FLC OF A B727 DUMPED FUEL AND RETURNED TO LAND AFTER THE #3 ENG WAS HAVING COMPRESSOR STALLS DURING TKOF INITIAL CLB. ATC WAS NOT NOTIFIED OF FUEL BEING DUMPED ON THE DOWNWIND LEG SINCE THE SO DISCONTINUED THE CHKLIST PRIOR TO THAT ITEM.

Narrative

JUST AFTER LIFT-OFF OUR #3 ENG EXPERIENCED A SERIES OF COMPRESSOR STALLS. WE CLEANED UP THE ACFT AT APPROX 1000 FT AGL AND STARTED THE PRECAUTIONARY SHUTDOWN CHKLIST (UP UNTIL THROTTLE AT IDLE). WE DUMPED FUEL ON L DOWNWIND TO A VISUAL APCH TO RWY 18L (APPROX 4 MI DOWNWIND). WE DIDN'T CALL ATC AIRBORNE ABOUT THE FUEL DUMP? POTENTIAL SAFETY PROB? (WE CALLED AFTER LNDG ON THE TELEPHONE.) OUR SHUTDOWN CHKLIST HAS A NOTE TO CALL ATC IF YOU DUMP; BUT I THINK THE SO SKIPPED IT OR EXITED THE CHKLIST EARLY. WE DIDN'T SHUT THE ENG DOWN BECAUSE IT LOOKED NORMAL AT IDLE THRUST PLUS WE WERE HVY (DUMPED TO MAX LNDG WT) AND THE WINDS WERE STRONG/GUSTY AT CVG. WHEN WE DECIDED NOT TO SHUT THE ENG DOWN; I THINK THE SO RETURNED TO THE NORMAL DSCNT/APCH CHKLIST I HAD ASKED FOR THE ON ENG INOP FOLLOW UP PREVIOUSLY (JUST IN CASE WE HAD TO SHUT DOWN). ANYWAY; I SHOULD HAVE MONITORED THE SO BETTER. (IT WAS A LITTLE HECTIC.) I NEEDED TO UNHECTIC THE SIT. I ALSO DON'T KNOW IF WE 'FORMALLY' DECLARED AN EMER -- PROBABLY SHOULD HAVE.