Atmospheric Pressure at Spout of Water Tank

[Gabe805]

Picture an open cylindrical tank with a spout at the bottom from which water is flowing. Why is the pressure at the spout equal to the atmospheric pressure? I thought pressure increases with depth (i.e. rho*g*h). The explanation I have been given is that fluid that is exposed to the atmosphere has atmospheric pressure. What happened to the pressure from the inside?

 

[CWatters]

The pressure falls as the water expands going down and emerging from the spout.

Consider what happens with a gas such as the C02 used in some fire extinguishers. The Gas expands a lot as it goes from the high pressure inside the tank to the low pressure outside. As it does so it will try to absorb energy from it's surroundings. If that can't happen fast enough the gas becomes colder. (See youtube videos on making dry ice using a C02 fire extinguisher)

Unlike a gas water isn't easily compressed - so it only has to expand a tiny bit for the pressure to drop a lot. You are very unlikely to notice such a small expansion as the water emerges.

 

[russ_watters]

Sorry, cwatters, but that really isn't correct -- because as you said, water is essentially incompressible.

In the ideal case of no loss, all of the [hydro]static pressure difference between the tank and atmosphere is converted to velocity pressure as the flow field constricts (not expands) and accelerates to enter the nozzle. You use Bernoulli's equation to solve for V.

In the real case, we just need to subtract the pressure loss due to friction and unstable flow before solving for velocity. For a poor transition, it can be as much as half the velocity pressure.

 

[Gabe805]

Ok, I guess I am just confused where the pressure goes from inside the spout. What causes the water to come out of the spout? Is it gravity or pressure or a mixture of both?

 

[Rippetherocker]

Ok, I guess I am just confused where the pressure goes from inside the spout. What causes the water to come out of the spout? Is it gravity or pressure or a mixture of both?

Since its an open tank the pressure above and below is the same i.e. atmospheric.
The water particle at the bottom of the tank experiences a load of the water column above it which is PRESSURE. The load is there because all of the water is being pulled by gravity but the bottom particle has nowhere to go, its being squished by a pressure.
As the spout is opened the particle can now fall freely and is essentially a falling drop.
Lets say YOU (water column) are standing on a CHAIR (bottom water particle) in a helicopter(tank bottom). The chair is experiencing the pressure of ur weight.
Now what happens if suddenly under the chair there develops a HOLE( spout)? Both the chair and you will fall. Will the chair still experience your weight i.e. pressure? NO. Both of you are freefalling.

I can't make it any simpler. The PRESSURE is due to GRAVITY!

 

[russ_watters]

Sorry I missed the follow-up:

Ok, I guess I am just confused where the pressure goes from inside the spout. What causes the water to come out of the spout? Is it gravity or pressure or a mixture of both?

Gravity creates the pressure. It's a type of pressure called hydrostatic pressure:
http://en.wikipedia.org/wiki/Hydrostatics

Bernoulli's principle tells how different forms of pressure are related and can be converted from one form to another:
http://en.wikipedia.org/wiki/Bernoulli's_principle

Imagine you have a plastic bag full of water, with a hole in it. Water might pour out slowly. Now step on the bag. Water shoots out, right? You've just simulated what would happen if a lot of bags of water were piled on top of each other -- or if they were all in one container with a hole at the bottom.

 

[Gabe805]

Since its an open tank the pressure above and below is the same i.e. atmospheric.
The water particle at the bottom of the tank experiences a load of the water column above it which is PRESSURE. The load is there because all of the water is being pulled by gravity but the bottom particle has nowhere to go, its being squished by a pressure.
As the spout is opened the particle can now fall freely and is essentially a falling drop.
Lets say YOU (water column) are standing on a CHAIR (bottom water particle) in a helicopter(tank bottom). The chair is experiencing the pressure of ur weight.
Now what happens if suddenly under the chair there develops a HOLE( spout)? Both the chair and you will fall. Will the chair still experience your weight i.e. pressure? NO. Both of you are freefalling.

I can't make it any simpler. The PRESSURE is due to GRAVITY!

Thank you. I understand now.

 

[Gabe805]

Sorry I missed the follow-up:

Gravity creates the pressure. It's a type of pressure called hydrostatic pressure:
http://en.wikipedia.org/wiki/Hydrostatics

Bernoulli's principle tells how different forms of pressure are related and can be converted from one form to another:
http://en.wikipedia.org/wiki/Bernoulli's_principle

Imagine you have a plastic bag full of water, with a hole in it. Water might pour out slowly. Now step on the bag. Water shoots out, right? You've just simulated what would happen if a lot of bags of water were piled on top of each other -- or if they were all in one container with a hole at the bottom.

Makes sense. Thank you for explaining it to me!