the bulk resistivity of tap water

I don't understand the question, the conductivity of tap water varies with it's chemical composition, in softwater areas it can approach zero, in hardwater areas it is around 0.7milli seimens.

Google conductivity of water.
Del

Assume the 10 number.

May we also assume this is a homework question?

Why on earth would you use needle point electrodes? The easy way (well, it ain't easy, but it's possible), is to use two fairly big parallel plate electrodes.

No homework. Those days are long gone for me. <cr> For two parallel plates one meter square with a cubic meter of water between them the problem is easy. The generalized problem is current flow through a conductive medium. I suppose the current flow would look like lines of flux, with some voltage gradient. <cr> I just need to be pointed in the right direction for the governing equations. <cr> Thanks, folks.

Plenty of information on the internet. Try this good link first:

https://www.snowpure.com/docs/thornton-presentation-conductivity-measurement.pdf

It's like Del said. Pure water is a dielectric. Impurieties will vary the resistance.

It also varies with temperature.

Local well-water conductivity is ~750μS/cm @ 15degC, for reference.

I can't imagine any circumstance where a formula will be any help other than to get you into the ball park.
If you are trying to build elecrodes, just build 'em and test 'em. If you actually want to measure conductivity you should use AC (about 15v p to p is fairly standard, or pulses to avoid polarising the water.
If you have an actual problem I'm sure we can help, if you tell us what it is...If you just want to play with maths I'm out.
Del

The actual problem was/is determining the current flow through and voltage gradient along a person in a swimming pool or a shower (not a KBR shower, though) who was getting a shock,assuming the contact area approaches zero. First the math, then wait for someone else who gets a shock under these circumstances and wants to know if the various fixes the electricians try will actually work before he/she climbs back into the pool or shower. It has to work on paper first, just like with all engineering.

It has to work on paper first, just like with all engineering.
Tell that to an Aborigine making a boomerang or a medieval bowyer.
Del

Try the following links.

http://en.wikipedia.org/wiki/Residual-current_device

http://en.wikipedia.org/wiki/Earth_leakage_circuit_breaker

DONT try and test and DONT let anyone get near the pool!!

From what you are describing there is an insulation fault and there is every possibility that someone entering the pool could be electrocuted.

http://www.google.co.nz/search?hl=en&num=100&ei=i5RbStSPBYWIsgO2wdGDCw&sa=X&oi=spell&resnum=0&ct=result&cd=1&q=pool+electrocution&spell=1

Get the electrician to check the pump motor and earthing system (also pool lights and any other controls that may be at 110V AC or above potential) before someone is killed. Electricity is not a toy.

The conductivity for any substance will approach zero for any substance as the cross sectional area approaches zero. For to calculate the conductance from conductivity G=σA/l (σ≡conductivity of the material, A≡Area, l≡length) So an infinitly slender swimmer will not be electricuted no matter what gradient of voltage exists in the water. Another way to think of this, if there's nothing there then there's nothing to conduct.

But people can easily get killed this way. The water will act almost like an impedance matching network to assure the most amount of power transfer to the swimmer for instead of current being applied to the small contact area of bare wires, the entire surface area in contact with water will carry current, despite water being considered a dielectric or insulation.

relevant application?

Yeow!!! Why does the opening music from MASH come to my mind.

Maybe the video on this thread would help?
Del

There's some problems with this post. I'm not sure what the location is, but in the US you're probably looking at jail time for "waiting for" somebody to feel a current in a pool. Locations like swimming pools and showers cannot (I mean may not, can not, shall not) depend on the lack of conductivity of the water as a safety measure. You must assume something like seawater. You have to use measures like good wiring/grounding and GFCI's to prevent this. The measurement has to take place in the line supplying the pool/shower, not in the water.

Please contact a qualified electrician who is familiar with the NEC, or the local equivalent.

Thanks for all your answers, especially for the photo of the two Darwin Award candidates in the pool.

I have some more research to do.

I'll be back with this the next time someone complains about a wet skin shock at 0.4 vac and above at 60 Hz and electricians are stumped. That may be a while, depending on how many forums I'm subscribed to.

Apparently left bracket forward slash p right bracket makes a carriage return.

:)