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The consertvation of energy in a hydraulic system could be understood by the formular (ENERGY = FORCE x DISTANCE) that represents mechanical energy. Now the hydraulic system consist mainly of two set of pistons which are the master where the energy is applied to the system and the slave where energy leaves the system to the load. Irrespective of the force diffence of the master piston and the slave piston, they will always give the same value when multiplied with distance moved by their respective pistons. This prove that the difference in forces experienced or distance moved by the master and slave piston did not alter the amount of energy in the hydraulic system since energy can be seen as force x distance ;)

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