Why Are Atom Plant Towers Shaped That Way?

They are like a cylinder but pinched in the middle. Are they parabolas that have been rotated around a line from the “pointier” part of the parabola to infinity, going more or less along with the two legs of the parabola, or some other shape? Maybe they are like suppose you have a cylinder made out of mesh on the sides and you then turn the top circle of the cylinder so that the threads of the mesh make the characteristic pinched lshape of the atomic towers?
Also, why do they go to all the trouble to make such a difficult shape in architecture? What is coming out of these chimneys?

They’re cooling towers, not chimneys. I’ve seen other cooling towers not associated with Nuclear Power Plants that have the same shape.

That said, I don’t know why they have that shape. They do look like hyperboloids, but it’s not clear to me that this would optimize cooling while retaining a stable structure.

What comes out is water. If you see one from far off it looks like a cloud is being pushed out sometimes. I don’t know why they have that shape but I guess it must be the best design for cooling water.

They are cooling towers for the hot water that had, as steam, turned the tubines to produce power.
Their shape is such to not need fans or pumps. Bottom of this page.

I will guess that you are referring to the Cooling Towers at Nuclear Power Facilities.
The Cooling Tower produces nothing other than simple harmless (except for the heat) steam. There is no radiation or smoke.
The purpose of these towers is to cool the secondary water that is used in the heat exchanger that helps keep the coolant water from overheating. The cooling tower water never goes anywhere near the actual coolant water.
The reactor coolant water is kept under high pressure and remains very tightly sealed away from the rest of the world.
The coolant water will go through Steam Generators and through conduction the secondary water simply absorbs some of the heat from the coolant water.
Owing to the extreme heat of the pressurized coolant water, the secondary water will then turn to steam. This steam will be fed throught the turbines, forcing them to turn, which will produce electricity.
Meanwhile, the steam is then fed into the condensers which returns the steam to water. The secondary water will then flow through the heat exchangers again transferring the heat through conduction to the external water.
It is the external water that is pumped through the cooling tower to the cooling pond.
The design of the cooling tower helps to force the water to separate from a large stream pouring out into smaller droplets that can cool easier. However, the amount of steam that escapes out the top should let you know do not go anywhere near the bottom.
Anyway, this is a simplified answer. I hope that it explainss it well enough, though.

Wow! The cooling tower doctor! Is there anything that isn’t on the internet???

They are known as hyperbolic paraboloids. They are shaped that way to enhance updrafts while providing structural support. - Jinx

Note that other power plants use that type of cooling tower as well. Several coal plants I have been to use hyperbolic cooling towers. Of course, this leads everyone to believe that they are really “them radiation plants…”. These towers are used with nuclear plants for three main reasons:

  1. They are high capital cost items, but have a low operations and maintenance (O&M) cost. Since a nuclear plant already has such a high capital cost, the cooling tower is a relatively small portion of the cost of the plant.

  2. Nuclear plants are designed for relatively long lives, and the payback for the reduced O&M costs can be expected to be realized.

  3. Nuclear plants are designed to run at very high capacity factors (typically more than 90%) in order to be able to pay for themselves. Since a hyperbolic natural-draft cooling tower has a much higher reliability than a forced-draft cooling tower (no fans and pumps), it allows the plant to stay online with a lower chance of breakdown, and thus achieve the high capacity factor desired.

They aren’t just associated with power generation facilities, either. If you’d like to get a closer look, there’s a pair right next to the M-1 motorway in Sheffield, England. They’re still preserved as a historical landmark (!) after having been part of the steel mill complex on whose site one can now find Meadowhall, the largest shopping mall in Europe. The film “The Full Monty” has a brief scene of them, too. The Supertram line goes right by the bases of the towers.

Apparently yes.

And not all nuclear power plant use them either.
All Swedish nuclear power plants use sea water for cooling, and look like this. They look rather silly if you ask me.

Off topic but a bit of local rivalry.

The Trafford Centre in Manchester is bigger than Medowhall.

Aha! That’s Barsebäck power plant. I was in there just a couple of weeks ago.
Now, alert readers may wonder why a nuclear power station has a 110 meter stack atop each reactor building.
These stacks are for ventilation, and are used for the release of gases (mainly air and steam) being pumped out of the condenser. They are also used in the event of an accident. If there is an overpressure in the reactor building, the gases are pumped out of the building and cleaned by being passed through a high column of activated carbon, and then released to atmosphere. The system can withstand an overpressure of up to 6 bar. This safety system is unique in the world.

Then there are the ones at San Onofre in California.

http://www.edison.com/images/cms_images/pl2528_large_SANONOFR_6819.jpg

Made to fool spy satellites into thinking they had a close up of a nude beach.

I always assumed they had that shape because much of the internal supporting structure can be made from straight beams. See these:

http://www.math.hmc.edu/faculty/gu/curves_and_surfaces/surfaces/hyperboloid.html

http://www.cs.utexas.edu/users/amenta/kobe.html

It is hyperboloid of one sheet (not a hyperbolic paraboloid as mentioned in an earlier post).