If we have a simple hydraulic lift with one piston which we push down (piston A), and the other piston (piston B) which is below the first one, why do we neglect the hydrostatic pressure difference in our equations?
Textbooks give the following equation: $$\frac{F_b}{A_b} = \frac{F_a}{A_a}$$
But why shouldn't that be like the following?: $$\frac{F_b}{A_b} = \frac{F_a}{A_a} + \rho g h$$
where h is the height difference between the pistons.
In short, why don't we consider the hydrostatic pressure difference due to the weight of the fluid in the vertical columns of a hydraulic lift and only consider the pressure due to the weights above the pistons?
