FLC OF G4 FAILS TO REMOVE THE OUTFLOW VALVE COVER DURING PREFLT. COVER COMES OFF INFLT AND IS INGESTED INTO R ENG. WITH NO ENG ANOMALIES AND AFTER CONSULTATION WITH MAINT THE FLT CONTINUES TO DEST.

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I DEPARTED RENO/TAHOE INTL ARPT; NV; IN A GULFSTREAM 4 ACFT. I WAS THE CAPT AND PIC; AND WE HAD 10 PAX ON BOARD AND A CREW OF THREE: THE FO; A FLT ATTENDANT; AND MYSELF. AS IS CUSTOMARY; THE FO PERFORMED THE PREFLT AND WALKAROUND. HE REMOVED THE GEAR PINS; ENG COVERS; ETC; BUT FOR SOME REASON; HE OVERLOOKED THE OUTFLOW VALVE COVER. THE OUTFLOW VALVE IS LOCATED ON THE R SIDE OF THE ACFT JUST BELOW AND AFT OF THE COCKPIT WINDOWS. THIS VALVE IS ONLY VISIBLE FROM THE R SIDE OF THE ACFT. THE VALVE COVER IS MADE OF A HARD PLASTIC MATERIAL AND IS SECURED IN PLACE BY 2 'PIP' PINS. IN THIS INSTANCE THE FO FAILED TO REMOVE THE OUTFLOW VALVE COVER. I TAKE FULL RESPONSIBILITY FOR THIS. WHEN I ASKED HIM LATER WHY HE HAD NOT REMOVED THE COVER HE STATED THAT HE HAD SIMPLY OVERLOOKED IT OR HAD NOT SEEN IT ON HIS WALKAROUND. IN ADDITION; THERE IS AN ITEM ON OUR CHKLIST PRIOR TO STARTING ENGS THAT REQUIRES A RESPONSE THAT THE EXTERIOR INSPECTION HAS BEEN COMPLETED. WE RECEIVED NO ABNORMAL INDICATIONS ON TKOF OR DURING THE CLB OF ANY KIND THAT WOULD HAVE INDICATED THE COVER WAS STILL IN PLACE. PASSING ABOUT FL240 WE HEARD A LOUD POP AND SHUDDER AS IF THE AIRPLANE HAD HIT A BIRD. I IMMEDIATELY GLANCED AT THE ENG INSTS AND SAW NO ABNORMAL INDICATIONS. WE CHKED ALL SYS; ENGS; HYDS; PNEUMATICS; AND ELECTRICAL AND EVERYTHING WAS NORMAL. WE THOUGHT; PERHAPS; THAT WE HAD BLOWN A MAIN TIRE BECAUSE THE FLT ATTENDANT RPTED A SMELL OF BURNING RUBBER BRIEFLY FOLLOWING THE INCIDENT. AFTER WE HAD TROUBLESHOT ALL SYS FOR POSSIBLE MALFUNCTIONS; WE PLACED A CALL TO OUR MAINT DEPT AND TOLD THEM WHAT HAD HAPPENED AND THEY SUGGESTED THAT WE LOOK THROUGH THE 'PEEP' HOLE INTO THE BOILER ROOM FROM THE AFT BAGGAGE COMPARTMENT AND THAT WE CHK THE WATER BOTTLES LOCATED IN THE BAGGAGE COMPARTMENT AS WELL. WE HAD ALREADY DONE THIS. THEY ALSO COMMUNICATED WITH GULFSTREAM AEROSPACE FOR ADVICE. WE CONSIDERED RETURNING TO RENO; BUT DECIDED TO CONTINUE TO OUR DEST; NEW ORLEANS UNTIL WE HAD SOME FURTHER EVIDENCE OF APROB. WE WERE WELL ABOVE MAX LNDG WT AT THE TIME WHICH PROMPTED US TO CONTINUE UNTIL FURTHER INVESTIGATION REVEALED A CAUSE OF THE INCIDENT. ABOUT 1 HR OUT OF NEW ORLEANS; AND AFTER MUCH ANALYSIS AND TROUBLESHOOTING; I FINALLY ASKED THE FO IF HE HAD REMOVED THE OUTFLOW VALVE COVER BECAUSE THAT WAS ABOUT THE ONLY THING LEFT THAT WE HAD NOT CONSIDERED AS THE CAUSE OF THE INCIDENT. AT THAT POINT; THE FO APPEARED TO HESITATE BEFORE RESPONDING; AND I KNEW WHAT HAD HAPPENED. WHEN WE ARRIVED IN NEW ORLEANS; WE SHUT DOWN AND GOT A LADDER AND INSPECTED THE R ENG FOR THE POSSIBILITY THAT THE OUTFLOW VALVE COVER HAD BEEN INGESTED. THE TWO 'PIP' PINS WERE STILL IN PLACE ON THE FUSELAGE AND THERE WERE SOME LIGHT SCUFF MARKS DOWN THE R SIDE OF THE FUSELAGE; ON THE LEADING EDGE OF THE R WING; AND ON THE LEADING EDGE OF THE R INLET COWL. THERE APPEARED TO BE NO DAMAGE TO THE ENG OR FAN BLADES. AT THIS POINT; I ASSUMED THAT THE COVER; OR A PIECE OF IT; HAD PROBABLY BEEN INGESTED BY THE ENG; BUT HAD DONE NO DAMAGE. WHEN WE STARTED THE ENGS; ALL INDICATIONS WERE AGAIN NORMAL; AND I MADE THE JUDGEMENT THAT WE COULD CONTINUE OUR TRIP SAFELY TO OUR HOME BASE OF WINSTON-SALEM; NC. THE REMAINDER OF THE TRIP WAS WITHOUT INCIDENT. UPON FURTHER INSPECTION BY OUR MAINT DEPT; SOME MINOR BLADE DAMAGE WAS DISCOVERED THROUGH A BOROSCOPE INSPECTION IN THE COMPRESSOR SECTION WHICH REQUIRED THAT THE AIRPLANE BE FLOWN TO MONTREAL TO THE ROLLS ROYCE FACILITY WHERE THE BLADES WERE DRESSED AND THE ENG RETURNED TO SVC. ROLLS ROYCE GRANTED A VARIANCE OF 10 HRS TO COMPLY WITH THIS WORK WHICH ALLOWED FOR THE FLT TO MONTREAL. THE WORK REQUIRED NO REPLACEMENT OF PARTS AND WAS DONE IN ABOUT 24 HRS. A CONTRIBUTING FACTOR TO THIS INCIDENT WAS THAT THE DEP TIME OUT OF RENO HAD BEEN MOVED UP ABOUT 1 1/2 HRS ON SHORT NOTICE. THIS PUT SOME PRESSURE ON THE CREW TO GET THE AIRPLANE READY IN TIME FOR THE PAX'S ARR. HOWEVER; OUR CREWS ARE ALL TRAINED NOT TO ALLOW TIME PRESSURES TO CHANGE HABIT PATTERNS OR PROCS. ON THE CONTRARY; WHENEVER OUR CREWS FEEL RUSHED; WE KNOW THAT THIS IS A RED FLAG WHICH SHOULD SERVE AS A WARNING TO BE ESPECIALLY ALERT FOR MISTAKES LIKE THIS ONE. IN THIS CASE; HOWEVER; THE SYS APPARENTLY BROKE DOWN BECAUSE A MISTAKE WAS MADE. SUPPLEMENTAL INFO FROM ACN 388555: I WAS AT FAULT FOR ALLOWING MYSELF TO GET IN A HURRY AND DO AN ABBREVIATED WALKAROUND; MISSING THE FACT THAT THE COVER WAS STILL ON THE ACFT. THE PROB COULD HAVE BEEN AVOIDED BY SLOWING DOWN AND ACCOMPLISHING A THOROUGH EXTERIOR PREFLT INSPECTION.