What requires more force, filling an elevated tank through the bottom or filling it by means of a pipe leading over the top?

The answer is that more work or force is required when the water is pumped over the top of the tank. Contrary to the popular notion, the water going into the tank from the bottom does not have to lift the weight of the water in the tank; it lifts only a column of water of the same area as the pipe. The level of the height and not the weight of the water governs. If you lift a column of water over the top of the tank it is clear that you must lift it higher than if you force it into the tank from the bottom. The pressure of a column of water in pounds to the square inch is calculated by multiplying the height of the column in feet by .434.