In the explanation that follows, the reader should note the
difference between the pound-mass (lbm) and the pound-force (lbf).
The general formula is pressure = density x gravitational constant
x height, or p = dgh. English units are usually kind of weird, but
they work out nicely in this one. The density of water, d, is
around 62 lbm/ft3. The gravitational constant, g, is 32.2 ft/sec2.
We'll say height, h, is in feet. So, p = 62* 32.2 * h
(lbm/ft-sec2). The conversion factor that makes all those weird
units go away is 1 lbf/32.2 lbm-ft/sec2. p = 62 * h lbf/ft2, where
h is in feet. (To put it in pounds per square inch (psi), divide by
144.) So, p = 0.43 psi for every foot in height of the water tower.
The reciprocal of that (1/0.43 = 2.33) gives you how many vertical
feet of water are required to exert a pressure of one pound on an
area of one square inch. We know that a cubic foot of water weighs
about 62 pounds. We also know that a cubic foot contains 1,728
cubic inches (12 x 12 x 12). So, a narrow of column of water that
is one inch wide by one inch deep by 1,728 inches high will weigh
62 pounds and exert a pressure of 62 pounds on the one-square-inch
area under it. But the questioner wants to know how tall the column
has to be to exert just one pound, not 62. Dividing 1,728 by 62,
yields 27.871 inches, which is approximately 2.33 feet.