PA28 PILOT EXPERIENCES FUEL EXHAUSTION DURING VECTORS FOR APPROACH AND MANAGES TO LAND SAFELY AT A SMALL AIRPORT SHORT OF DESTINATION.

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THE FLT WAS PLANNED FOR 3.50 HRS OF FLT TIME. THE FIRST LEG WAS FLOWN FROM ZZZ1 TO ZZZ2 TO PICK UP A SINGLE PAX. FROM ZZZ2 THE FLT CONTINUED TO ZZZ3. THE PAX WAS DROPPED OFF AND THE FLT WAS CONTINUED AS A RETURN LEG TO ZZZ1. ACFT WAS PREFLTED BY ME; AND FOUND TO HAVE FULL FUEL IN THE L WING TANK AND FULL FUEL IN THE R WING TANK. INSPECTION SHOWED 48 GALS USEABLE FUEL ONBOARD AT THE START OF THE FLT. PREFLT PLANNING ESTIMATED FUEL USE FOR THE OUTBOUND LEG WOULD TOTAL 16.0 GALS; AND FUEL USE FOR THE RETURN LEG WOULD TOTAL 16.0 GALS; WITH AN ESTIMATED RESERVE REMAINING OF 16 GALS (APPROX 1.50 HRS OF FUEL IN THIS ACFT). I REMOVED THE FUEL CAPS FROM BOTH TANKS AFTER LNDG AND TAXI AT ZZZ2 AND OBSERVED BOTH TANKS WERE NEARLY FULL. I TOOK ON MY PAX AND WE FLEW TO ZZZ3. I SWITCHED FUEL TANKS SHORTLY AFTER DEP FROM ZZZ2 AND FLEW FOR APPROX 1 MORE HR ON THE SECOND TANK. I REMOVED THE FUEL CAPS FROM BOTH TANKS AFTER LNDG AT ZZZ3 AND OBSERVED THE FUEL LEVEL IN BOTH TANKS WAS ABOUT EQUAL; AND APPEARED TO BE A SMALL DISTANCE BELOW THE TABS (LESS THAN 17 GALS USABLE IN EACH TANK). I DEPARTED ZZZ3 IN VFR CONDITIONS; WITH ATC TA'S. I SWITCHED FUEL TANKS APPROX 1 HR INTO THE FLT. I NOTED A HESITATION AND DROP IN ENG RPM. I IMMEDIATELY PERFORMED A CHK OF ENG CTLS AND ALSO CHANGED FUEL TANKS. THE ENG BEGAN TO PERFORM NORMALLY ALMOST IMMEDIATELY. I CONTINUED THE FLT BUT RATHER THAN CONTINUE ON TO ZZZ1 I REQUESTED A LNDG AT ZZZ2 AND STATED TO THE CTLR I WAS LOW ON FUEL. I WAS VECTORED TO THE S AND THEN VECTORED BACK TOWARD ZZZ2 ARPT BY THE TRACON CTLR. AS I CONTINUED OVERWATER TOWARD THE FIELD; THE ENG LOST PWR. I PERFORMED AN EMER CHK OF ALL CTLS AND SWITCHED FUEL TANKS (BACK TO THE TANK THAT HAD PREVIOUSLY BEEN EXHAUSTED). I BEGAN A GLIDE TOWARD THE LAND; AND DECLARED AN EMER FOR FUEL EXHAUSTION TO THE CTLR THAT I WAS STILL ASSIGNED TO. I REQUESTED VECTORS TO ZZZ WHICH I KNEW WAS IN THE VICINITY; AND WHICH I BELIEVED I HAD IN SIGHT. THE CTLR CONFIRMED THAT THE FIELD WAS ON MY CURRENT HDG. I WAS LOSING ALT AND TOLD THE CTLR THAT IT DID NOT APPEAR THAT I WOULD BE ABLE TO REACH THE FIELD. THE PROP WAS WINDMILLING AND EVENTUALLY THE ENG RESTARTED; AND CONTINUED RUNNING; AS I SWITCHED BTWN TANKS REPEATEDLY. I WAS ABLE TO MAKE A NORMAL LNDG ON THE GRASS FIELD AT ZZZ AND EXITED THE RWY AS SOON AS MY GND SPD WAS REDUCED. I WAS ABLE TO TAXI THE ACFT TO AN OPEN AREA CLR OF THE TXWY AND RWY. I SECURED THE ACFT; AND USED A CELL PHONE TO CALL THE TWR AT ZZZ2 TO ADVISE THEM THAT I HAD LANDED SAFELY AND NORMALLY. INSPECTION REVEALED NO USEABLE FUEL IN EITHER WING FUEL TANK. THIS WAS THE FIRST TIME I HAVE FLOWN THIS ACFT. I BELIEVE THAT THE FUEL BURN RATE FOR THIS ACFT IS HIGHER THAN I WAS ADVISED.