How to Calculate Water Pressure from Tank Volume

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Water pressure is not a direct function of water tank volume, but of depth. For example, if you spread out 1,000,000 gallons of water 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 you know some lateral measurement of the tank in addition to the volume, you can calculate the water pressure at the tank’s bottom point.

  1. Find Water Pressure of Upright Cylinder

  2. Determine the water pressure at the bottom of a full, upright cylinder by dividing the volume by the product of pi (?) multiplied by radius squared (R^2): V = ?R^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 ?, is the constant ratio of the circumference to the diameter in all circles. An approximation of pi is 3.14159.

  3. Find Water Pressure of Cylinder on its Side

  4. 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.

  5. Find Water Pressure at Bottom of Spherical Tank

  6. 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 (?), taking the cube root of the result and doubling it: (3V ÷ (4?))^(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 3/4?)^(1/3) x 2 x 0.4333 = 26.00 PSI.

    Tips

    • 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 (?) times the cube of the radius (R): V = (4?/3) x R^3.

References

About the Author

Paul Dohrman's academic background is in physics and economics. He has professional experience as an educator, mortgage consultant, and casualty actuary. His interests include development economics, technology-based charities, and angel investing.

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