Re: [Phys-l] About drinkable water resistivity

[Brian Whatcott <betwys1@sbcglobal.net>]

At 07:13 AM 7/4/2008, M. Roberto Carabajal Perez,  you wrote:
> Hello:
>
> I would appreciate  that you commented about an experiment we did
> trying to show common water resistivity. We submerge both analog
> multitester testing probes in a plastic recipient (5 litres) full with
> water and we obtained a reading near 15000 ohms. The measure was
> repeated with different low current densities.
> We observe that inside tank limits, resistivity practically didn't vary
> with distance among probes. What could be an acceptable model to explain
> this ?.  Can we make relations with measuring earth resistivity problem
> ?
>
> My best regards.
> Roberto


The usual model for electrical conductance is the measure
of current for a particular test material cross section area,
multiplied by the distance between the test electrodes.
This is factored with a coefficient representing the
particular material, and  a factor representing the
temperature at which the test is taken.

 We could represent this algebraically as resistance R
 = rho times distance L / cross section area A
where rho is the label we apply to the innate resistivity
coefficient  of the material (at some temperature),
 or in short,       R  = rho.L  / A

You ask why, if L the separation is increased,
 why does the resistance not increase?
The other terms which could co-vary are the material resistivity rho
 or the effective cross-section A.
It would be relatively easy to decide which of these parameters
 is varying.

For example, if the meter probes were placed near each end of a
submerged glass tube of constant cross-section: then if the electrode
 separation were varied, the effective cross-section could not.
  If cross section is the variable of interest, we expect the resistance
 to decrease as electrodes are  placed closer inside the glass tube.

I have a water testing meter which can be obtained quite cheaply
 (~$25).   It has two stainless pin electrodes about 6 mm long,
 placed about the same distance apart.    This indicates in terms
of parts per million total dissolved solids, but really measures
water conductivity in microSiemens per centimeter and applies
a factor of about 0.7 to this value.

When I tested two water samples, I got these results:
tap water 470 ppm total dissolved solids.
distilled water  5 ppm  tds.
The EPA sets an upper limit for water authorities to aim
at of 500 ppm.

To address your second query: if we can treat earth bulk
conductivity as reasonably constant for reasonable depths, then
your experimental results might well apply here too, so that
 surface electrode separation is not particularly critical.

I should mention the temperature dependence of resistance - you
are aware that incandescent lights have much higher resistance
 when glowing white hot than at room temperature.
With water the relation runs in the other direction - resistance
 may drop between 2 to 8% per degree Centigrade increase,
depending on water purity and on temperature - it is markedly
 non-linear with temperature, modeled at times by a
five term polynomial.


Brian Whatcott    Altus OK    Eureka!