I have a four year old water heater that is leaking out the pressure release down tube and there is an expansion tank fixed to the cold side. I tested the pressure on the expansion tank and it reads 0.00. Is there supposed to be some amount of pressure reading in the expansion tank or can I add some air to the tank to stop the pressure relief valve from leaking?

Thanks

You may have a bad pressuure relaese valve but do you have a way to check the actual pressure inisde the heater? The valve might be doing what is made to do. The valve is only about $10 so putting in a new one won't hurt too much. This would be a good time to drain the tank and clear out sediment. Kill the fuel to the tank and open the drain cock at the bottom of the tank.

What is the temperature of your hot water? What is the psi of your water? [pressure]