydraulic devices will benefit from this discussion.

  • #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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