Question about liquid flow

[urbanleg]

Hi,

I was wondering,

 

let us assume we have a swimming pool of 10x10 meters and infinite height.

on the bottom of that pool we have a small hole. lets say the diameter of the hole is 1 cm.

now, we start filling the swimming pool with water.

let us assume as well that: the amount of water being filled to the pool >> the amount of water flowing out of the small hole.

 

ofcourse as time goes by the amount of water flowing out of the hole increases. (since the pressure increases as the pool is being filled with water.)

 

let us define the amount of water flowing of the small hole by x (liters per second)

 

my question is this:

 

does lim(x) = infinity ? (when t goes to infinity as well)

 

 

thanks allot

urbanleg

Edited October 24, 2011 by urbanleg

[insane_alien]

in the ideal case of a perfect newtonian fluid then yes, exherting an infinite pressure will cause an infinite flow.

 

in reality you'll run into all sorts of problems that prevent this occuring. fusion, collapse into a black hole etc. etc.

[urbanleg]

in the ideal case of a perfect newtonian fluid then yes, exherting an infinite pressure will cause an infinite flow.

 

in reality you'll run into all sorts of problems that prevent this occuring. fusion, collapse into a black hole etc. etc.

 

 

WOW! [mindblown]

thats amazing:)

 

thanks for the quick answer!

[CaptainPanic]

This is a funny thought experiment.

 

In the most simplified form, and talking about perfect Newtonian fluids, it is true. The resulting flow is then linear with the pressure, so an infinite column of liquid (note I do not say 'water') should give an infinite flow.

 

However... (life is never that simple)...

 

Water is a solid (ice), even at temperatures far above room temperature at really high pressures! So, an infinite column of water would not flow at all...

[insane_alien]

Water is a solid (ice), even at temperatures far above room temperature at really high pressures! So, an infinite column of water would not flow at all...

 

and going up beyond that you get fusion of the hydrogen then neutron degenerate matter and finally, blackhole.

 

and then there is the pains of 'how did you get a infinite uniform gravitational field?' and 'what are the walls made of?'

[urbanleg]

thanks guys. very interesting indeed

[J.C.MacSwell]

Hi,

I was wondering,

 

let us assume we have a swimming pool of 10x10 meters and infinite height.

on the bottom of that pool we have a small hole. lets say the diameter of the hole is 1 cm.

now, we start filling the swimming pool with water.

let us assume as well that: the amount of water being filled to the pool >> the amount of water flowing out of the small hole.

 

ofcourse as time goes by the amount of water flowing out of the hole increases. (since the pressure increases as the pool is being filled with water.)

 

let us define the amount of water flowing of the small hole by x (liters per second)

 

my question is this:

 

does lim(x) = infinity ? (when t goes to infinity as well)

 

 

thanks allot

urbanleg

 

At some point the gravitational attraction of the Earth becomes insignificant to the extended column of water. So the question is closer to "what is the pressure of an infinite column of water 10 X 10 meters?" and adjust locally for the Earth as it may still be highest at the "bottom".

 

Without doing the math I would hazard a guess that it converges to a limit, and does not create a black hole.

Edited October 24, 2011 by J.C.MacSwell