I plan to install a 500 gallon water tank at an elevation of 20 feet above ground level. The tank will be filled with water periodically using a submersible pump in a well. A pressure tank will be installed on the ground directly below the water tank and connected by pipes to the water tank. Will the flow of water from the tank 20 feet above ground level be enough to provide the required pressure in the pressure tank without additional pumping?

I may not be understanding you question.

If the question is "Will a 500 gal open tank of water provide adequate pressure on a smaller tank 20 foot below? The answer is no. It will provide only about 8 to 10 lbs. of pressure, depending on the level of water in the 500 gal tank. You only have the weight of a 20' column of water to create pressure.

That's different question than "I have a well and a 500 gallon storage tank with an additional tank at an elevation 20" below. What will the pressure be?"

The pressure on both tanks will be determined by the cut on/cut off settings of the well pump. Both tanks are pressurized by compressing the air in the tanks as the water is being pumped in.

Then your question becomes "If that is true, why did the well man tell me I need an additional pressure tank?"

As previously stated the pressure is created by compressing the air in the tank. As water flows thru the tank it absorbs a small amount of the air. As the volume of air in the tank is depleted it takes a smaller change in water volume to create the desired change in pressure. This called "water logged". This causes short cycling of the pump which shortens the life of the pump.

When the tank is water logged, it must be emptied of water, thus restoring the air volume.

The smaller tank with proper controls and piping can be used to regulate the volume of air in the main tank. Eliminating the necessity of periodically draining the main storage tank and prolonging the life of the pump.

Now, I realize that I probably read a lot into you question that isn't there.

P.S. You do realize that 500 gallons of water weighs about 4100 pounds.