In a hydraulic lift, compressed air exerts a force $${F_1}$$ on a small piston having a radius of $$5\,cm.$$  This pressure is transmitted to a second piston of radius $$15\,cm.$$  If the mass of the load to be lifted is $$1350\,kg,$$   find the value of $${F_1}$$ ? The pressure necessary to accomplish this task is

Solution :
Since pressure is transmitted undiminished throughout the fluid (Pascal's law)
$$\eqalign{ & {F_1} = \frac{{{A_1}}}{{{A_2}}}{F_2} = \frac{{\pi \left( {5 \times 5} \right)}}{{\pi \left( {15 \times 15} \right)}}\left( {1350 \times 9.81} \right) \cr & \approx 1.5 \times {10^3}N \cr} $$
The air pressure that will produce this force is
$$P = \frac{{{F_1}}}{{{A_1}}} = \frac{{1.5 \times {{10}^3}}}{{\pi {{\left( {5 \times {{10}^{ - 2}}m} \right)}^2}}} = 1.9 \times {10^5}Pa$$