Static Water Pressure vs Height

Question

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.

Answer 1

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

0.433*h = psi

You can find the pressure increase from 12 psi by solving for h. h = 12 psi/0.433 (psi/ft) = ~27.7 ft.

Pressure can be defined as P = F/a from, Newton's 2nd law.

F = m X g = volume x density x g = height x area x density x g

Substitute F into the pressure equation gives

P = height x density x g

Answer 2

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.

Answer 3

12 PSI = 12 pounds per square inch
So there is a force of 12pounds holding up each square inch
So you just need to work out how high a 1 square inch column of water would be to weigh 12pounds - notice how the height doesn't depend on the area

(it's easier in metric!)