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I have quite a perfect understanding of hydraulic lift, yet there is one huge problem that is contradicting my understanding. for a hydraulic lift where you push on on side of diameter d1 piston, and the object on a piston of diameter d2, you get the equation:

F1/A1 = F2/A2 just to support the object (car) without lifting it. but when you want to lift the car a certain height, you get F1/A1 = F2/A2 + pgh where p is the density of the fluid. this all makes sense.

but why when you do calculations to find the change in pressure force to lift the car a certain height h, it doesnt work. what im doing is:

F1' = A1(F2/A2 + pgh) minus F1 = A1(F2/A2) to get the change in pressure force to life the car a certain height. so Delta F = A1pgh right?

But subbing in values does not get the correct change in pressure. they use some question DeltaF=pg(A1 + A2)h which is something i have never seen before. I dont get the flaw in my logic, please someone help im about to cry.