## Tuesday, May 4, 2010

### We Have a Winner!

We have a winner for our “fish out of water” estimation contest.  The question: How far would the oceans sink if we took all the fish out?

According to Wikipedia, the biomass of marine fish is 800-2000 million tonnes, so I’ll assume 1500 million tonnes.  Biomass is the total amount of mass a set of organisms has.  Fish (or at least live fish) don’t float, nor do they sink.  This suggests their density is about equal to that of water 1.0 g/cm3.  From these numbers we can compute the total volume of fish,

volume = (mass) / (density)
= (1500 million tonnes) / (1.0 g/cm3)
= 1.5×109 m3.

The ocean comprises about 71% or 3.6×1014 m2 of the Earth’s surface.  From this, we can compute how much the oceans would sink by taking all the fish out,

depth sunk = (total volume) / (area of the oceans)
= (1.5×109 m3) / (3.6×1014 m2)
= 4.2 microns.

That’s about 240 times smaller than a millimeter.  This may seem small, but if you’ve ever been fishing, you know that fish are much more rare than you’d expect.  Most of the time you look over the side of the boat you’ll see nothing.

Congratulations to our winner, Nathan Moore!