Pascal’s Law
Pascal’s Law
Hydrostatic Pressure - Results when a fluid is under pressure
and its not moving.
Formula:
The pressure exerted on a confined fluid is transmitted undiminished in
all directions and acts at right angles to the containing surfaces
P=
F
ν
F
A
Where:
ω P = Pressure
ω F = Force
ω A = Area
pis ton
Exposed piston area
Confined fluid
Device used to measure
pressure in a fluid power
system:
Pressure gauge
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Piston
P=
Pascal’s Law
F
Example 2-1
A
P
P
Fig. 1
The piston and cylinder shown in figure 1 have a diameter (D) of 2 in and
are loaded with a force (F) of 1000 lbs. What is the pressure (P) inside the
cylinder?
Force and pressure Values
Quantity
Force
Area
Pressure
D
U.S Customary Unit
lbs
in2
lbs/in2 or psi
Where:
Metric (SI) Unit
Newtons (N)
m2
N/m2 or Pa
1. Calculate Area
2. Calculate Pressure
2
A = Pi X D
4
Pi = 3.1416
D = diameter
P=
3
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A = area
F
1 psi = 6.89 kPa
A
14.7 psi = 1bar
4
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Piston
Example 2-2
D
Piston
P
P
Fig. 1
The piston and cylinder shown in figure 1 have a diameter (D) of 1.5 in is
under 500 psi of pressure. What is the force (F) applied to the system?
1. Calculate Area
2. Calculate Force
Example 2-3
2
A = Pi X D
4
5
P
P
Fig. 1
The piston and cylinder shown in figure 1 are required to support a force of
2500 lbs. We do not want to exceed a pressure of 1000 psi. What cylinder
size is required?
A=
F= PXA
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D
F
P
D= 4XA
Pi
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1
Transmission and
Multiplication of Force
Transmission and
Multiplication of Force
One of the most useful features of fluid power is the ease
with which it is able to multiply force.
This is accomplished by using an output piston that is
larger than the input piston.
F
OUT
= A OUT
A IN
XF
One of the most fundamental laws of nature is that we
cannot get more energy out of a system than what we put
into it, so that the work done must remain constant.
If an output force is increased by a factor of 10, the
distance traveled by the output piston must decrease by the
same factor.
IN
d in =
7
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Example 2-4
250 lbs
F
OUT
=
A OUT
A IN
XF
IN
d in =
A OUT
Figure 1 shows an input cylinder with a diameter of 1 in and an
output cylinder with a diameter of 2.5 in. A force of 250 lbs is
applied to the input cylinder. What is the output force?
How far would we need to move the input cylinder to move the
output cylinder 1 in?
1. Calculate the input piston Area
F out
1 in
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2.5 in
2.
3.
4.
Calculate the output piston Area
Calculate the output force
Calculate the input distance
9
A IN
X d out
8
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X d out
A IN
A OUT
Example 2-5
v in =
A OUT
A IN
X v out
The output cylinder in the previous example is required
to move at 4 in/s. At what speed must the input cylinder
move?
250 lbs
1 in
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F out
2.5 in
10
T o be continued…
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