The science
Pascal's principle: pressure applied to an enclosed incompressible fluid is transmitted undiminished, so p = F_pump / A_pump = F_ram / A_ram. Here the hand force is multiplied by the lever ratio (6.2) and efficiency (79 %), then by the area ratio A_ram / A_pump. The ram can only rise when p ≥ m g / A_ram.
Volume is conserved: each pump stroke moves A_pump · s of oil into the ram, which rises by A_pump s / A_ram. Force is multiplied but distance is divided by the same factor, so work is not created (energy check).
Simplifications: incompressible oil, no leakage, ideal check valves, constant 79 % mechanical efficiency, relief at 75 MPa, travel limited to 90 mm. Illustrative sizes, not a rated jack.
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