Water pressure is not directly a function of water tank volume, but, rather, of depth. For example, if 1,000,000 gallons of water were spread out so thin as to be only 1 inch deep at any point, it wouldn't have much pressure at all. If the same volume were poured into a column with sides measuring 1 foot wide, the pressure at the bottom would be ten times greater than at the bottom of the ocean. If some lateral measurement of the tank were known in addition to the volume, then you would be able calculate the water pressure at the tank's bottom point.
Determine the water pressure at the bottom of a full, upright cylinder by dividing the volume by the product of pi (π) multiplied by radius squared (R^2): V = πR^2. This gives the height. If the height is in feet, then multiply by 0.4333 to get pounds per square inch (PSI). If the height is in meters, multiply by 1.422 to get PSI. Pi, or π, is the constant ratio of the circumference to the diameter in all circles. An approximation of pi is 3.14159.
Determine the water pressure at the bottom of a full cylinder on its side. When the radius is in feet, multiply the radius by 2 and then multiply the product by 0.4333 to get the water pressure in PSI. When the radius is in meters, multiply the radius by 2 and then multiply by 1.422 to get PSI.
Determine the water pressure at the bottom of a full spherical water tank by multiplying the volume (V) by 3, dividing it by the product of 4 and pi (π), taking the cube root of the result and doubling it: (3V/(4π))^(1/3). Then multiply by 0.4333 or 1.422 to get PSI, depending on whether the volume is in feet-cubed or meters-cubed. For example, a spherical tank of volume 113,100 cubic feet that's full of water has a water pressure at its bottom of (113,100 x 3/4π)^(1/3) x 2 x 0.4333 = 26.00 PSI.
Tips & Warnings
- The calculations in Step 3 are based on the height being twice the radius (R) and the formula for the volume of a sphere being four-thirds of pi (π) times the cube of the radius (R): V = (4π/3)*R^3.
- "Fundamentals of Physics"; David Halliday and Robert Resnick; 1992
- Argonne National Lab: Water Pressure in Closed System
- Photo Credit diesel storage tank image by Jim Parkin from Fotolia.com
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