Thursday, March 01, 2007

Bouyancy and the Arctic

Dang, I hate to bump such a controversial topic off the top line. Oh well. So this year is apparently the International Polar Year. Scientists from several nations will be pooling their resources to conduct a wide range of studies on the Earth's poles, including its polar ice caps. With all the hullaballoo regarding global warming recently, you have probably heard that the arctic sea ice is supposed to melt and raise the sea level by many feet. That got me thinking about bouyancy.

Bouyancy is the force of a displaced fluid (or gas) acting on the object which has displaced it. The force is equal to the mass of fluid displaced, and the displaced mass is related to the displaced volume of fluid. So if an object is submerged in water such that 1 cubic meter of the object is under water (thus displacing 1 cubic meter of water), then the bouyant force on the object will be 1000 kg/m^3 * 1 m^3 * 9.8 m/s^2 = 9800 newtons.

Whether or not an object will float depends on its density and sometimes its shape. If the density of the object is greater than the density of the fluid, it will sink, otherwise it will float. So, if an object has a density half that of water, it will float with half of its volume above the water and half below. The exception is if the object is shaped so that air is forced down under the water level along with the object- thats how large steel ships can float.

So... the arctic. Assuming for the moment that the arctic ice is all floating and is not supported by any land, lets treat it as a bouyancy problem. Lets pretend the density of ice is 80% that of water (its not, but it makes the math easy and doesn't change any physics). If a block of ice is floating in water, 80% of it is below water, and 20% above. Lets now say that the ice melts. What happens to the water level- does it go up or down? If you said up, you're wrong. If you said down, you're also wrong. It should stay the [1]same- the 20% above the water level will contribute to an increase in water level of .8 * .2 = .16 of the volume of the original ice. But the ice that was below the water level will also melt, freeing up some space: .8 * .8 = .64. So the total volume that is now below the water level is .64 + .16 = .8, which was what was originally below the water level, so theres no rise.

When you read hysterical news articles about the sea level rising and submerging entire cities because of the melting arctic ice, don't believe it.

Unfortunately, Greenland and Antarctica are completely different. No bouyancy there to save us [2].


[1]. If the sea ice is all fresh water ice, then it will actually raise the sea level by 4 mm- not even enough to flood New Orleans.

[2]. See this rather long article for more details of Antarctic and Greenland ice melt.


Cabeza said...

Very interesting post, Nick. It was nice to get a little refresher on physics and remind me that I enjoyed that class in high school. You could totally be the next Mr. Severson.

Part of the ice-melt problem is that people like to be alarmist. Physics can't solve that.

One question--on note 1. Isn't all ice fresh water ice? I thought salt wouldn't freeze into ice.

Nick said...

You're right- strictly speaking and ice crystal will contain no salt ions. But As the water crystallizes it can trap bubbles of ice water, and when the water in those bubbles all manages to freeze (at -21 C- the point when the water has been saturated with salt), the ice will have pockets of solid salt and possibly air, making it even less dense than water. See this page for more info.

Cabeza said...

And as a cheap plug, in the continual effort to renew my personal blogging, I have placed a new post on Fruit at the Bottom.

Julie C said...

sounds like I'm gonna have to do an experiment - do you know how much salt is in salt water? then I could freeze some salt water in ice cubes, then float the ice cubes in a clear pitcher of salt water with a lid (because I don't want evaporation to really be a factor), and watch and measure the height of the water to see if it changes. Fun!