Pascal's Principle and Hydraulics

Pascal's Principle

Blaise Pascal was a French mathematician, physicist and religious philosopher who lived in the mid-seventeenth century. He made some significant observations about fluid and pressure. He noticed that the shape of a container had no effect on pressure. He also noticed that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid, as well as to the walls of the container. When it says "enclosed fluid," that means that in order for Pascal's Law to be true, you have to be looking at a liquid in a closed container.

Pascal's Principle and Hydraulics

Hydraulic systems use incompressible fluids, such as oil or water, to transmit forces from one location to another within the fluid. Hydraulics are used in most breaking systems. Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

Therefore Pascal's law can be interpreted as saying that any change in pressure applied at any given point of the fluid is transmitted undiminished throughout the fluid.

How do Hydraulics Work?

Imaging if you have a U-tube filled with water and pistons are placed at each end, pressure exerted against the left piston will be transmitted throughout the liquid and against the bottom of the right piston. The pressure that the left piston exerts against the water will be exactly equal to the pressure the water exerts against the right piston.

Now suppose the tube on the right side is made wider and a piston of a larger area is used; for example, the piston on the right has 10 times the area of the piston on the left. If a 1 N load is placed on the left piston, an additional pressure due to the weight of the load is transmitted throughout the liquid and up against the larger piston. The additional pressure is exerted against the entire area of the larger piston. While the pressure exerted is the same, since there is 10 times the area, 10 times as much force is exerted on the larger piston. Thus, the larger piston will support a 10 N load - ten times the load on the smaller piston.

Pascal's Law and Mechanical Advantage ----Pascal's law allows forces to be multiplied.

Generally, the mechanical advantage is calculated as:

MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)

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.

hydraulic press

The 100 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 1000 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:

Area1/Area2= Distance moved 2/Distance moved 1

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

Mechanical Advantage(MA) = D1/D2 = A2/A1

For the sample problem above, the MA would be 10:1 (10 inches/ 1 inch or 10 square inches / 1 square inch).


Test your Understanding:
1. What is the Mechanical Advantage of a hydraulic car lift similar to that shown above where A1= 2 and A2 = 20 sq. in. and the applied force is 100 lbs.
a) 40
b) 60
c) 2
d) 10

2. What does Pascal's Principle state?
a) Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
b) any change in pressure applied at any given point of the fluid is transmitted with a decreasing value throughout the fluid.
c) for a fluid with zero viscosity, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
d) any change in pressure applied at any given point of the fluid is transmitted undiminished throughout the fluid.

3. A hydraulic press has an input cylinder 1 inch in diameter and an output cylinder 6 inches in diameter. Assuming 100% efficiency, find the force exerted by the output piston when a force of 10 pounds is applied to the input piston.
a) 100 pounds
b) 360 pounds
c) 60 pounds
d) 286 pounds

4. What is the Mechanical Advantage of a lever that can lift a 500 pound weight using a load of 20 pounds.
b) 10
c) 20
d) 25

5. How much weight will needed to be applied to a hydraulic system that has a MA of 20 to lift a 1000 pound load.
a) 2000 pounds
b) 500 pounds
c) 50 pounds