What was found
#1 HYD LOW QTY FOLLOWED BY HYD SYSTEM 1 FAIL ON CLIMB OUT. #1 HYD LOW QTY MESSAGE CAME ON DURING CLIMB OUT OF IAH/ QTY WAS SHOWING AMBER. SAW THE CARROTS WERE SLOWLY MOVING DOWN THEN LOST SYSTEM 1 HYD PRESSURE AND THEN #1 HYD SYSTEM FAILURE MESSAGE APPEARED. #1 EDP WAS RUNNING FOR 30 MINUTES. ONCE ON THE GROUND THEY SHUTDOWN THE #1 ENGINE AND TURNED OFF #1 ELECTRICAL PUMP IN FLIGHT. REMOVED AND REPLACED #1 HYDRAULIC EDP. CASE DRAIN / PRESSURE FILTER BOWL WAS ABSENT OF CONTAMINATION. UPON OPS CHECK, FOUND UPPER HYDRAULIC HOSE FROM EDP SEVERELY LEAKING WITH A 1 INCH GASH. REMOVED AND REPLACED UPPER HYDRAULIC HOSE. OPS AND LEAK CHECK SAT. ADDED 5 LITERS OF HYDRAULIC FLUID DUE TO HYD SYSTEM #1 WAS EMPTY. PERFORMED LANDING FREE FALL CONDITION-INSP CHECK. INSP/CHECK SAT.