How high does a column of water need to be to have 5 psi at the bottom of the column?

Question

Please provide backup... Thanks!

Answer 1

One pound is about 453.6 grams.

5 pounds is therefore 2268 grams.

Water (pure, 4 degrees C) weighs one gram per cubic centimeter.

2268 grams of water occupies 2268 cubic centimeters.

Consider a rectangular column of 2268cc's of water which has a base of one square inch.

1 inch is 2.54 centimeters, so 1 square inch is 6.45 square centimeters.

2268 cubic centimeters divided by 6.45 square centimeters is 352 centimeters.

The column would be 352 centimeters tall.

This is 139 inches, or 11 feet, 7 inches.

A column of pure water 139 inches tall would exert 5 pounds of force over a 1 square inch area.

I converted to grams per cubic centimeter and then back from centimeters to inches because water is the material with which the initial unit "gram" was defined, therefore it's easy to remember. I could have looked up the pounds per cubic inch value for water and saved some steps.

I rounded to 3 significant digits because of the fact that I have 3 digits in the 2.54 centimeters per inch conversion, but on reflection, I recognize that this is a DEFINITION. It is exact. It is equivalent to 2.5400000000000.... etc.

Answer 2

The ~11.5 foot answers are most correct.

My reasoning (without going through the same kind of calculations they did) is:
I remember from physics history that the first vacuum water pumps (before steam engines) could only lift a column of water about 32 feet. Atmospheric pressure is about 14 psi. The ratio 5/14 is 0.36 and 32 feet * 0.36 is darn close to 11.5.

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Answer 3

1 psi is equal to 2.307 feet of water

so 5 psi equals 11.54 feet of water

so the column of water needs to be that high, 11.54 feet

Answer 4

5psi ÷ 0.433psi/foot = 11.55 feet high.

(Mathematical proof..
1 cubic foot of water = 62.4 pounds
1 ft³ has a base area of 12" x 12" = 144 in²
62.4lb ÷ 144in² = 0.433psi).

Answer 5

Head of water (in feet) = (pressure (in psi) times 2.31)/specific gravity.
Specific gravity of water is 1.0, so head = psi times 2.31, therefore head equals 11.55 feet.

Answer 6

64 PCF / 144 SQ IN / SQ FT = .444 PSI PER FT.

11.25 FT.

Answer 7

2.31 feet of water = 1 psi

5psi = 11,55 feet of water.

Water weighs 62.4 pounds per cubic foot
There are 144 square inches per square foot
62.4 pounds per cubic foot/144 square inches per square foot =0.433 pounds per inch squared per foot of depth = 2.31 feet per pounds per square inch

Answer 8

1 foot of water = 2.31 psi.

5/2.31 = 2.16 feet of water

you need 2.16 feet of water

Answer 9

(5lbs/in^2) / (62.4lbs/ft^3) (1ft^3/1,728in^3) = 138.46 inches