Free energy from high altitude towers?

RGClark

On sci.astro there is discussion on whether there would be air flow from bottom to top of a high hollow tower given that it was tapered from bottom to top.
Think it's feasible?


Bob Clark




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Newsgroups: sci.astro, sci.physics, sci.engr.mech, sci.space.policy
From: rgregorycl...@yahoo.com
Date: 30 Apr 2005 05:52:28 -0700
Local: Sat,Apr 30 2005 5:52 am
Subject: Re: An atmospheric envelope for ground-based telescopes.


operator jay wrote:
> Therefore to have the pressure
> > remain constant with altitude you could have the tower around the
scope
> > have a cross-section that decreases exponentially with altitude at
this
> > same rate. Then the tower could be open to the atmosphere at the
top
> > since the pressure equilibrium will prevent air from rushing down
to
> > the bottom of the tower.

> That doesn't seem right. If air wanted to rush down, why not let it
rush
> down, and install a turbine for free energy. And, if air were
rushing
> around, wouldn't it rush UP, from high pressure to low pressure?



If you had a straight cylindrical tower with no taper then the air
would equilibriate just as it does with the normal atmosphere and you
would have the same approximate exponential decrease of pressure with
height with no air flow between top and bottom.
But you do raise a good point. It would appear that if you suddenly
opened the bottom of a tapered tower, then since the pressure was
uniformly at 10 mbars throughout the tower, the outside air at normal
pressure should rush in and up the tower.
It would appear that this should continue. For imagine a tapered tower
closed at both the top and bottom. No matter what pressure we put in
this tower initially it will be maintained at constant pressure
throughout its entire length. So if normal atmospheric pressure was at
the bottom of this closed tower it would remain so all the up to its
top at 100,000 ft. Now if we open this tower at the bottom, there
should be no flow of air in or out because the pressure at the bottom
is already at normal pressure. Then by opening it at the top there will
be a pressure difference at the top and you should get air flow out at
the top and therefore air in flow at the bottom.
However it would appear the pressure would not remain at normal
pressure in the tower when you have the air flow because of the
Bernoulli principle that says when the velocity increases the pressure
decreases.
The question is how much would it decrease.


Bob Clark

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Newsgroups: sci.astro, sci.physics, sci.engr.mech, sci.space.policy
From: "Robert Clark" <rgregorycl...@yahoo.com>
Date: 30 Apr 2005 12:23:04 -0700
Local: Sat,Apr 30 2005 12:23 pm
Subject: Re: An atmospheric envelope for ground-based telescopes.


George Dishman wrote:
> <rgregorycl...@yahoo.com> wrote in message
> news:1114869854.713927.303200@l41g2000cwc.googlegroups.com...
> > George Dishman wrote:
> <snip>
> Ok, I misread the quote, I thought the taper
> went the other way.

> > For a tower tapered *smaller* as you go upward there won't be an
> > upward force due to the tapered sides.


> Correct, there would be a downward force on
> the outside of the tower which is a small
> fractio of the crushing force when the inside
> is evacuated.


> Once the air enters, there will be an equal
> upward force on the inside so the structure
> no longer carries the extra force (weight)
> of the outside air, but that upward force
> has an equal-but-opposite downward force on
> the air, otherwise the air accelerates in a
> direction to reduce the unbalanced force.


> > In the equations on the "Hydrostatic equilibrium of the atmosphere"
> > page, the cross-section area A won't cancel out if it is changing
with
> > z.


> Split the column into numerous narrow columns
> side by side. Each column either has the
> downward force of the tube or open space at
> the top. Air moves sideways to equalise the
> pressure at any level so the columns ending
> on the inside of the tube have the same
> pressure as a free-standing column, and the
> pressure for that is the same whether it is
> inside or outside the tube.


> Bottom line is that the air pressure inside
> and out is the same at any given height once
> equilibrium is reached. Otherwise we could
> drill a small hole halfway up, put a turbine
> in the hole and generate free power forever.


> George



That such power *might* be possible doesn't prove this wouldn't work
any more than the fact that the drawing of power from flowing rivers
would be "free" means that can't work.
You might be able to use the Bernoulli principle to determine if there
is a velocity change between the ends given there is a pressure
difference at the top and bottom.
This is usually applied to incompressible fluids but Professor M.S.
Cramer in this post suggests you can apply this energy principle even
for compressible gases as long as the Mach number (ratio of the speed
to the speed of sound) is low:

Newsgroups: sci.astro, sci.physics, sci.mech.fluids, sci.engr.mech,
sci.space.policy
From: M.S. Cramer <macra...@vt.edu>
Date: Mon, 08 Nov 2004 12:03:37 -0500
Local: Mon,Nov 8 2004 9:03 am
Subject: Re: Question about Poiseuille's formula.
http://groups-beta.google.com/*group...72f6dc7*003aca

In that thread the dividing line was given as about Mach 0.3.


Bob Clark

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Danger

Okay, I've had way too much beer to try reading all of that. My first instinct in this is that if you open the top and bottom of a sealed tower (sealed at MSL pressure), the pressure differential between the top and bottom environments would cause air to rush out of the top for equalization, but none would enter the bottom because that part is already in equilibrium with its surroundings. You'd end up with the same pressure gradient inside the tower as outside. A turbine at the top would get power from the initial outrush, then go idle. It's definitely not free energy, considering how much you would have to expend to build the thing in the first place.

russ_watters

Not correct (and Danger is). Pressure inside a tower is identical to the pressure outside unless you actually evacuate (or pressurize) the tower. Air pressure is simply the weight of the column of air above where you are measuring the pressure.

One concept which would work is heating air at the bottom of a tower (can be done by the sun) and allowing it to expand and flow up through the tower. The taller the tower, the more energy generated. Trouble is, you need a really tall tower for it to be useful.