How does pascals principle related to hydraulic lifts

Pascal's Law and Mechanical Advantage Pascal's law allows forces to be multiplied. Generally, the mechanical advantage is calculated as:. Applied to the system shown below, such as a hydraulic car lift, Pascal's law allows forces to be multiplied. The cylinder on the left shows a cross-section area of 1 square inch, while the cylinder on the right shows a cross-section area of 10 square inches.

The cylinder on the left has a weight force on 1 pound acting downward on the piston, which lowers the fluid 10 inches. As a result of this force, the piston on the right lifts a 10 pound weight a distance of 1 inch. The pound load on the 1 square inch area causes an increase in pressure on the fluid in the system. This pressure is distributed equally throughout and acts on every square inch of the 10 square inch area of the large piston.

As a result, the larger piston lifts up a pound weight. The larger the cross-section area of the second piston, the larger the mechanical advantage, and the more weight it lifts. See also: What is Mechanical Advantage. The formulas that relate to this are shown below:.

This system can be thought of as a simple machine lever , since force is multiplied. The mechanical advantage can be found by rearranging terms in the above equation to. For example, in the figure below, P3 would be the highest value of the three pressure readings, because it has the highest level of fluid above it. If the above container had an increase in overall pressure, that same added pressure would affect each of the gauges and the liquid throughout the same.

For example P1, P2, P3 were originally 1, 3, 5 units of pressure, and 5 units of pressure were added to the system, the new readings would be 6, 8, and Applied to a more complex system below, such as a hydraulic car lift, Pascal's law allows forces to be multiplied.

The cylinder on the left shows a cross-section area of 1 square inch, while the cylinder on the right shows a cross-section area of 10 square inches.

The cylinder on the left has a weight force on 1 pound acting downward on the piston, which lowers the fluid 10 inches. As a result of this force, the piston on the right lifts a 10 pound weight a distance of 1 inch. The 1 pound load on the 1 square inch area causes an increase in pressure on the fluid in the system. This pressure is distributed equally throughout and acts on every square inch of the 10 square inch area of the large piston.

Since the pressure changes are the same everywhere in the fluid, we no longer need subscripts to designate the pressure change for top or bottom:. Hydraulic systems are used to operate automotive brakes, hydraulic jacks, and numerous other mechanical systems Figure. This results in an upward force. 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. Thus, a pressure. 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 N force is applied to the left cylinder in Figure and the right cylinder has an area five times greater, then the output force is 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 Figure. Consider the automobile hydraulic system shown in Figure.

A force of N is exerted on the pedal cylinder. Pressure created in the pedal cylinder is transmitted to the four wheel cylinders. The pedal cylinder has a diameter of 0. Calculate the magnitude of the force. Then we can use the following relationship to find the force. This value is the force exerted by each of the four wheel cylinders. Note that we can add as many wheel cylinders as we wish.

If each has a 2. A simple hydraulic system, as an example of a simple machine, can increase force but cannot do more work than is done on it. Work is force times distance moved, and the wheel cylinder moves through a smaller distance than the pedal cylinder. Furthermore, the more wheels added, the smaller the distance each one moves.