What is hydraulic lift? What is its principle? Discuss its working.

Hydraulic lift is a machine which is based on Pascal's law. In these devices fluids are used for transmitting presure. 

Hydraulic lift consists of two cylinders of different cross-sectional areas connected with a pipe. The cylinders are filled with incompressible liquid and frictionless pistons are fitted in both the cylinders as shown in figure below. 



Let 'a' and 'A' be the area of cross-section of smaller piston and bigger piston respectively. The load to be lifted is placed on bigger cross-section and effort is applied on smaller piston.
Let a force 'f' be applied on the smaller piston.

The pressure exerted by f on piston is,

            $\mathrm{P}=\frac{\mathrm{f}}{\mathrm{a}}$    ... (1) 

Now, according to Pascal's law, the pressure transmitted to bigger piston is also P.

Thus, force on bigger piston is, given by, 
$$\begin{gathered} \mathrm{F} = \mathrm{PA} = \frac{\mathrm{A}}{\mathrm{a}}\mathrm{f} \\ \mathrm{We} \mathrm{have}, \mathrm{A} > \mathrm{a}. \\ \mathrm{Let}, \mathrm{A} = \mathrm{\eta a} \\ \mathrm{So}, \mathrm{F} = \mathrm{\eta f} \end{gathered}$$ 

That is, the transmitted force gets multiplied by a factor $\mathrm{\eta }$ of applied force.