Location: Outside U.S.
Date: February 2009
I am doing a project on the physics of submarines
including a study (combined with literature) of Jules Verne' "Vingt
mille lieues sous les mers". I need to know exactly how
incompressible water is. A friend of mine told me, that some company
had built a machine capable of compressing water to 9/10 of its
normal size. How much pressure would you need to do that? Let us say
sea water density is 1 (just to do it easy) what would it be in a
depth of 10 km (about 1000 bar)? I would appreciate any help on any
of the above questions. Andreas
Any number of chemical and/or engineering handbooks can you provide you with the
numbers. For example the CRC Handbook of Chemistry and Physics. You have to be
careful to keep the measurements in a consistent set of units. You also have to
be careful to distinguish what is being compressed. There are about a dozen
different crystal structures of solid water.
The compressibility of water is influenced by its temperature. The
numbers I found were that its compressibility at 0°C is 5.1 x 10^-5
per bar, and this decreases to a minimum of 4.4 x 10^-5 per bar at
45°C. If you take the 0° value, you can easily calculate that at a
pressure of 1000 bar, a specific volume of water at atmospheric
pressure, will compress about 5.1%, hence its density will have
increased by that amount. Looking at it the other way, the water will
have compressed to a little less than 95% of its original volume.
To compress it to 90% of its original volume at 0°, you would need a
pressure of around 2000 bar, which is equivalent to over 18 km of
depth. The deepest point in the ocean is only 10.9 km.
It should be pointed out that pressures of 2000 bar are not that hard
to reach in industrial equipment. Modern plastic injection molding
machines commonly reach 1000 to 1500 bar, and even fuel injection
systems in modern diesel motors can reach pressures approaching 2000
bar. Water jet cutting machines (that cut through hardened steel plate
using only a jet of water) can operate at pressures as high as 6000
The Internet makes it easy to look up the compressibility of water (or
the bulk modulus of water, which is the inverse). The modulus is about
2.2 billion pascals. To attain a 10% reduction in volume would require a
pressure of about 200 million pascals or 30,000 psi. This pressure can
easily be attained in a high pressure cell, or even with a mechanical
pump. (In a modern diesel engine, the fuel is squirted into the
cylinders at about 30,0000 psi).
It should be kept in mind that the compressibility/modulus numbers are
only correct for (relatively) small amounts of compression. That is
because for small amounts of compression, the behavior is what is called
"linear" and a single number can be used. The amount of squeezing is
proportional to the amount of pressure. For very large amounts of
compression, someone needs to do the experiment and determine the value
for a particular pressure. Also, the compressibility/modulus numbers
depend on the temperature.
At a depth of 10 km the pressure would be about 100 million pascals,
1000 bar, and the water would be compressed about 5%. The density would
thus be about 5% higher.
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