Pascal's
Principle
Blaise
Pascal was a French mathematician,
physicist and religious philosopher who lived in the midseventeenth
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 Utube 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 crosssection
area of 1 square inch, while the cylinder on the right shows
a crosssection 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 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 crosssection 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).
