vertical 20m pipe

[waseem19]

This is not an actual problem , it is just that i had an argument with a friend on what will happen if you had a big pipe say a 1000mm dia 20m long , filled with water and supported vertically, you have a perfect seal at top and suddenly you removed a stopper from the bottom , what will happen ?

I said that water will cavitate in the middle and the lower 10m column will fall down, leaving the top 10m in the pipe.

he said that cavity will occur to all of the top 10m column, water will evaporate there leaving the bottom 10m hanged.

what do u think will happen ?

 

[CostasV]

In my opinion, the main factor in this problem is the diameter of the pipe, which is 1000mmm. This size of diameter is far from the size where the water presents sticky effects (I dont remember the right word).
So I think that water at level zero will start "falling" at some area of level zero, while at the rest area of level zero, the water will start "going upwards". This movement is in the order of mm or cm at the most. Also this movement is the way that air is formated in bubbles. And when the boundary at level zero is "crossed" by bubbles, then all the water will flow leaving the pipe empty.

On the other hand, if the diameter is around 2-3 mm, then the boundary at level zero does not allow the air to brake it. In this case all the 20 m water column will start falling untill there are only around 10 m of water in the lower part of the pipe to balance the atmospheric pressure.

Costas

 

[zdas04]

With a 1m diameter, the pipe would empty itself in a very few seconds. The ratio of surface tension to capillary attachment to surface area is just wrong for the "finger over the straw" trick to work. I've seen it work for a few seconds in 50 mm pipe, but even there the equilibrium is not stable.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[waseem19]

Costas,

concerning the 2-3mm pipe , so no cavity will occur ?
if the pipe is 40m long , then as you said the water column will start falling down ,will it also continue to fall down untill there is 10m only left at the bottom ? what does the pressure look like in the upper empty 30m ?

 

[cah2oeng]

Varsamidis is right, that diameter isn't small enough for capillary action to occur.

If you had a small enough diameter pipe, here's what would happen:

Cavitation would occur at the top while water poured out the bottom. If the pipe was long enough, the weight of the water remaining in the pipe will eventually reach equilibrium with the vapor pressure in the cavity and the surface tension (both act to hold the water up, although surface tension would be negiligible in this case). All the surface tension would do in this case is prevent fingering of air into the pipe.

You would never end up with water sticking to the top of the sealed pipe. The only way it would be possible is if the pipe was short enough and thin enough that the surface tension capacity was much greater than the weight of the water.

 

[CostasV]

To waseem19,

If the pipe has diameter of 2-3 mm and 40 m height, then all of the 40 m mcolumn would "fall" down inside the pipe, leaving the top part of the pipe empty. As the top part of the pipe has almost zero pressure, all the dissolved gases that were in the water will form bubbles that will go up to "fill" the empty pipe. There will also be an evaporation of the water to "fill" the empty pipe. But these gaseous phenomena will take some time. On the other hand the "falling" phenomenon will be faster. So we can say that for a small period of time the top of the pipe will have approx. zero pressure.

To the rest I agrree with ce621a about the conditions of equilibrium.

 

[katmar]

It's much easier to discuss these things when particular numbers are used as an example. Let us take a temperature of 20 C. At this temperature the vapour pressure of water is 2.3 kPa and the density is 998.3 kg/m3.

As noted by others, if the diameter of the pipe is large all the water will run out the bottom. But if it is sufficiently narrow you will get an equilibrium at the bottom of the tube where gravity acting on the water is trying to cause it to run out, while the surface tension and (most importantly) the atmospheric air are holding the water in.

Imagine starting with the 20 m column full of water and then removing the stopper (finger?) from the bottom. The pressure at the bottom of the column is higher than the atmospheric pressure holding it in, and it would therefore start running out.

The water would instantaneously boil, filling the top section with vapour. An earlier comment that this boiling process takes time is wrong. To prove it to yourself take a clear plastic syringe half filled with water, put your finger over the end (with no needle!!!) and pull the plunger out a bit. You will see it boil straight away.

If the atmospheric air pressure is 101.3 kPa the pressure at the bottom of the water column must be the same (neglecting the minor force of surface tension) when it comes to equilibrium.

Since the vapour pressure is 2.3 kPa the pressure exerted by the height of water must be 99 kPa (= 99,000 Pascal). Using the relationship of Density x gravity x height = pressure we get the height as
99000 / (9.81 x 998.3) = 10.11 metres

If your pipe was exactly 20 m long you would therefore finish up with the top 9.89 m full of water vapour at a pressure of 2.3 kPa, and a column of liquid water 10.11 m high at the bottom.

 

[cah2oeng]

Well put, katmar. I was too lazy to put together the numbers.

Finding the limiting diameter for this problem would be interesting. You'd have to do some sort of stability analysis (similar to groundwater fingering). Best you could get is probably order of magnitude, but I'm betting it's on the order of millimeters (i.e. like a straw).

 

[arto]

Hate to be un-analytical/non-nerdly, but when we did this way back when in Cub Scouts, with a full glass of water, we put a cardboard over the opening to keep the air out. Works fine till things get wet -the first bubble & you've lost the "siphon" or vacuum effect. Then the kitchen floor gets all wet. ;-)

 

[arto]

ps: I just went to get a drink & was reminded of this - sounds like your design/calculations would work for a humongous water cooler!!