I have a 240 volt submersible water well pump. I hook it up directly to 240 to see if it'll run. It should run until I turn off the power, but it doesn't. It runs for around three seconds and then it turns off for 10, runs for 3 seconds turns off for 10 and so on. What's the problem? I have a 20 amp breaker.
You need to have a submersible pump submersed when testing. Most deep well pumps ALSO need adequate back pressure to limit the current they draw (normally provided by that long pipe up the well to the surface.)
Running dry is bad for all submersible pumps, and "in a bucket" (i.e. with no output restriction when outside of the well, or without adequate head in a well) is bad for most. They expect to be in water (generally near 10C/50F) when operating, and that water serves as lubricant and coolant.
Your on/off cycling is probably caused by the pump's protective circuitry shutting it down due to overheating.