MD88 CREW BELIEVING THAT THEY MAY HAVE A FUEL LEAK AND ASSUMING THAT THEY HAVE AN INDICATION PROBLEM DIVERTS TO AN ENROUTE ALTERNATE SELECTED BY THE DISPATCHER. DURING THE DESCENT THE RIGHT ENGINE FLAMES OUT WITH 2000 LBS OF FUEL SHOWING ON THE QUANTITY GAUGE.

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DEPARTED ZZZ1 FOR ZZZ2. THERE WAS NO OPEN WRITE-UPS IN THE LOGBOOK; BUT MAINT HAD CLRED; EARLIER THAT MORNING; A WRITE-UP FOR THE R WING FUEL QUANTITY INDICATOR READING ABNORMALLY LOW. MAINT HAD CHKED THE INDICATOR AND FOUND IT TO BE OPERATING NORMALLY. WE TOOK OFF WITH MAIN WING FUEL TANKS INDICATING FULL AND THE CTR FUEL TANK APPROX HALF FULL; WHICH CONCURRED WITH THE PLANNED FUEL LOAD; AND OUR FUEL SLIP. UPON TKOF I NOTICED THE ACFT REQUIRED A LOT OF R AILERON DEFLECTION TO MAINTAIN WINGS LEVEL. THIS NECESSITATED APPROX 3 UNITS OF R AILERON TRIM. ALTHOUGH THIS WAS NOT A NORMAL AMOUNT OF TRIM; I HAVE FLOWN MD88'S WHICH NEEDED 2 OR 3 UNITS OF AILERON TRIM BEFORE; SO I JUST ASSUMED THIS WAS ANOTHER ONE OF THOSE BENT MD88'S. ONCE THE ACFT WAS TRIMMED; EVERYTHING SEEMED NORMAL. THE LEVELOFF FUEL CHK INDICATED WE WERE APPROX 1000 LBS FAT ON FUEL WHICH WE ATTRIBUTED TO NOT BURNING THE PLANNED 1800 LBS ON TAXI OUT. APPROX 1 HR AND 25 MINS INTO THE FLT; AT ABOUT XA00Z; I HAD JUST FINISHED A POS RPT (ABOUT 8 MINS AFTER PASSING DIW; DIXON; ON AR19) AND I NOTICED THE R WING FUEL TANK INDICATED APPROX 1750 LBS LOWER THAN THE L WING TANK. THE ENGS WERE BURNING FROM THEIR RESPECTIVE TANKS; AND THE FUEL USED INDICATORS INDICATED APPROX THE SAME FUEL USED. THE FO REMINDED ME THE R WING FUEL TANK HAD BEEN PREVIOUSLY WRITTEN UP AS INDICATING LOW; AND MAINT HAD SIGNED IT OFF IN ZZZ BEFORE OUR FLT. WE FELT THE FUEL GAUGE WAS PROBABLY ACTING UP AGAIN; BUT FOLLOWED THE QRH CHKLIST FOR FUEL LEAK JUST TO BE SAFE. WHILE FOLLOWING THE FUEL LEAK CHKLIST; THE FUEL SPLIT CONTINUED TO INCREASE; AND WE DETERMINED THE INDICATED FUEL USAGE FROM THE R TANK WAS TWICE THE RATE OF THE FUEL FLOW INDICATOR. (100 LBS PER MIN FUEL QUANTITY GAUGE DECREASE VERSES 50 LBS PER MIN FUEL FLOW.) AT THAT FUEL USAGE; WE ESTIMATED WE HAD OVER 45 MINS OF FUEL IN THE R TANK IF THERE REALLY WAS A LEAK; OR OVER 120 MINS OF FUEL IF IT WAS JUST A BAD FUEL GAUGE AND THE R TANK ACTUALLY CONTAINED THE SAME AMOUNT OF FUEL AS THE L TANK (6700 LBS). WE DECLARED AN EMER; AND THE FO FLEW THE ACFT TOWARDS ZZZ4 WHILE I COORDINATED WITH MAINT; ATC; THE FLT ATTENDANTS; AND OUR PAX. OUR INITIAL PLAN WAS TO LAND AT EITHER ZZZ4 OR ZZZ5; BUT MAINT ASKED IF WE COULD LAND AT ZZZ3. SINCE WE SUSPECTED WE JUST HAD A BAD FUEL GAUGE; AND HAD PLENTY OF FUEL EVEN IF IT WAS A FUEL LEAK; WE SIMPLY ADJUSTED OUR DSCNT PROFILE TO LAND IN ZZZ3. WE COMPLETED ALL THE APPROPRIATE ABNORMAL CHKLISTS AND FINISHED COMMUNICATING WITH ALL THE APPROPRIATE AGENCIES AS WE DSNDED THROUGH APPROX 10000 FT ABOUT 40 MI FROM ZZZ3. WE HAD EVEN BRIEFED THE PROCS FOR A POSSIBLE ENG FLAMEOUT IF INDEED WE DID HAVE AN ACTUAL FUEL LEAK. I ASSUMED ACFT CTL; AND SURE ENOUGH THE R ENG FLAMED OUT; EVEN THOUGH THE R WING FUEL TANK STILL INDICATED 2000 LBS OF FUEL. NOTE: WE WERE NOT XFEEDING AS PER THE FUEL LEAK CHKLIST. WE CONTINUED A NORMAL DSCNT INTO ZZZ3 AND PERFORMED AN UNEVENTFUL 28 DEG FLAP; ENG OUT LNDG ON RWY XXL. THE FIRE TRUCKS MET US AND LOOKED US OVER ON THE RWY. WITH NOTHING ABNORMAL INDICATED; WE TAXIED TO A GATE. AT THE GATE; WE DEPLANED THE PAX AND TALKED WITH MAINT. WE STILL INDICATED ABOUT 1800 LBS OF FUEL IN THE R WING TANK; BUT WHEN A FUELER STUCK THE TANK; IT WAS ACTUALLY EMPTY. THE FUELER THEN EXAMINED OUR FUEL SHEET; AND POINTED OUT THAT ALTHOUGH IT INDICATED THE CORRECT FUEL LOAD IN ZZZ; THE PRIOR TO SVCING COLUMN SHOWED THE L WING TANK HAD 5450 LBS WHILE THE R WING TANK SHOWED 9400 LBS/FULL. AND; THE ZZZ FUELER HAD NOT ADDED ANY FUEL TO THE R TANK. THE ZZZ3 FUELER STATED THE PRACTICE IN ZZZ3 IS TO ROUTINELY STICK THE TANKS IF THE ARRIVING ACFT SHOWS A FUEL IMBAL OF 1500 LBS OR GREATER. THE ZZZ FUELER HAD NOT STUCK THE TANK. NOTE: ZZZ MAINT HAD WORKED ON THE ACFT AND HAD XFER AN KNOWN QUANTITY OF FUEL FROM R TANK TO CTR TANK SEVERAL TIMES. QUANTITY REMAINS SAME. R TANK READS CORRECTLY. ZZZ3 AND PLACARD REMOVED. LESSONS LEARNED: 1) HAD WE DETECTED THE PRIOR TO SVCING DISCREPANCY IN THE FUEL SHEET; WE COULD HAVE ASKED THE FUELER TO STICK THE TANKS TO CONFIRM ACTUAL FUEL LOAD INSTEAD OF RELYING ON THE FUELER TO ANALYZE THE SITUATION PROPERLY. 2) IF THE FUELER HAD ATTEMPTED TO ADD FUEL TO ALL TANKS UNTIL THE AUTO SHUTOFF OCCURRED; INSTEAD OF TRUSTING THE FUEL GAUGES; HE WOULD HAVE REALIZED THE R WING TANK WAS NOT FULL AS INDICATED BY THE GAUGE. (NOTE: I AM ASSUMING THIS IS WHAT HAPPENED. I HAVE NOT SPOKEN WITH THE FUELER.) 3) THE R WING LOW AILERON REQUIRED AFTER TKOF WAS NO DOUBT A RESULT OF HAVING PROBABLY 4000 LBS TOO LITTLE FUEL IN THE R WING TANK. 4) WE OVERFLEW ZZZ4 AND ELECTED TO LAND IN ZZZ3 AS WE FELT WE SIMPLY HAD A MALFUNCTIONING FUEL GAUGE. BY THE TIME THE ENG FLAMED OUT; WE WERE ON A NORMAL DSCNT PATH TO ZZZ3; SO WE CONTINUED AS PLANNED.