Looking for compressibility and thermal expansion coeffecients for fresh and salt water

Using Google: compressibility fresh salt water "coefficient of thermal expansion" ... I get only 235 hits. Maybe one of them can help you.

I have also scanned hard copy graphs into an image (scanner to file), then get digital-image coordinates of characteristic points along the curves (MS Paint), and convert those digital-image coordinates to x and y axis values (Excel or Quatro Pro). So you could "do it yourself".

David A. Smith

If you have to do this use a free tool a bit more suited to the task.

I was more interested in where this data comes from i.e: Is it real collected data or does it come from a scientific calculation? Are there any other known sources apart from these USN Research ones that I have?

thanks for your help Paul.

Thanks! I calculate the necessary skew to rotate the graph by fractions of a degree and "de-skew" it as necessary, rather than only rotation by integer multiples of 90 degrees. But perhaps that is also done in "WinDIG".

Dear Paul,

Basically what you are asking for is an equation of state for water from which you can calculate these properties. Usually, even when someone is fitting experimental data, they have some kind of a theoretical equation of state (such as a viral expansion) and they determine the coefficients to best fit the data.

For pure water, probably the best you can do is the International Association for the Properties of Water and Steam (IAPWS). NIST sells FORTRAN code that will calculate these properties. See:

Again, this is just for pure water, not seawater.

From what you described, it sounds like you have just a couple of graphs out of this publication, not the entire publication. If you could get hold of the entire publication, they might tell you the formulas they use.

I may have found your old NOLTR report at

Here is their description:

Accession Number : AD0635120 Title : SPECIFIC VOLUME, THERMAL EXPANSION, AND ISOTHERMAL COMPRESSIBILITY OF SEA WATER. Corporate Author : NAVAL ORDNANCE LAB WHITE OAK MD Personal Author(s) : Wilson, Wayne ; Bradley,David Report Date : 02 JUN 1966 Pagination or Media Count : 52 Abstract : The specific volume has been measured for distilled water and for five samples of sea water near salinities of 10,

20, 30, 35, and 40%. These measurements were obtained for temperatures between 0 C and 40 C, and for pressure up to 14,000 psi. The Tumlirz equation of state has been fitted to the experimental data by the method of least squares. This equation was then used to compute tables for the specific volume, the thermal expansion, and the isothermal compressibility over the full range of variables considered. This data is compared with that obtained from the works of other authors. Descriptors : (*SEA WATER, THERMODYNAMICS), THERMAL PROPERTIES, EXPERIMENTAL DATA, TABLES(DATA) Subject Categories : PHYSICAL AND DYNAMIC OCEANOGRAPHY THERMODYNAMICS Distribution Statement : APPROVED FOR PUBLIC RELEASE Search DTIC's Public STINET for similiar documents. Members of the public may purchase hardcopy documents from the National Technical Information Service.

It looks like you'll have to pay some money to the NTIS to get a copy of the report, but it sounds like it may have the equations you need.

Also, I was able to download a pdf of this article: Daniel G. Wright, "An Equation of State for Use in Ocean Models: Eckart?s Formula Revisited," Journal of Atmospheric and Oceanic Technology, Volume 14, Issue 3 (June 1997) pp. 735?740. It looks like it may have what you need. The references look interesting too.

Olin Perry Norton

What he said. WinDig is D. Lovy's love gift to the universe: it can control a scanner - or use bmps from elsewhere. Can pick out several line colors and digitize smoothly, precisely, accurately. There are other applications called WinDig too - but this is the plot digitizer.

Brian Whatcott Altus OK

at

OF SEA WATER.

five samples of sea water near salinities of 10,

0 C and 40 C, and for pressure up to 14,000 psi.

method of least squares. This equation was then

isothermal compressibility over the full range of

of other authors.

DATA, TABLES(DATA)

Technical Information Service.

Thanks very much for these links , these sites are just what I was looking for. I am trying some cubic regression to fit the curves on the compressibility graph but the curve is different at any given pressure or temperature. So I have 6 curves on this graph ,1 bar, 100 bar, 200 bar....500 bar and with a cubic regression , at 1 bar, of

-9.9993065667812e-11X^3 + 1.3862700228823e-8X^2 + -5.2356362249489e-7X

• 5.0846305263158e-5 So if this is my equation for a curve at 1 bar and it's a different equation/curve at 100 bar, 200 bar etc , how do I find a trend in equations so I can find a value at maybe 126 bar. So the equation changes for each pressure, and its not not just a case of doing regression on one curve to find a calc. ;-) I'm sure these links will be very usefull. :) thanks for your help. Paul

Fit a surface, not a line.

I'm not sure I know how to do that , but I will look into it.

thanks for the help Paul

Dear pchristor:

MathCAD (and probably more) can help.

David A. Smith

You might check out some of the external references at the bottom of:

Paul,

I'm the author of a nonlinear regression curve fitting program called NLREG (see

If you will send me your data via e-mail, I'll try to fit a surface to it.

Dear Paul,

I hope you can get a copy of the Wilson and Bradley report. I think that is the source of your old graphs. If so, it sounds like the full report will have the curve fit coefficients you need. It's a nuisance that you'll have to order it from the NTIS, but I think you should, if you really use this stuff on a regular basis.

Let me give you a word of advice about curve fitting in general:

I'm a strong advocate of doing curve fitting with equations that actually mean something -- equations that have some theoretical basis in terms of a model of the system you're trying to describe. It may not be a perfect model, but you can fix that by including some fudge factors in your curve fit.

That's apparently what Wilson and Bradley did. They took an equation of state, and used fitting to get the values for the coefficients in that model. I'm not familiar with the Tumlirz equation of state, but maye you can Google it.

Many people like to use polynomials to do curve fitting. You need to be careful with that. If you can't get a good fit with just a few terms, then adding more terms can create a polynomial that goes crazy in the intervals in between the data points.

Olin Perry Norton

Dear Olin Perry Norton:

"Olin Perry Norton" wrote in message news:eptqsq$ibb$ snipped-for-privacy@nntp.msstate.edu... ...

In those cases, I have had good luck:

1) solving for the independent variable in terms of the dependent variable, or 2) using the method of "orthogonal polynomials" ... to get better fits.

David A. Smith

The greatest thing since sliced bread... once I figured out you pick a data point by double clicking on the "curve of interest".

David A. Smith

I've used Engauge Digitizer (download from Sourceforge) to digitize scanned graphs. It uses three points to define the coordinates and figures out the rotatation and non-orthogonal axes. I've never used WinDig so I can't compare but it seems to have very similar features based on the WinDig website.

Dave Parker West Palm Beach, FL, US

Dear dgp:

Yes, you are correct. One or both axes can be assigned as logarithmic also. Only downsides are the "Windows 95" interface (no long file name support), and the basics of program operation seem not to be listed in the help file. But it way cool not to have to do this in Paint + Excel.

David A. Smith

??? There are the Hints on the main WinDIG Help Index page and then there is the Getting Started entry.