14.3 Pascal's principle and hydraulics  (Page 2/6)

Applications of pascal’s principle and hydraulic systems

Hydraulic systems are used to operate automotive brakes, hydraulic jacks, and numerous other mechanical systems ( [link] ).

We can derive a relationship between the forces in this simple hydraulic system by applying Pascal’s principle. Note first that the two pistons in the system are at the same height, so there is no difference in pressure due to a difference in depth. The pressure due to $F_1$ acting on area $A_1$ is simply

According to Pascal’s principle, this pressure is transmitted undiminished throughout the fluid and to all walls of the container. Thus, a pressure $p_2$ is felt at the other piston that is equal to $p_1$ . That is, $p_1=p_2.$ However, since $p_2=F_2\text{/}{A}_2,$ we see that

This equation relates the ratios of force to area in any hydraulic system, provided that the pistons are at the same vertical height and that friction in the system is negligible.

Hydraulic systems can increase or decrease the force applied to them. To make the force larger, the pressure is applied to a larger area. For example, if a 100-N force is applied to the left cylinder in [link] and the right cylinder has an area five times greater, then the output force is 500 N. Hydraulic systems are analogous to simple levers, but they have the advantage that pressure can be sent through tortuously curved lines to several places at once.

The hydraulic jack    is such a hydraulic system. A hydraulic jack is used to lift heavy loads, such as the ones used by auto mechanics to raise an automobile. It consists of an incompressible fluid in a U-tube fitted with a movable piston on each side. One side of the U-tube is narrower than the other. A small force applied over a small area can balance a much larger force on the other side over a larger area ( [link] ).

From Pascal’s principle, it can be shown that the force needed to lift the car is less than the weight of the car:

where $F_1$ is the force applied to lift the car, $A_1$ is the cross-sectional area of the smaller piston, $A_2$ is the cross sectional area of the larger piston, and $F_2$ is the weight of the car.

Calculating force on wheel cylinders: pascal puts on the brakes