Truncated cone on stream of water

[Numeriprimi]

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 :-)

 

[Simon Bridge]

Why would it not be - as long as some of the water pushes on the cone?

 

[Numeriprimi]

Ok. But how? How can I solve by some equation? :)

 

[Simon Bridge]

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.

 

[cjl]

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.

 

[Simon Bridge]

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.

 

[boneh3ad]

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.

 

[Simon Bridge]

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?

 

[CWatters]

 

[Simon Bridge]

Cool!

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