B737-700 CAPT REPORTS TWO INCIDENTS OF INAPPROPRIATE PRESSURE FROM MAINT TO CONTINUE TO HIS DESTINATION RATHER THAN RETURNING FOR MAINT INSPECTION OF MECHANICAL/ENVIRONMENTAL CONCERNS ENCOUNTERED EARLY IN THE RESPECTIVE FLTS.

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I HAD ARRIVED AT THE ARPT EARLY TO MAKE SURE I HAD ENOUGH TIME TO THOROUGHLY REVIEW THE WX AND PAPERWORK ASSOCIATED WITH MY FLT TO ZZZ1. WHEN I ARRIVED AT THE GATE IT WAS OBVIOUS THAT MAINT WAS WORKING ON THE AIRPLANE. I WAS APCHED BY A MAINT TECHNICIAN WHO TOLD ME THEY HAD BEEN INSTRUCTED TO POS THE JET AT THE GATE AND THEY WERE NOT FINISHED WITH THE WORK ASSOCIATED WITH HAVING CHANGED THE #1 (L) ENG. PREVIOUSLY I HAD KNOWN NOTHING ABOUT THE ENG CHANGE. SHORTLY THEREAFTER; THE TECHNICIAN ASKED ME IF I WOULD BE WILLING TO DO THE ENG RUN TEST WHEN THEY WERE READY. THEY HAD ASKED THAT PAX NOT BE BOARDED SO AS TO ALLOW THEM TO DO THE ENG RUN. HOWEVER; CONTRARY TO THEIR INSTRUCTIONS; PAX HAD BEEN BOARDED AND PROCEDURALLY THEY COULD NOT CONDUCT THE ENG RUN. I AGREED TO DO THE ENG RUN. WITH A MAINT REPRESENTATIVE IN THE COCKPIT JUMPSEAT; WE COMMENCED THE ENG RUN TEST. OUR FIRST ATTEMPT AT THE ENG RUN WAS UNSUCCESSFUL. THE ASSOCIATED ENG DRIVEN HYD PUMP LOW PRESSURE LIGHT DID NOT EXTINGUISH WHEN THE START BUTTON WAS ENGAGED AND THE ENG MOTORED. IGNITION DID NOT TAKE PLACE AFTER THE OTHER PARAMETERS WERE MET AND THE FUEL LEVER WAS PLACED ON. WE DISCONTINUED THE START. AFTER A QUICK LOOK AROUND; WE 'DISCOVERED' THE ENG FIRE 'T' HANDLE HAD BEEN PULLED IN ACCORDANCE WITH THE MAINT DIRECTIONS ASSOCIATED WITH THE ENG CHANGE. THE 'T' HANDLE HAD NOT BEEN RETURNED TO ITS NORMAL POS. THE 'T' HANDLE WAS RETURNED TO ITS USUAL POS AND WE TRIED THE ENG RUN AGAIN. PREDICTABLY; THIS SECOND ENG RUN WAS SUCCESSFUL. THE VARIOUS CHKS WERE CONDUCTED AND THE ENG WAS SHUT DOWN FOR FINAL INSPECTION. THE PAPERWORK WAS COMPLETED AND WE DEPARTED THE GATE SOME 36 MINS LATE WITH A BRAND NEW ENG ON ITS MAIDEN FLT. THE DEP WAS NORMAL UP UNTIL ABOUT FL240 ON OUR CLB TO THE HIGHER ASSIGNED CRUISE ALT. THE MASTER CAUTION ILLUMINATED; WITH THE HYD LIGHT ON THE FO'S ANNUNCIATOR PANEL. I LOOKED UP ON THE OVERHEAD AND NOTICED THE #1 (L) ENG DRIVEN HYD LOW PRESSURE LIGHT ILLUMINATED. INSTINCTIVELY I LOOKED AT THE L HYD PRESSURE AND QUANTITY INDICATORS. I BELIEVED I SAW THE L HYD QUANTITY INDICATOR SHOWING 60%. HOWEVER; ALMOST IMMEDIATELY THE L HYD QUANTITY INDICATOR WENT BACK TO SOME 90% FULL INDICATION AND REMAINED THERE. THE PRESSURES (BOTH SYS) WERE STABLE AROUND 3000 PSI. WE LEVELED THE JET OFF AROUND FL260 AND I ASKED THE QUESTION: WHAT'S THE PROB?' THE FO AND I DECIDED THAT WE HAD A FAILED #1 ENG DRIVEN HYD PUMP. THE ASSOCIATED ELECTRIC PUMP WAS OPERATING NORMALLY; AND WE HAD NORMAL PRESSURES AND QUANTITIES IN BOTH HYD SYS. THERE WERE NO OTHER WARNING LIGHTS ILLUMINATED. WE CONSULTED AND ACCOMPLISHED THE ASSOCIATED QRH. AFTER A SHORT DISCUSSION BTWN THE FO AND ME; WE DECIDED TO RETURN TO ZZZ (THE DEP ARPT) FOR A PRECAUTIONARY LNDG. MY EXPERIENCE (INCLUDING AN A&P LICENSE) AND INTUITION TOLD ME TO SUSPECT SOMETHING MORE SERIOUS THAN A SIMPLE FAILURE OF A HYD PUMP ON A BRAND NEW ENG DURING ITS FIRST FLT. I CONTACTED DISPATCH TO NOTIFY THEM OF MY CONDITION AND OUR DESIRE TO RETURN. DISPATCH PLACED MAINT CTL ON THE RADIO. AT THIS POINT; MAINT CTL BEGAN TO TAKE THE 'LEAD' IN THE RADIO CONVERSATION; AS HE BEGAN ASKING THE QUESTIONS. HE ACKNOWLEDGED THE ENG DRIVEN HYD PUMP FAILURE AND THEN ASKED ME IF I HAD ANY 'SECONDARY' INDICATIONS. I DON'T REMEMBER WHETHER OR NOT I MENTIONED THE MOMENTARY LOW HYD QUANTITY INDICATION BUT IT WAS INDICATING NORMALLY NOW. I BELIEVE I ANSWERED NO. THEN THE MAINT PERSON ON THE RADIO SAID SOMETHING LIKE; 'IF YOU WANT TO CONTINUE TO ZZZ1; WE WILL CONCUR/SUPPORT (?) THAT DECISION