Cross Section of Water Flowing Down Vertical Pipe: The Mystery Unveiled

[R Power]

hi
We all know when velocity of fluid increases then cross section decreases for same mass flow rate and this can be well seen at water flowing from a height as in waterfalls.
But why this doesn't happen when water flows down through a vertical held pipe of constant cross section. Well you may say that since cross section of pipe is constant so it's velocity will remain same but why then velocity doesn't increase due to gravity?

 

[tiny-tim]

Hi R Power!

hi
We all know when velocity of fluid increases then cross section decreases for same mass flow rate and this can be well seen at water flowing from a height as in waterfalls.
But why this doesn't happen when water flows down through a vertical held pipe of constant cross section. Well you may say that since cross section of pipe is constant so it's velocity will remain same but why then velocity doesn't increase due to gravity?

Because of conservation of mass (and incompressibility, ie constant density, of water) …

in steady flow, so long as the water fills the whole width of the pipe, the rate at which water enters one end of the pipe must equal the rate at which it leaves the other end.

 

[sophiecentaur]

It will not flow as fast as a stone dropped over the same vertical distance.

 

[R Power]

Because of conservation of mass (and incompressibility, ie constant density, of water) …

Mass flow rate will even remain same if velocity of water increases (due to gravity) and correspondingly cross sectional area of water within the pipe decreases.

 

[DeShark]

hi
We all know when velocity of fluid increases then cross section decreases for same mass flow rate and this can be well seen at water flowing from a height as in waterfalls.
But why this doesn't happen when water flows down through a vertical held pipe of constant cross section. Well you may say that since cross section of pipe is constant so it's velocity will remain same but why then velocity doesn't increase due to gravity?

Can you give a physical example of such a flow?

 

[R Power]

Can you give a physical example of such a flow?

i already gave example - in waterfalls from mountains. You can also it yourself. Put water in a glass then empty the glass slowly(so that you can observe) by tilting it and see as water reaches more and more near ground it's cross section decreases and velocity increases due to gravity.
My question is why such thing does not happen in vertical pipes

 

[R Power]

It will not flow as fast as a stone dropped over the same vertical distance.

why?

 

[sophiecentaur]

i already gave example - in waterfalls from mountains. You can also it yourself. Put water in a glass then empty the glass slowly(so that you can observe) by tilting it and see as water reaches more and more near ground it's cross section decreases and velocity increases due to gravity.
My question is why such thing does not happen in vertical pipes

and "why"

You are suggesting that the water should leave the sides of the pipe as it falls and form a column inside? That would involve the formation of a space between liquid and pipe. This would constitute a low pressure region which will support the water below it in the pipe, delaying the fall. The water inside is not, in fact, in free fall, but affected by the pressure situation of the whole column (which communicates throughout at the speed of sound in the water).

Your model of a waterfall seems right but the situation in a rigid pipe is very different. Perhaps you'd see the effect in a pipe constructed so it could not actually stretch but could alter its diameter. That would be a good design task!