# Why don't we include $\rho g h$ in a hydraulic jack below?

Consider a hydraulic jack with massless pistons as follows.

The famous equation for this system is

$$\frac{F_1}{A_1}=\frac{F_2}{A_2}$$

My question is why isn't the equation as follows?

$$\frac{F_1}{A_1}=\frac{F_2}{A_2} + \rho g h$$

It is based on my understanding that any points in the same horizontal line have the same pressure.

Could you spot my misconception?

• This is a good exercise to learn a bit of thinking like a physicist. You've done the "be careful and pedantic in deciding what the physics is" part. Now do the "figure out what contributions we can safely ignore" part... – dmckee --- ex-moderator kitten Mar 11 '14 at 16:04

## 2 Answers

Your second equation is correct. The $\rho gh$ term is small compare to the force needed to lift a car for example in a real jacking situation, however.

Your second equation is correct when there is a piston height difference.this equation is derived from pascal law.law states the initial difference remains same.it only talks what happens when you apply a force on one end and how the pressure of incompressible liquid transmit that force to the other end.