If a fully opened 1/2" faucet / hose bib produces 4 US Gallons /
minute what formula do I use to calculate the pressure (in psi) in the
pipe at the faucet?

The equation that determines pressure in a pipe is L = (2/3)d^2 *
p^1/2 (from http://groups.google.com/groups?selm=2CCB6CA5A8A5D211AFD700A0240AFD6C04F3345F%40MCDC-US-NEWS&oe=UTF-8&output=gplain),
where d is the diameter of the pipe in mm, L is the flow of the pipe
in liters/minute, and p is the pressure in the pipe in bar.

4 gallons per minute = 15.14 liters/min (from
http://www.teaching-english-in-japan.net/conversion/gallons).  0.5
inches is equal to 12.7 mm (from http://www.mgs4u.com/chart.htm).

Now, to find the pressure, using the above equation, we have 15.14 =
2/3 * (12.7)^2 * p^(1/2). Solving for p, we find p = .0198 bar. To
convert to psi, multiply by 14.503 and the result is .288 psi (from
http://www.chromatography.co.uk/TECHNIQS/Other/Pressure.htm).

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Request for Answer Clarification by antonyupward-ga on 17 Jun 2003 19:22 PDT

Chris, 

Great detail...and fast...thanks

How does this pressure (.288psi) relate to the pressure ratings found
on faucets, washing machines etc. that says "This faucet will product
18 gpm (at 45 psi)" or "This dishwater requires water pressure in the
range of 40-60psi"?

In my example below - which is for my domestic water service .288 psi
is a long way from the sort of 40-60psi numbers being quoted on most
plumbing fixtures.

In the example below how do I calculate the psi which is equivelent to
the numbers being indicated on most plumbing fixtures - so I can get
an idea of what the flow rate will be in my house for a given faucet
or fixture.

Thanks
Antony

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Clarification of Answer by chis-ga on 18 Jun 2003 21:49 PDT

The pipe and GPM you specified are very low numbers and produce a much
lower pressure than a typical facuet or pipe needed for a dishwasher.
If you want to calculate the GPM for a 40 psi pipe that is .5 inches,
plug in 40 divided by 14.503 (to convert from psi to bar) for the
pressure and .5 inches in MM (multiply by 25.4) into the equation and
solve for L. Once you have L, convert it to gallons per minute by
dividing by 3.79.

Great answer...very fast...lots of references for follow-up.

Here is a handy online calculator to confirm his answer:

http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm#calc