### Re: Depth, Pressure, Density of Water

Date: Thu Oct 15 10:49:36 2009
Posted By: Rob Fatland, Staff, Research and Education, Freelance Science Educator
Area of science: Physics
ID: 1253714058.Ph
Message:
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Thanks for your question. I will cover a few physical aspects about water
and energy; but with regard to exploding nuclear devices under water to
move rock I will refer you to the book The Firecracker Boys.

1 tonne of TNT is 4000 Joules of energy; this means a megaton is 4
billion Joules of energy. By comparison a typical cyclone (hurricane)
releases something like 700 megatons of energy every day. In other words:
Nuclear blasts are very hot and locally destructive but they are peanuts
in comparison to the earth's energy budget.

Water is for all intents and purposes incompressible. It's density
depends on how much salt is dissolved in it and it's temperature; you can
reserach this if you are interested. But at the bottom of the trench and
at the top of the water column the density doesn't change. The pressure
does. The pressure varies with depth. Hence at the bottom of the trench
the pressure is quite high and the density is about 1000 kg per cubic
meter of water. By comparison rock might have a density of 4500 kg per
cubic meter.

Suppose you are able to focus your blast to try and lift a column of
water of one hundred square meters in cross section (say a disk about 12
meters across) and 7.5 miles high (approximately 12,000 meters high).
Let's solve for how high you can lift this column of water using 4
billion Joules of energy.

The mass of the water will be the density (constant as noted) times the
volume. The volume is 120,000 cubic meters of water (10 meters x 12,000
meters). The density is 1000 kg per cubic meter. You should check my
calculations because I am doing this from memory.

A Joule of energy is a newton - meter. A newton is a unit of force, one
kilogram meter per second^2. Let's suppose your column of water rises z
meters; what is z? You have 4,000,000,000 Joules available and your water
column weighs 120,000,000 kilograms. One kilogram exerts a force of about
10 Newtons. So you have to support 1,200,000,000. I think by dividing
1,200,000,000 into 4,000,000,000 (you get about 3 1/3) gives you z. So
supposing you can focus the energy entirely into lifting the water
column. More likely your energy goes in all directions and your water
column doesn't do very much... in fact I suspect that most of your
detonation energy will go into vaporizing water, creating an enormous
pocket of steam. Whether this bubble of steam would reach the surface or
simply get mixed back into the ocean I don't know; but I suspect it would
mostly get mixed back into the ocean.

Hope that helps; it may not be correct but some of the ideas are probably
ok.
Best
-Rob

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