We just installed a new pump to our well. The old one it seems had not been used for years and was broken. We got an initital good flow and after a few minutes the sprinkler lost its pressure. There are 2 pouts on the outflow, I turned the other one on and then turned it off the sprinler started up again for a couple of minutes with great pressure and then suddenly died again. I thought maybe after a couple of minutes the water table dropped below the well point, but that doesn't explain why when I turned on the other faucet and turned it off again why the sprnkler would kick back in. Can someone give me some advice as to where to go from here and would possible installing a 10 or 20 gallon pressure tank help this problem?

Changing the pump may have stirred up some crud. Taking things apart and cleaning everything may fix it. If it plugs again soon, you may need to install a whole house water filter just after the pump.