As we have seen, the pressure in a fluid increases with depth, due to the weight of the fluid above the point of interest. In this section we will see that a completely enclosed fluid may be subjected to an additional pressure by the application of an external force. If an applied pressure P1 is increased or decreased, the pressure at any other point within the confined liquid changes correspondingly. This is called Pascal's principle.
"Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls."
Pascal's Principle can help us do work. If you look at the enclosed fluid on the right you can imagine applying a pressure (P1) to the small piston which would equal F1/A1. According to Pascal's Principle this pressure would be transmitted to all other parts of the liquid such as the underside of the other piston so P2 = P1. This would mean that F1/A1 = F2/A2. According to this ratio, if the area of piston 2 is two times larger than the area of piston 1 that would mean we could lift twice as much weight than our input force!!!
Problem #1: In the hydraulic car lift shown on the right, the input piston on the left has a radius of 0.0120 m and a negligible weight. The output plunger on the right has a radius of 0.150 m. The combined weight of the car and the plunger is 20,500 N. Suppose that the bottom surfaces of the piston and plunger are at the same level, so that h=0 in the picture. What is the magnitude F1 of the input force that is needed to support the car?
Problem #2: Let's assume the same data as above except that the bottom surfaces of the piston and plunger are at different levels, such that h=1.10 meters. The car lift uses hydraulic oil that has a density of 800 kg/m3 . What is the magnitude F1 of the input force that is now needed to support the car?