Hi there.
I have some old printed graphs which I use to get values for
calculations, namely:
compressibility of fresh water

compressibility of sea water (salinity 3.5%)
coefficient of thermal expansion of fresh water
coeficient of thermal expansion of sea water (salinity 3.5%)
These hard copies have the ref: USN RESEARCH NOLTR 66-103
These graphs are suitable for water from 0 to 500 bar, and from 0 to
20 C.
Does anyone know where I can get a soft version of these graphs, or
does anyone know a mathematical function to reproduce these graphs?
TIA
Paul.

On Jan 31, 5:18 am, snipped-for-privacy@yahoo.co.uk wrote:

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

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.

Dear Ed Ruf:
On Jan 31, 9:54 am, Ed Ruf <"Ed Ruf (REPLY to E-MAIL IN SIG!)"

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".

On Wed, 31 Jan 2007 11:54:05 -0500, Ed Ruf <"Ed Ruf (REPLY to E-MAIL

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

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

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

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: http://www.nist.gov/srd/nist10.htm
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
http://stinet.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier 0635120
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

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

On 1-Feb-2007, snipped-for-privacy@yahoo.co.uk wrote:

Paul,
I'm the author of a nonlinear regression curve fitting program called NLREG
(see http://www.nlreg.com ).
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

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

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