“20000 Leagues Under the Sea” Part1 Ch12

Question 1: Captain Nemo gives the dimensions and displacement of the Nautilus as follows:

“Here, M. Aronnax, are the several dimensions of the boat you are in.  It is an elongated cylinder with conical ends.  It is very like a cigar in shape, a shape already adopted in London in several constructions of the same sort.  The length of this cylinder, from stem to stern, is exactly 232 feet, and its maximum breadth is twenty-six feet.  It is not built quite like your long-voyage steamers, but its lines are sufficiently long, and its curves prolonged enough, to allow the water to slide off easily, and oppose no obstacle to its passage.  These two dimensions enable you to obtain by a simple calculation the surface and cubic contents of the Nautilus.  It’s area measures 6032 feet; and its contents about 1500 cubic yards — that is to say, when completely immersed it displaces 50,000 feet of water, or weighs 1500 tons.”

What are the dimensions of submarines today?

Answer: see http://www.milnet.com/pentagon/subclass.htm#SturgeonClass.  For example the Los Angelos class submarines are 360 ft in length, has a beam of 33 feet, a draft of 32 feet, and displaces 6,927 tons submerged. It’s speed is 25+ knots submerged.

Another website with dimensions of U.S. submarines is: http://www.nationalgeographic.com/k19/evolution_main.html

Note: the above quote of Captain Nemo probably means cubic feet of water since 50,000 cubic feet of water times the weight of water per cubic foot (approximately 62.428 lbs) equals 3,121,398 lbs.  Divided by 2000 lbs per ton this yields about 1561 tons.

Question 2: Professor Arronax posed a question to Captain Nemo concerning the bouyancy of objects increasing very slightly with depth and how the Nautilus compensated for this when diving.  Captain Nemo replied by talking about the compressibility of water:

Now if water is not absolutely incompressible, it is at least capable of very slight compression.  Indeed, after the most recent calculations this reduction is only .000436 of an atmosphere for each thirty feet of depth.  If we want to sink 3000 feet, I should keep account of the reduction of bulk under a pressure equal to that of a column of water of a thousand feet.  The calculation is easily verified.

How does one measure the compressibility of water?  How much is water compressed in volume per thirty feet of depth?

Answer 2:Compressibility of matter can be measured via the speed of sound in a substance, the relationship being:

the square of the velocity is inversely proportional  to the product of the density and compressibility

 according to the website:

http://van.physics.uiuc.edu/qa/listing.php?id=6961

This same website has another page that lists a table of compressibility of water with pressure and temperature, e.g. at 20 degress Celsius and 1000 atmospheres water is compressed to 0.9619 of the volume it would have had as a liquid at one atmosphere at 0 degrees Celsius.  Here’s a link to that webpage:

http://van.physics.uiuc.edu/qa/listing.php?id=2251

Another website that discusses the curious properties of water density with temperature and pressure is:

http://www.lsbu.ac.uk/water/explan2.html#minden

In the engineering world, the compressibility of liquids is often described by a material property called the Bulk Modulus Elasticity and can be defined as:

E = – dp / (dV / V)

where

E = bulk modulus elasticity

dp = differential change in pressure on the object

dV = differential change in volume of the object

V = initial volume of the object

the website:

 http://www.engineeringtoolbox.com/bulk-modulus-elasticity-d_585.html 

contains this definition along with a table of the Bulk Modulus Elasticity of water and other common fluids of engineering interest.

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