All about pascal's law, it's history, theory of law,derivation of equation, it's applications, descriptive examples of hydraulic brakes and hydraulic lift.

1. By:
Lokesh Maheshwari 1
PASCA

2. S.No. TOPIC Page No.
1. Aim of Project 3
2. Introduction 4
3. History of Pascal’s law 5
4. Pascal’s Law 6 – 8
5. Applications 9
6. Hydraulic Lift 10 – 12
7. Hydraulic Brake 13 – 17
8. Conclusion 18
9. Bibliography 19
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3. AIM OF PROJECT
To study about Pascal’s Law:-
• Its history and discovery
• More about Pascal’s law
 Its define
Its mathematical derivation and expression
• Applications of Pascal’s law
 Hydraulic Lift
 Hydraulic Brake
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4. INTRODUCTION
In this project we will see how Blaise Pascal, a French scientist,
discovered Pascal’s Law. How is it used in fluid mechanics and daily life?
Pascal’s law’s uses has been increased over time in
scientific area as well as in daily life. It is very much used in places where
there is a work of lifting heavy loads and applying same force at same
time to multiple areas with a single lever.
So, it is a very important law and we will know some
basic concepts of it.
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5. History Of Pascal’s Law
Pascal's law was discovered by a French scientist Blaise
Pascal during an experiment that was allegedly performed
in the 1600's.
A 10 m long pole was vertically inserted into a barrel that
was filed with water. As the water was poured into the
vertical tube, Pascal discovered that the pressure from the
water caused the barrel to burst.
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6. Pascal’s Law
Pascal’s Law, also called Pascal’s Principle, in fluid (gas or liquid)
mechanics, states 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.
This fact may be demonstrated in a simple way.
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7. Figure shows an element in the interior of a fluid at rest. This element
ABC-DEF is in the form of a right-angled prism. In principle, this
prismatic element is very small so that every part of it can be considered
at the same depth from the liquid surface and therefore, the effect of the
gravity is the same at all these points. But for clarity we have enlarged this
element. The forces on this element are those exerted by the rest of the
fluid and they must be normal to the surfaces of the element as
discussed above. Thus, the fluid exerts pressures Pa, Pb and Pc on this
element of area corresponding to the normal forces Fa, Fb and Fc as
shown in Figure on the faces BEFC, ADFC and ADEB denoted by Aa,
Ab and Ac respectively. Then
Fb sin = Fc, Fb cos = Fa (by equilibrium)
Ab sin = Ac, Ab cos = Aa (by geometry)
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8. Fb / Ab = Fc / Ac = Fa / Ac ; Pa = Pb = Pc
Hence, pressure exerted is same in all directions in a fluid at rest. It again
reminds us that like other types of stress, pressure is not a vector quantity. No
direction can be assigned to it. The force against any area within (or bounding) a
fluid at rest and under pressure is normal to the area, regardless of the
orientation of the area.
Now consider a fluid element in the form of a horizontal bar of uniform cross-
section. The bar is in equilibrium. The horizontal forces exerted at its two ends
must be balanced or the pressure at the two ends should be equal. This proves
that for a liquid in equilibrium the pressure is same at all points in a horizontal
plane. Suppose the pressure were not equal in different parts of the fluid, then
there would be a flow as the fluid will have some net force acting on it. Hence in
the absence of flow the pressure in the fluid must be same everywhere. Wind is
flow of air due to pressure differences.
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9. Applications of Pascal’s Law
• Hydraulic Lift
• Hydraulic Brake
• Hydraulic Jack and Hydraulic Press
• Artesian Wells and Dams
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10. Hydraulic Lift
A hydraulic lift is a device for moving objects using force
created by pressure on a liquid inside a cylinder that
moves a piston upward. Incompressible oil is pumped
into the cylinder, which forces the piston upward. When
a valve opens to release the oil, the piston lowers by
gravitational force. The principle for hydraulic lifts is based on Pascal‘s law for
generating force or motion, which states that pressure change on an
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11. incompressible liquid in a confined space is passed equally throughout the
liquid in all directions.
The concept of Pascal‘s law and its application to hydraulics can be seen
in below, where a small amount of force is applied to an incompressible
liquid on the left to create a large amount of force on the right.
In a hydraulic lift as shown in Figure two pistons are separated by the space
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12. filled with a liquid. A piston of small cross section A1 is used to exert a
force F1 directly on the liquid. The pressure P= F1 /A1 is transmitted
throughout the liquid to the larger cylinder attached with a larger piston of
area A2, which results in an upward force of P × A2.
Therefore, the piston is capable of supporting a large force (large weight of,
say a car or a truck, placed on the platform)
F2 = PA2 = F1 A2 /A1
By changing the force at A1, the platform can be moved up or down. Thus, the
applied force has been increased by a factor of A2 /A1 and this factor is the
mechanical advantage of the device.
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13. Hydraulic Brake
A hydraulic brakes system is a braking mechanism
that uses brake fluid to transmit force into the
system. The fluid transfers pressure from the
control mechanism to the braking mechanism.
Hydraulic braking systems are widely used in low-
speed four-wheelers such as the Tata Ace. It works
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14. with the drum type, while the disc type is used in almost all cars. In this
type of braking system, the mechanical forces transmitted by the driver on
the brake pedal are converted to hydraulic pressure by a device known as
a master cylinder, and then this hydraulic pressure is sent to the final drum
or disc. It goes to stop or accelerate the caliper vehicle.
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15. Construction
The construction of hydraulic braking systems involves the following part arrangement :-
• Brake pedal or lever
• Wreath also known as actuating rod
• Master cylinder
• One or two pistons
• A return spring
• Gasket or O rings
• Brake fluid and Fluid reservoir
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16. Working
The following process occurs when the driver applies a brake in a
vehicle equipped with hydraulic brakes mounted on the drum. The
speed or activation of the brake pedal causes a master cylinder to
move a rod connected between the pedal and the piston, which in turn
pushes the piston of the master cylinder inside the master cylinder like
a medical syringe.
This movement of the pistons inside the master cylinders causes
compression of the brake fluid inside the master cylinder, which in turn
converts mechanical energy to hydraulic pressure. This highly
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17. compressed brake fluid from the master cylinders moves inside the brake,
and this hydraulic pressure transfers from the master cylinder to the brake
drum.
When this high-pressure brake fluid o enters the wheel cylinder or drum
cylinder due to its high pressure, there is movement in the cylinder piston,
which in turn expands the static brake shoe attached to it.
Due to the expansion of the brake shoe, a friction contact is formed
between the brake shoes and the drum lining (rotating drum part), which in
turn converts the kinetic energy of the vehicle into heat energy & finally
braking.
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18. • A change in pressure applied to an enclosed fluid is transmitted
undiminished to all portions of the fluid and to the walls of its
container. Pascal's principle, an experimentally verified fact, is what
makes pressure so important in fluids.
• It has many applications in daily life. Several devices, such as hydraulic
lift and hydraulic brakes, are based on Pascal's law. Fluids are used for
transmitting pressure in all these devices. In a hydraulic lift, as shown
in the figure above, two pistons are separated by the space filled with a
liquid.
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19. REFERENCES
• NCERT book
• Britannica
• Wikipedia
• IQS Directory
• Google
• Mechanical Jungle
• Brainly
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