Question

To what height should a cylindrical vessel be filled with a liquid for the total force on the vertical surface of the vessel to equal the force on the bottom?

Answer 1

Answer: h = r.

Explanation:

The pressure on the individual elements of the vertical surface of the vessel (in terms of the height of the liquid column) increases from 0 to h, proportionally to the distance of the elements from the free surface of the liquid. Therefore, to calculate the total force on the vertical surface, it is necessary to take the mean value of the pressure, which is equal to h/2. The force will then be proportional to 2πrh X h/2. The force on the bottom will be proportional to πr²h. Equating these two values, we obtain the result we are seeking.