Truncated cone on stream of water

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Discussion Overview

The discussion revolves around the feasibility of levitating a truncated cone using a stream of water, exploring the underlying physics and potential equations to describe the phenomenon. Participants consider the mechanics involved, including fluid dynamics and conservation of momentum, while also discussing experimental approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant questions the possibility of levitating a truncated cone with a stream of water and seeks a formula to determine the necessary height for the cone.
  • Another participant suggests that as long as some water pushes against the cone, levitation should be possible.
  • Several participants discuss the principles of fluid dynamics, referencing hovercraft and leaf-blowers as analogous systems that utilize similar mechanics.
  • There are suggestions for practical experiments, such as dropping a shallow cone and observing the effects of different hole sizes and quantities on the cone's behavior in water.
  • Some participants note that both air and water can be treated as incompressible for the purposes of these experiments, although one participant expresses uncertainty about the compressibility of air in practical scenarios.
  • There is mention of using Bernoulli's equation to calculate the pressure difference acting on the cone, which could help in determining the conditions for levitation.
  • One participant expresses confusion about the exact physical setup, including the orientation of the cone and the stream of water.
  • Another participant indicates that any shape can theoretically be balanced on a jet of water, but emphasizes the importance of understanding the specific conditions before providing equations.

Areas of Agreement / Disagreement

Participants generally agree on the basic principles of fluid dynamics involved in the discussion, but there are uncertainties regarding the specific setup and conditions for levitation. Multiple competing views on the interpretation of the problem and the relevance of compressibility remain unresolved.

Contextual Notes

Limitations include unclear definitions of the physical setup, such as the orientation of the cone and the stream of water, as well as unresolved mathematical steps related to the application of Bernoulli's equation in this context.

Who May Find This Useful

This discussion may be of interest to individuals exploring fluid dynamics, experimental physics, or those looking for insights into practical applications of theoretical concepts in mechanics.

Numeriprimi
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Hello.
My friend said a truncated cone that is the upside down (the hole is open downwards) may be held in the air by a stream of water... How? It is really true?
Ok, consider a constant mass flow of water. How can I create a formula, which tell how high I have to place the cone? - (I want to try it)

Thank you very much,
sorry for my bad English :-)
 
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Why would it not be - as long as some of the water pushes on the cone?
 
Ok. But how? How can I solve by some equation? :)
 
You have a problem with the idea of levitating on a jet of fluid?
How do hovercraft work? A leaf-blower? It's the opposite of a rocket.
It's normal conservation of momentum and Newton's laws - though fluid flow can get very complicated.You can see the effect by building a shallow cone and dropping it.
Works well with cup-cake cups.

Hold it open-end down and drop it - observe.

Now put a hole in the bottom and try again.

Experiment with different size and quantity of holes.

The main difference between air and water for this experiment is that water does not compress.
 
Simon Bridge said:
You have a problem with the idea of levitating on a jet of fluid?
How do hovercraft work? A leaf-blower? It's the opposite of a rocket.
It's normal conservation of momentum and Newton's laws - though fluid flow can get very complicated.


You can see the effect by building a shallow cone and dropping it.
Works well with cup-cake cups.

Hold it open-end down and drop it - observe.

Now put a hole in the bottom and try again.

Experiment with different size and quantity of holes.

The main difference between air and water for this experiment is that water does not compress.

Actually, for the purposes of these experiments, both air and water can safely be thought of as incompressible. The compressibility of air doesn't really come into play unless you start looking at pretty high velocities (>mach 0.3) or fairly large pressure differentials.
 
Actually, for the purposes of these experiments, both air and water can safely be thought of as incompressible. The compressibility of air doesn't really come into play unless you start looking at pretty high velocities (>mach 0.3) or fairly large pressure differentials.
That's a good point - since the cone is being levitated in the flow.
If it were held in place, the compressability would be important.

[edit - thinking over that - I'm not sure I buy it entirely, I seem to be able to get air compression just waving my arms around. Have to think about it. [edit] ... Oh I see what you mean...]

I think the important thing here is to lead OP through the concepts - I hope numeriprimi tries the experiments.

The equations for arbitrary flow and arbitrary cone shapes can get horribly nasty.
I could probably whomp up a back-of-envelope for the specific case of a stationary (levitating) cone and laminar flow just by figuring the change in momentum to get the fluid over the surface.

@Numeriprimi: what do you need the equation for?

That produces the details - for incompressible, laminar flow you can use Bournoulli's equation to work out the pressure difference above and below the cone. With the dimensions of the cone, that translates into a force ... which you set equal to the weight of the cone and it levitates.

For general flows, it gets tricky because of turbulence.
 
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I'm not even entirely sure what the physical situation here is. I assume he means a cone frustum, but Is the stream aligned with the axis of the cone? I am not sure how the hole he references is oriented. What is the meaning of "upside down" in this context? A picture would be nice.
 
Technically you can balance any shape on a jet of water, if you are careful ... I just figure that it is oriented as a (conical) parachute or why should the hole make a difference.

I'm hesitating about posting a basic equation because this sort of thing is actually very common as an assignment question - I'd like to see OP give it a go first.

@numeriprimi: any of this useful?
 
 
Last edited by a moderator:
  • #10
Cool!

Though I'm not sure that OP so much doubts that it can be done as want's to know the math.
 

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