A B737-300 CREW DECLARE AN EMER AFTER A MISSED APCH BECAUSE OF LOW FUEL AND INDIRECT ALTERNATE ARPT ROUTING.

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WE WERE ISSUED A HOLD ON OUR WAY TO ZZZ. THERE WERE TSTMS OVER THE ARPT CLOSING IT TO ARRIVING TFC. WE WERE ISSUED AN EFC AND THIS PUT US 400 LBS WITHIN OUR FUEL LIMIT. LATER WE WERE ISSUED ANOTHER EFC -- THIS PUT US OVER OUR FUEL. WE CONTACTED DISPATCH FOR A RELEASE TO DIVERT. ATC THEN CAME ON AND CLRED US BACK TO ZZZ ON OUR STAR. LOOKING AT OUR FUEL WE HAD 300 EXTRA LBS. DISPATCH CAME BACK WITH A RELEASE TO ZZZ1. WE INFORMED THEM WE WERE RELEASED TO ZZZ. THEY CONCURRED AND WE CONTINUED TO ZZZ. DURING THE APCH WE RECEIVED EXTENSIVE VECTORS. ABOUT 20 MI OUT; WE NOTICED WX BUILDING AGAIN OVER ZZZ. THE 2 PLANES AHEAD OF US MISSED THEIR APCH; AS WE DID. DURING THE MISSED APCH AND HDOF WE REQUESTED DIVERSION TO OUR ALTERNATE OF ZZZ1. ATC INFORMED US THERE WAS SEVERE WX OVER ZZZ1 AND ENRTE. WE GOT WITH DISPATCH AND THEY TOLD US TO DIVERT TO ZZZ2 AS IT WAS VFR. AFTER TURNING AROUND WITH A VECTOR; WE PLUGGED IN DIRECT ZZZ2 AND NOTICED WE WERE AT MINIMUM FUEL. WE INFORMED ATC AND THEY GAVE US A NON-DIRECT RTE TO ZZZ2. AFTER SETTING IN THE RTE IT WAS NOW EMER FUEL. WE INFORMED ATC IF WE STAYED ON A NON-DIRECT RTE WE WILL HAVE TO DECLARE AN EMER. THEY ASKED OF OUR INTENTIONS AND WE TOLD THEM WE WOULD DECLARE AN EMER. WE WERE THEN CLRED DIRECT ZZZ2. WE WERE LATER CLRED DIRECT THE OM FOR RWY. WE LANDED WITH 4.1 FUEL -- THANKS TO THE PRIORITY HANDLING. THE REST OF THE DAY WENT OK; AS WE WERE FUELED AND REDISPATCHED BACK TO ZZZ. WE ALSO HAD A 5 KT OVERSPEED ON FLAPS 5 DEGS ON OUR MISSED APCH. I CONTRIBUTE THIS TO THE MODERATE TURB; WITH LARGE GAINS IN AIRSPD ON THE MISSED APCH. WE HAD A QUICK VECTOR AWAY FROM THE LARGE CELL IN FRONT OF US. IT WAS ALSO VERY BUSY AND INTENSE WITH COMS.