Pascal's Principle and Hydraulics

Hydraulic systems use a incompressible fluid, such as oil or water, to transmit forces from one location to another within the fluid. Most aircraft use hydraulics in the

braking systems and landing gear. Pneumatic systems use compressible fluid, such as air, in their operation. Some aircraft utilize pneumatic systems for their brakes,

landing gear and movement of flaps.

Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is any equal increase at every other point in the

container.

A container, as shown below, contains a fluid. There is an increase in pressure as the length of the column of liquid increases, due to the increased mass of the fluid

above.

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 10.

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. As a result, the larger piston lifts up a 10 pound weight. The larger the cross-section area of the second piston,

the larger the mechanical advantage, and the more weight it lifts.

The formulas that relate to this are shown below:

P1 = P2 (since the pressures are equal throughout).

Since pressure equals force per unit area, then it follows that

F1/A1 = F2/A2

It can be shown by substitution that the values shown above are correct,

1 pound / 1 square inches = 10 pounds / 10 square inches

Because the volume of fluid pushed down on the left side equals the volume of fluid that is lifted up on the right side, the following formula is also true.

V1 = V2

by substitution,

A1 D1 = A2 D2

A = cross sectional area

D = the distance moved

or

A1/A2= D2/D1

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(IMA) = D1/D2 = A2/A1

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

Given these simple formulas, try to answer the questions below.

Exercises:

1.A hydraulic press has an input cylinder 1 inch in diameter and an output cylinder 6 inches in diameter.

a.Assuming 100% efficiency, find the force exerted by the output piston when a force of 10 pounds is applied to the input piston.

(answer)

b.If the input piston is moved through 4 inches, how far is the output piston moved?

(answer)

2.A hydraulic system is said to have a mechanical advantage of 40. Mechanical advantage (MA) is FR (output) / FE (input). If the input piston, with a 12 inch

radius, has a force of 65 pounds pushing downward a distance of 20 inches, find

a.the volume of fluid that has been displaced

(answer)

b.the upward force on the output piston

(answer)

c.the radius of the output piston

(answer)

d.the distance the output piston moves

(answer)

3.What pressure does a 130 pound woman exert on the floor when she balances on one of her heels? Her heels have an average radius of 0.5 inch.

(answer)

4.A car has a weight of 2500 pounds and rests on four tires, each having a surface area of contact with the ground of 14 square inches. What is the pressure the

ground experiences beneath the tires that is due to the car?

(answer)

Extension :

5.The input and output pistons of a hydraulic jack are respectively 1 cm and 4 cm in diameter. A lever with a mechanical advantage of 6 is used to apply force to

the input piston. How much mass can the jack lift if a force of 180 N is applied to the lever and efficiency is 80%?

(answer)

Back to Aeronautics Lessons

Created by Carol Hodanbosi

WWW pages edited by Jonathan G. Fairman - August 1996

Physics.

the law that an external pressure applied to a fluid in a closed vessel is

uniformly transmitted throughout the fluid.

Tire pressure conversions :

metric - english system

Tire pressure

Kilo Pascal - (KPa)

Pound /Square inch

160

23,2

170

24,7

180

26,1

190

27,6

200

29,0

210

30,5

220

31,9

230

33,4

240

34,8

250

36,3

260

37,7

270

39,2

In an enclosed fluid at rest, any changes in pressure are transmitted undiminished to all points in the fluid and act in all directions.

This is the principle that underlies hydraulics. Since pressure is the force per unit area, a greater area exposed to fluid pressure will experience a greater force than a

smaller area exposed to the same pressure. This means that by applying a small force to a small area of an enclosed fluid, a large force will be applied to a large area in

the same fluid. This is the principle that the brakes in your car depend on: you apply force to your brake pedal, which applies pressure to fluid in the "brake line" (a metal

tube filled with oil). The increase in pressure in the brake fluid is transmitted to the brake pad (at your wheel). The surface of the brake pad in contact with the fluid is

larger than the surface of the brake pedal in contact with the fluid. Since the surface is larger, it feels more force. In this way, a hydraulic apparatus (your brake

system) magnifies the force of your foot on the brake pedal so much that it can stop a car.

Pascal's principle

also called PASCAL'S LAW, in fluid (gas or liquid) mechanics, statement that

in a fluid at rest in a closed container a pressure change in one part is

transmitted without loss to every portion of the fluid and to the walls of the

container. The principle was first enunciated by the French scientist Blaise

Pascal.

Pressure is equal to the force divided by the area on which it acts.

According to Pascal's principle, in a hydraulic system a pressure exerted

on a piston produces an equal increase in pressure on another piston in

the system. If the second piston has an area ten times that of the first, the

force on the second piston is ten times greater, though the pressure is the

same as that on the first piston. This effect is exemplified by the hydraulic

press, based on Pascal's principle, which is utilized in such applications as

hydraulic brakes.

Pascal also discovered that the pressure at a point in a fluid at rest is the

same in all directions; the pressure would be the same on all planes passing

through a specific point. This fact is also known as Pascal's principle, or

law.

Pascal was a French mathematician and man-of-letters. Pascal's mother died early and he was left, at

the age of seven, to be with his father and his sister, Jacqueline (Jacqueline was to enter a Jansenist

convent.) His father, high up in the French judiciary, undertook to personally see to his son's education.

Pascal, even as a beginning youth, was a brilliant light in the intellectual community as then existed in

France; many could not believe that such brilliant insights could come from such a mere youth. Up

through the years, until 1654, Pascal divided his life between mathematics and the social life of Paris.

Pascal was credited with the invention of the barometer and certain mathematical formulations which

"heralded the invention of the differential calculus." It was, in 1654, that Pascal was to have a mental

crises and broke completely with his circle, and, claiming to have had religious revelations, went to join

and live with his sister in the religious community in which she had belonged. He was to continue with

his writing, but it now took a distinct religious tone; often, given his position as a Jansenist, a faction of

the Roman catholic church, against the position and the teachings of the Jesuits."

Pascal, Blaise (1623-62):

Pascal was a French mathematician and man-of-letters. Pascal's mother died early and he was left, at

the age of seven, to be with his father and his sister, Jacqueline (Jacqueline was to enter a Jansenist

convent.) His father, high up in the French judiciary, undertook to personally see to his son's education.

Pascal, even as a beginning youth, was a brilliant light in the intellectual community as then existed in

France; many could not believe that such brilliant insights could come from such a mere youth. Up

through the years, until 1654, Pascal divided his life between mathematics and the social life of Paris.

Pascal was credited with the invention of the barometer and certain mathematical formulations which

"heralded the invention of the differential calculus." It was, in 1654, that Pascal was to have a mental

crises and broke completely with his circle, and, claiming to have had religious revelations, went to join

and live with his sister in the religious community in which she had belonged. He was to continue with

his writing, but it now took a distinct religious tone; often, given his position as a Jansenist, a faction of

the Roman catholic church, against the position and the teachings of the Jesuits."

Pascal, Blaise , 1623–62, French scientist and religious philosopher. Studying

under the direction of his father, a civil servant, Pascal showed great precocity,

especially in mathematics and science. Before he was 16 he wrote a paper on

conic sections which won the respect of the mathematicians of Paris; at 19 he

invented a calculating machine. Credited with founding the modern theory of

probability, Pascal also discovered the properties of the cycloid and contributed to

the advance of differential calculus. In physics his experiments increased

knowledge of atmospheric pressure through barometric measurements and of the

equilibrium of fluids (see Pascal's law). As a young man, Pascal came under the

influence of Jansenism, and in 1651 his sister Jacqueline, who had also embraced

Jansenist beliefs, entered the convent at Port-Royal, the center of the movement.

As a result of the death of his father and of his own narrow escape from death,

Pascal in 1654 experienced what he called a "conversion" and thereafter turned

much of his attention to religion. When Antoine Arnauld, a noted Jansenist, was

attacked by the Jesuits, Pascal championed him in his Lettre escrite à un

provincial (1656). Those Provincial Letters, rendered into Latin, quickly circulated

throughout Europe, and they still hold a leading place in the literature of polite

irony. Pascal's religious writings were posthumously published as Pensées de M.

Pascal sur la religion et sur quelques autres sujets (1670). For a modern edition

see Thoughts: An Apology for Christianity (tr. 1955). In the Pensées, famous both

as a religious and philosophical classic, Pascal states his belief in the inadequacy

of reason to solve man's difficulties or to satisfy his hopes. He preached instead

the final necessity of mystic faith for true understanding of the universe and its

meaning to man.

See biographies by A. J. Krailsheimer (1980), H. H. Davidson (1983); studies by E.

Cailliet (1944, repr. 1973), R. Hazelton (1974), and S. E. Melzer (1986).

PRESSURE LAB

our leaders left hand under the car tire

Purpose: The purpose of this lab is to verify Pascals law

(P=f/a)

Materials: a demo car, car jack, ply wood, ink, paper towel,

paper, pen, graph paper.

Procedures:1) Jack up the car.

2) Clean the tire with a paper towel

3) Put the graph paper on the ply wood then put that

under the cleaned tire

4) Then drop the car

5) Then raise the car

6) Now take the graph paper out of the botom of the tire.

7) Next count the number of squares where a 5 small by 5

small is = to 1 square inch, that is covered by the ink of the

tire

8) #7 =A then aply it to the formula.

Data:

14.7 psi + 32= 46.7 P

A= 6 sq inches

P=F/A

46.7=F/6

F=560.4 lb. this is the weight of the frought end of the car.

Conclusion: in conclusion I found out that the weight of the

tire is 560.4 and this verifyed Pascal's law where pressure

is = to Force or weight /area.

Optional Unit VI: Fluid Mechanics

C. Pascal's Principle

Key Concepts

Pressure exerted on an enclosed liquid is transmitted equally to every part of the liquid and to the walls of the container.

(Pascal's principle)

A manometer relies on Pascal's principle to measure pressure in gases.

Pascal's principle is important in understanding hydraulics, the study of the transfer of forces through fluids.

In a hydraulic lift, a force (F) applied to an input piston having a small surface area (A(in)) is transferred to an output piston

having a larger surface area (A(out)). There is no loss in pressure from the input to the output pistons (neglecting friction). As a

result, the output force (F(out))is much larger than the input force (A(out)).

P(out) = P(in) (Pascal's principle)

F(out)

=

F(in)

A(out)

A(in)

Due to conservation of energy, and , the small piston has to travel a proportionately greater distance, d.

Fin · din = Fout · dout

Alternatively, since the volume moved is constant,

din · Ain = dout · Aout

The mechanical advantage of a hydraulic lift is given by:

Mechanical advantage =

F(out)

=

F(in)

A(out)

A(in)

Learning Outcomes

Students will increase their abilities to:

1.Define the following terms: manometer, hydraulics, hydraulic lift.

2.State Pascal's principle.

3.Give some examples which illustrate Pascal's principle.

4.Explain why the output force on a hydraulic lift exceeds the input force.

5.Solve problems involving Pascal's principle.

Teaching Suggestions, Activities and Demonstrations

1.Experimentally investigate pressure in liquids. Challenge students by posing the problem to be considered experimentally.

See if they can come up with their own experimental designs.

2.Bring in a used carburettor from an automobile. (Some students may have access to these.) Examine the venturi. Explore

the principles which make the carburettor operate.

3.Take a short length of used vacuum cleaner hose and spin it in a circle to produce an interesting sound. The class can

speculate as to how the sound is produced.

4.Cut out wooden blocks having different shapes. Predict their orientation when they float in water. Irregular shaped

blocks may float in some interesting ways. Relationships between the orientation for stable equilibrium, the shape of the

block, and the centre of gravity can be made. This activity provides students with an understanding of how predictions

are made in science.

P(out) = P(in) (Pascal's principle)

F(out)

=

F(in)

A(out)

A(in)