OK, so I have water at a known pressure, lets say 12psi. I have 2 pipes, installed vertically, one 2" diameter, the other 1/2" diameter. To what height (in feet) will the water raise to in each case? I said it would be the same, but I can't explain why. Remember this is a static pressure, as the water is not flowing.
The diameter of the pipes has no effect at this scale.
Water weighs 62.22 lb /ft3 at room temp. Divide that by 144 in2/ft2 and you get .432 PSI/Foot (height). If you divide that by 12 you get .036 PSI per inch. You can also look up 'inches of water', which yields .036009 PSI per inch.
12 PSI / .036 PSI per inch yields about 331.2 inches... which comes to 27.6 feet.
So, if you have an set of pipes which are vertical and open at the top, and a water pressure reading of 12 PSI at the base, the water will rise 27.6 feet.
Pressure depends on depth (or height), density By knowing that a cubic inch of water is equal to ~0.036 pounds, you can multiply that by 12 to determine how much pressure one foot of water exerts. So for every foot, there is ~0.433 pounds of force, or psi. You can write pressure in terms of height as
You can find the pressure increase from 12 psi by solving for
Pressure can be defined as
12 PSI = 12 pounds per square inch
(it's easier in metric!)