ENG SPUTTERS AND STUTTERS. EMER OFF ARPT FORCED LNDG PERFORMED BY INSTRUCTOR PLT.

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WE EXPERIENCED A ROUGH RUNNING ENG AND LOSS OF RPM. WE HAD JUST BEEN VECTORED ONTO THE LOC FOR RWY 13L. IMMEDIATELY WHEN THE ENG QUIT; I TOOK CTL FROM MY STUDENT AND BEGAN EMER RESTART PROCS. BOTH ENG FUEL GAUGES WERE SHOWING PLENTY OF FUEL. L TANK FULL; R TANK LESS THAN 3/4 TANK. WE WERE RUNNING ON THE L TANK SO I IMMEDIATELY SWITCHED TO THE R TANK. WHEN I DID; THE ENG QUIT COMPLETELY. AT THIS POINT; I THOUGHT I WOULD SWITCH BACK TO THE L TANK SO I WOULD HAVE AT LEAST A ROUGH RUNNING ENG THAN NO ENG. WHEN I SWITCHED BACK TO THE L TANK; THE ENG SPUTTERED AND SURGED A LITTLE; BUT AT LEAST IT WAS RUNNING. THIS GAVE US THE ABILITY TO GET TO A SOD FARM AND LAND WITHOUT INCIDENT. AFTER LNDG; WE DID A VISUAL WALKAROUND AND AT THIS TIME NOTICED THE L TANK WAS LOW ON FUEL; EVEN THOUGH THE TANK SHOWED FULL. WHEN THE MECH CAME OUT HE DRAINED APPROX 3/4 OF A GALLON OUT OF THE L TANK AND NOTICED LOTS OF SEDIMENT IN THE SAMPLE. I FEEL THAT FAULTY INST INDICATIONS WERE A CONTRIBUTING FACTOR IN THE INCIDENT; AND AS A RESULT OF FULL INDICATIONS; THE L TANK WAS RUN LOW WHICH CAUSED THE SEDIMENT TO BE PULLED FROM THE TANK INTO THE ENG CAUSING THE ENG PROB. ON PREFLT INSPECTION; NO SEDIMENT WAS DRAWN FROM THE TANK. THIS COULD HAVE BEEN PREVENTED BY TIMING FUEL BURNOUT OF EACH TANK. IN THE FUTURE I WILL KEEP A WRITTEN TALLY OF HOW LONG I FLEW ON EACH TANK. SUPPLEMENTAL INFO FROM ACN 250837: THE FAA PEOPLE ARRIVED AND PERFORMED THEIR INSPECTION.