discovered the fundamental law for the science of
hydraulics. Pascals law tells us that pressure on a
confined fluid is transmitted undiminished in every
direction, and acts with equal force on equal areas,
throughout the confining vessel or system.
According to Pascals law, any force applied to a
confined fluid is transmitted in all directions
throughout the fluid regardless of the shape of the
container. Consider the effect of this in the systems
shown in views A and B of figure 3-4. If there is
resistance on the output piston (view A, piston 2) and
the input piston is pushed downward, a pressure is
created through the fluid which acts equally at right
angles to surfaces in all parts of the container.
If the force 1 is 100 pounds and the area of input
piston 1 is 10 square inches, then pressure in the fluid is
10 psi ( 100 ÷ 10). It must be emphasized that this fluid
pressure cannot be created without resistance to flow,
which, in this case, is provided by the 100-pound force
acting against the top of the output piston 2. This
pressure acts on piston 2, so for each square inch of its
area, it is pushed upward with the force of 10 pounds.
In this case, a fluid column of a uniform cross section is
considered so the area of output piston 2 is the same as
input piston 1, or 10 square inches; therefore, the
upward force on output piston 2 is 100 poundsthe
same as was applied to input piston 1. All that has been
accomplished in this system was to transmit the 100-
pound force around a bend; however, this principle
underlies practically all-mechanical applications of
At this point, it should be noted that since Pascals
law is independent of the shape of the container, it is
not necessary that the tubing connecting the two
pistons should be the full area of the pistons. A
connection of any size, shape, or length will do so long
as an unobstructed passage is provided. Therefore, the
system shown in view B of figure 3-4 (a relatively
small, bent pipe connects the two cylinders) will act the
same as that shown in view A.
Multiplication of Forces
Some hydraulic systems are used to multiply
force. In figure 3-5, notice that piston 1 is smaller than
piston 2. Assume that the area of the input piston 1 is 2
square inches. With a resistant force on piston 2, a
downward force of 20 pounds acting on piston 1
creates 10 psi (20 ÷ 2) in the fluid. Although this force
is much smaller than the applied forces in figure 3-4,
Figure 3-4.Force transmitted from piston to piston.
the pressure is the same because the force is
concentrated on a relatively small area.
This pressure of 10 psi acts on all parts of the fluid
container, including the bottom of output piston 2;
therefore, the upward force on output piston 2 is 10
pounds for each of its 20 square inches of area, or 200
pounds (10 x 20). In this case, the original force has
been multiplied tenfold while using the same pressure
in the fluid as before. In any system with these
dimensions, the ratio of output force to input force is
always 10 to 1 regardless of the applied force; for
example, if the applied force of input piston 1 is 50
pounds, the pressure in the system is increased to 25
psi. This will support a resistant force of 500 pounds on
output piston 2.
Figure 3-5.Multiplication of force in a hydraulic system.