I have a submersible water pump system with a bladder type tank which has been working fine for a number of years. Recently, I noticed that the pump would cycle on periodically, even when no water was being used. After ensuring that there were no plumbing leaks (turned water supply to house off), I find that the pump will still cycle, even though no water is being used. I assume that this is due to a leaky check valve at the pump itself.

I installed a check valve on the pump side of the tank, and this did stop the pump from cycling. However, now I find that I get a lot of air in the system and can't figure out what's causing this.

Can this be due to cavitation due to constriction of flow at the check valve? It's a 1-inch valve.