FO OF AN MLG FAILED TO FOLLOW ATC MISSED APCH INSTRUCTIONS AND TURNED DOWNWIND TO KEEP ARPT IN SIGHT BECAUSE OF A SPLIT FLAP PROB AND CAUSED A CONFLICT WITH ANOTHER ACFT ALREADY IN THE TFC PATTERN.

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LAX-PHX. APPROX 10 MI OUT ON FINAL RWY 8R AT PHX; A B737- 300 ASYMMETRICAL STUCK TRAILING EDGE FLAPS AT APPROX 18 DEGS AND 23 DEGS. WHILE SLOWLY GETTING DIRTY; ON A 25-30 MI FINAL FOR RWY 8R AT PHX; THE TRAILING EDGE FLAP GOT STUCK. APPROX 15 SECONDS AFTER DISCOVERY OF THE SPLIT FLAP CONDITION; A DECISION WAS MADE TO GAR. AT GAR THE ACFT WAS APPROX 5 MI OUT ON FINAL. A LEVEL OFF AT APPROX 2000 FT AND SOON AFTER A SLOW CLB AS DIRECTED TO 3000 FT TOOK PLACE. MISSED APCH; THE GEARS WERE RAISED AND THE FLAPS WERE LEFT IN POS DUE TO THE STUCK ASYMMETRY. THE GEAR/FLAP HORN SOUNDED VERY LOUDLY UPON GEAR-UP. AFTER APPROX 10 SECONDS WITH THE GEAR/FLAP HORN SOUNDING VERY LOUDLY; IT WAS REALIZED THAT THE GEAR SHOULD BE LOWERED. THERE WAS PLENTY OF FUEL TO HANDLE THE INCREASED FUEL BURN WITH GEAR DOWN FLT. THE TWR HAD BEEN INFORMED OF THE GAR RIGHT AWAY. APPROX OVERHEAD THE UPWIND NUMBERS I (COPLT); ON MY OWN INSTINCT; TURNED DOWNWIND. INSTINCT TOLD ME TO KEEP THE ARPT/RWY IN SIGHT AT ALL TIMES UNTIL I WAS SURE OF THE RESULT OF OUR FLAP PROB. A TURN WAS MADE DOWNWIND WHILE THE CAPT WAS ON THE PA TO THE PAX. THE CAPT RETURNED TO THE #1 RADIO AND DECLARED AN EMER TO TWR. AFTER APPROX 145 DEGS OF TURN DOWNWIND; THE CREW WAS INFORMED BY TWR OF A TFC CONFLICT WITH AN 'EXPERIMENTAL ACFT.' A NO TCASII SMALL ACFT. WE WERE GIVEN A FREQ CHANGE AND A CLB BY EITHER TWR OR DEP CTL; CLB TO 6000 FT AND DIRECTED TO CONTINUE OUR TURN TO 250 DEGS. WE WERE THEN SUBSEQUENTLY VECTORED AROUND BY DEP WHILE WORKING THE CHKLIST. THE FLAPS; PER CHKLIST; WERE RAISED AND MADE SYMMETRICAL TO FLAPS 15 DEGS. IT WAS DECIDED NO FURTHER TROUBLESHOOTING WOULD OCCUR AND A FLAPS 15 DEG LNDG WOULD BE MADE. 15 DEG REF SPD ON A LONG; DRY; RWY 8R. AN UNEVENTFUL DIRTY CONFIGN APCH AND LNDG RESULTED. ON THE GND ATC ASKED US TO CALL ON THE PHONE. IT WAS DISCOVERED THAT A TFC CONFLICT (HAD OR ALMOST HAD?) OCCURRED WITH THE 'EXPERIMENTAL ACFT.' THE INSTINCT OR GUT DESIRE FOR THE COPLT TO KEEP THE AIRFIELD IN SIGHT WITH A SHALLOW R TURN DOWNWIND WITHOUT CLRNC CAUSED THE PROB. CAUSE; INSTINCT. SOLUTION? PERHAPS ONE SOLUTION; A SPARE TWR CTLR STANDING BY AT ALL TIMES SOLELY TO ASSIST WHEN AN EMER TAKES PLACE.