What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
(-23) After leveling off at a cruising altitude of 5000 ft in IMC conditions, the pilot stated that the engine began to run rough and surge. The pilot declared an emergency and returned to Greensboro. During the vectors to Greensboro the engine continued to surge and run rough. The aircraft landed without further incident at Greensboro. Examination of the aircraft revealed that the fuel gauge would not read correctly when any of the four tanks were selected. Additionally, evidence of an oil leak was noted on the engine cowling. The pilot stated that during the return flight she and the passenger (also a pilot) attempted switching tanks several times but could not get the engine to run smoothly on any tank. The aircraft was examined by maintenance technicians who found problems with a leaking oil cooler, a deteriorated induction duct, oil in the carb. Box, debris in the fuel strainer, and broken contacts for the fuel gauge selector. This most likely resulted in the pilot selecting a fuel tank that did not contain adequate fuel for the intended flight.
As the FAA filed it
(-23) AFTER LEVELING OFF AT A CRUISING ALTITUDE OF 5000 FT IN IMC CONDITIONS, THE PILOT STATED THAT THE ENGINE BEGAN TO RUN ROUGH AND SURGE. THE PILOT DECLARED AN EMERGENCY AND RETURNED TO GREENSBORO. DURING THE VECTORS TO GREENSBORO THE ENGINE CONTINUED TO SURGE AND RUN ROUGH. THE AIRCRAFT LANDED WITHOUT FURTHER INCIDENT AT GREENSBORO. EXAMINATION OF THE AIRCRAFT REVEALED THAT THE FUEL GAUGE WOULD NOT READ CORRECTLY WHEN ANY OF THE FOUR TANKS WERE SELECTED. ADDITIONALLY, EVIDENCE OF AN OIL LEAK WAS NOTED ON THE ENGINE COWLING. THE PILOT STATED THAT DURING THE RETURN FLIGHT SHE AND THE PASSENGER (ALSO A PILOT) ATTEMPTED SWITCHING TANKS SEVERAL TIMES BUT COULD NOT GET THE ENGINE TO RUN SMOOTHLY ON ANY TANK. THE AIRCRAFT WAS EXAMINED BY MAINTENANCE TECHNICIANS WHO FOUND PROBLEMS WITH A LEAKING OIL COOLER, A DETERIORATED INDUCTION DUCT, OIL IN THE CARB. BOX, DEBRIS IN THE FUEL STRAINER, AND BROKEN CONTACTS FOR THE FUEL GAUGE SELECTOR. THIS MOST LIKELY RESULTED IN THE PILOT SELECTING A FUEL TANK THAT DID NOT CONTAIN ADEQUATE FUEL FOR THE INTENDED FLIGHT.