When comparing head pressure in a 1" pipe and a 10" pipe that are both 20' tall, which statement is true?

In fluid mechanics, the pressure at the bottom of a column of fluid in a pipe depends primarily on the height of the fluid column and the density of the fluid, not on the diameter of the pipe. In this case, both the 1" pipe and the 10" pipe are filled with the same fluid and are both 20 feet tall. Therefore, the height of the fluid column (20 feet) is identical in both cases, leading to the conclusion that the head pressure, which can be calculated using the formula ( P = \rho g h ) (where ( \rho ) is the fluid density, ( g ) is the acceleration due to gravity, and ( h ) is the height of the fluid), will be the same.

Since the pressure is solely a function of the height of the fluid column and independent of the cross-sectional area of the pipe, the conclusion that the pressure in both cases is the same holds true. This is why the correct answer states that the pressure is the same. The other options suggest variations based on the pipe diameter, which does not impact head pressure in this context.