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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.

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closed as too localized by Manishearth Jun 23 '13 at 11:24

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Welcome to Physics! Please see our homework policy. We expect homework and homework-like problems to have some effort put into them, and deal with conceptual issues. If you edit your question to explain (1) What you have tried, (2) the concept you have trouble with, and (3) your level of understanding, I'll be happy to reopen this. (Flag this message for ♦ attention with a custom message, or reply to me in the comments with @Manishearth to notify me) – Manishearth Jun 23 '13 at 11:24

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.

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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
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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!)

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