Compression Of Water

[Khandro]

I'm reading Leonardo's notebooks, and in "The Nature of Water" he writes,
"........., seeing that water cannot be compressed within itself like air."
No pun intended, but does this assertion from the fourteen hundreds still hold water today, - can water be compressed?

[Khandro]

society; carrot juice isn't water and must contain a large amount (?) of fibre and other matter which might react differently to water. One thing is certain, if you empty out a litre of water, you will be able to return that litre to the vessel exactly, allowing for a drop or two, and it will still weigh 1 kilogramme.

[jomifl]

Khandro, not theoretical at all perhaps hypothetical depending on your DIY competence. :-) Having constructed the above mentioned device what you do next is measure the amount of deflection of the rod when the weight is put on top (should be about 2%?) then add more weight and measure the deflection each time. Thus you get a plot of volume against pressure. This is what is known as empirical science. It is how we find things out. You too can do this, but it's a lot easier to look it up.
http://www.engineeringtoolbox.com/fluid-…

[jomifl]

Well that link didn't work so try this one;
http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html

[Khandro]

Thanks jom. but you know I'm only a simple-minded guy, the chart is a bit too advanced for me. What I'm asking in a nutshell is; if you add a ton of weight to you device will the water continue to compress much beyond 2%. Common sense seems to suggest that the process cannot be limitless.

[jomifl]

OK Khandro, if you look at the chart at for example the 1bar (pressure)curve (blue)where it intersects the 5 degrees C vertical line(black)you have a density of almost exactly 100kg/metre cubed. If you go up the 5C line where it intersects the 25 bar curve you will see that the density has increased to about 1006 k/m3 ie. the water has been compressed. If you follow up the 5C line you will see that the density increases by about the same amount for every increase of 25 bar, you can see that the water continues to be compressed as the pressure increases. This will presumably continue until the water becomes a solid when a different law will apply. This is outside the limits of the chart and my knowledge. :-)

[Khandro]

Many thanks jom, but is this theoretical? I know that the pressure can be increased, but will the water become smaller in volume, thereby showing Leonardo to be wrong when he said [it] "cannot be compressed within itself", (given the small degree of error we have accepted.)

[jim360]

The model used to generate those graphs breaks down at or near a pressure comparable to a property of water known as "Bulk modulus", when the density is predicted to suddenly be infinite and then become negative -- so the behaviour cannot continue indefinitely, no. I'd expect a more reasonable graph to go something like: density increase (so volume decreases) as this model predicts up until a certain point where electromagnetic forces dominate, and then at some point that will break down as the force applied overcomes these forces, and the water collapses in on itself.

If I find time I'll try and draw and share a graph explaining what I mean, but it shouldn't be treated as too accurate as I've not yet got around to doing any calculations.

[jomifl]

Leonardo was correct enough for the condtions and technologies of his time. The chart would almost certainly be based on experiments as even you or I could make an apparatus (as in my earlier post) that could make the measurements. The pressure at the bottom of the Marianas trench (30,000 feet) is roughly 1000 bar ( 1 bar per 30 feet depth) so is outside the range of the chart but the relationship of density with pressure doesn't seem to change significantly between 1 bar and 200 bar and I can't see any reason why it would change much beyond 1000 bar, I imagine it would still be compressible even if not to the same degree.

[Teddio]

Without sounding too disrespectful, Leonardo was wrong. He had no way of performing a simple experiment where he could investigate the relationship between volume and pressure for water, using a large range of pressures. If you take a litre of water, and expose it to very high (but earthly) pressures, then it will decrease in volume. The mass must stay constant so the density will increase.
Here's an interesting question on a related topic: what volume of liquid will result if one litre of pure water is mixed with one litre of pure ethanol ?

[jim360]

That's like saying Newton was wrong about mechanics. It makes Science black-and-white and fails to capture the middle ground in between -- that Newton was right up to a particular degree of accuracy and over a particular range. Relativity is a correction and not a replacement to Newton's work; The density behaviour of water is a correction to the view that Water is incompressible -- but over pressure changes away from 1 atmosphere of the order da Vinci was able to apply, he was right.

[Old_Geezer]

The prediction was zero compression, the result was some compression. Isn't that an infinite % error ? (My calculator tells me it's an error :-( )

[jim360]

Alternatively, the prediction was d(p) = constant -- density as a function of pressure is a constant, when in fact the law is of a form:

d(p) ~ A/(1-p/E)

where A is some constant and E is a very large number. To first order this is approximately:

d(p) = A*(1+p/E) = A + (A/E)*p +Order(p^2)

The ratio A/E is very small, so that for small values of p density is approximately constant -- over a range of pressure from 1 atmosphere to about 400 atmospheres the correction to the law:

density = constant

is approximately 2%.

[jomifl]

So, I think your question has been answered by a joint effort.
Leonardo was pretty close to being correct and in practical terms he was to all intents and purposes.
Water is slightly compressible and can almost certainly be compressed beyond the degree of compression found at the deepest point of the oceans.

[Khandro]

Thank you one and all! Another fascinating thing in "The Nature of Water" is that he seems to be the first person (not mentioned by Greeks or Romans) to record a phenomenon about ripples. Everyone knows what happens when you pitch a stone into the still water of a pond; a series of ripples radiate out from the point of entry, but do you know what happens when you pitch two in at the same time a few yards apart? - go see, it's amazing!

[jim360]

Double-slit diffraction. Sometimes it's worth stepping back and just appreciating these patterns for what they are.

[Khandro]

jim; Quite! I'm re-reading a 3 volume collection of Leonardo's notes, well over 800 pages, and it's full of such 'simple' observations,- sort of scientific haiku's, things you know, but don't really. Like, when a wheel turns, the centre revolves at a slower speed than the edge, but when water revolves as in a whirlpool it is the centre that revolves faster than the outer.
Of course there is the scientific explanation, but as you say; "stepping back" and observing can be life-enhancing.

[ossian]

This is very strange indeed. How big was the bottle of carrot juice, two litres, 500 mls ? One third of a cup is a lot of juice. Can you estimate what percentage of the original volume such an amount represents. Perhaps you might have the makings of a little business here just by decanting and refilling bottles of carrot juice!!! I look forward to hearing the results of a repeat of the operation.

Ossian

[ossian]

Well, Society, Have you repeated the experiment yet with the bottle of carrot juice???????

Ossian