Final answer:
The most likely cause for a water pump running continuously with the control relay de-energized is a stuck contact in the relay. Inspecting and replacing the relay can resolve this issue.
Step-by-step explanation:
If the control relay of a water pump is de-energized and the pump continues to run continuously, the most likely cause is a stuck contact in the relay. When the control relay is de-energized, the contacts should open, stopping the flow of electricity to the pump and turning it off. However, if the contacts become stuck in the closed position, the pump will continue to receive power and run.
To fix this issue, the control relay should be inspected and replaced if necessary. It is important to ensure that the contacts are clean and free from any debris or corrosion. By replacing the faulty relay, the pump's operation can be restored to normal.