A pressure tank is used to prevent a pump from cycling (switching on and off frequently) for a system with frequent demand. Such systems are common in small residental or commercial applications for example laundary water supply. A pressure tank simply uses air pressure to keep the pressure in the storage tank at a desirable level for the demand. So, the supply pump will only have to run when the tank is at a minimum level. For the most of the time after the initial pump-up, the pump remains off and the charged (pressurized) air pocket (which is now at a higher pressure than the pre-charge pressure) does the work. I tried to illustrate the idea in the following diagrams:
Now compare the above system to the system with a pressure tank installed between the supply and demand:
By drawing the graph I wanted to show how air pressure maintains water supply preventing the pump to have to cut in frequently. To illustrate how this works, consider the following diagram:
Since this post is titled "how to size a pressure tank", I also illustrated, in the note below, the fundamentals behind the commonly used "acceptance factor" when sizing a commercial pressure tank:
