Pump or Pressure Tank Problem

I have connected my pressure system at my new house. We are using our existing submersible pump and well from our previous mobile home but are using a new pressure tank. The system will kick on at 30psi an kick off at 50psi as expected and hold 50 psi while the faucet is not opened. The problem is that when the faucet is opened on the tank tee the pressure falls to 30 psi and stays there for about a minute or so and then drop all the way down to 10 and stays there, I assume at this point it is just the pump pumping water with no pressure building in the tank. The exact moment the tank tee faucet is closed, the pressure pops up to 30psi and begins to build to 50psi and does so in about 40 or 50 seconds. The pump is a 1/2 HP and the tank is a 33 gallon that I had precharged to 28psi as per installation sheet. All electrical connections are verified working by doing all the ohm and voltmeter tests.

Is the problem that the pump screen is partially clogged and cannot pump the volume required? Or is the problem something with the pressure tank? Pump sat idle in well for 6 months. We have had record amounts of rain over summer so I do not think it is a water table issue.

Thanks

I tested the gpm of the pump by filling a 5 gallon pail. I could fill the pail in about 20 seconds, so there seems to be no shortage of flow from the pump. I think it must be that since I am opening the tank tee drain valve that basically water is flowing straight from the well out the valve instead of pressurizing the tank. I am hoping that once I finish connecting all my supply lines that this will not be a problem for general use.

It sounds to me that the water level in the well falls low enough to make the pump struggle to deliver water from that depth. Check teh static water level in teh well and how far it falls whe nit can't deliver more water.

BTW, the 5 gallons is coming from the tank, so the pump isn't delivering much water.

I did the bucket fill test after turning off the pump, draining down the tank, leaving the drain valve open with the hose end in the pail. At that point I flipped on the breaker and started my stopwatch. And as I said, it filled the pail in about 20 seconds. So you don't think that if a faucet was opened up further down the line that I would not see different results.