A DC9-30 IN CRUISE AT FL290; INDICATED THAT THE L FUEL QUANTITY INDICATOR DROPPED 4000 LBS. ON GND; WHEN TANK STICKS WERE CHKED; L TANK WAS FOUND EMPTY.

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WHILE IN CRUISE PHASE OF FLT; L-HAND FUEL GAUGE DROPPED FROM APPROX 6000 LBS TO 2000 LBS. ACFT HAD HISTORY OF L-HAND FUEL GAUGE PROBS. DID COMPANY PROC FOR ERRONEOUS FUEL INDICATIONS AND CONTINUED TO DEST. WHILE WORKING APCH CTL APPROX 15 NM FROM ARPT; SUSPECT FUEL GAUGE APCHED ZERO LBS. FEELING UNCOMFORTABLE WITH SUSPECT FUEL GAUGE AT ZERO; I TURNED ON IGNITION AND OPENED FUEL XFEED VALVE. WE HAD NORMAL LNDG AND TAXIED TO PARKING. AFTER DEPLANING; I WENT DOWN AND DROPPED L-HAND WING DRIPLESS FUEL STICKS TO CHK AMOUNT OF FUEL IN WING TANK. ALL 4 STICKS DROPPED TO BOTTOM OF TANK. THERE WAS NO FUEL IN L-HAND WING TANK. AFTER A REVIEW OF ACFT LOGBOOK FUEL RECORDS AND FUEL SLIP FOR FLT; WE NOTICED AN ERROR IN THE FUEL GAUGE AMOUNTS. AT THE TIME OF REFUELING COCKPIT L-HAND FUEL GAUGE SHOWED 3500 LBS; YET AT THE WING FUELING STATION THE FUEL AMOUNT WAS RECORDED AS 6600 LBS. OUR COMPANY MAINT PERSONNEL ARE UNCLR HOW THIS COULD HAPPEN. THE L-HAND FUEL QUANTITY INDICATING SYS WAS ONCE AGAIN PLACED ON MEL AS INOP.