The pilot stated that he had just purchased the accident airplane. After completing a familiarization flight with the previous owner, the pilot had the main fuel tanks topped off and then departed. After flying for 20 minutes, the pilot noticed that the header fuel tank indicator was showing empty. The pilot returned to the departure airport and told the previous owner that something was wrong with the fuel system. The owner informed him that it should be fine, and the pilot refueled the header fuel tank and departed again for his destination. During the flight the engine lost all power and the pilot conducted an emergency landing to a field. During landing the airplane flipped over inverted and was substantially damaged. An examination of the wreckage by a mechanic revealed that the fuel pump to the header tank was not operating at the correct flow rate.