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Can anyone prove the hydraulic formula to raise a mass m by distance d where the force on the piston must be increased by delta F = rho g (A1 + A2) d

where A1 is the area of the piston where the force is being applied, A2 is the area of the piston on the side supporting the mass m. rho is density of hydraulic fluid and g is accn due to gravity.

Have I explained this clearly? Any help to a very rusty physicist greatly appreciated!