Fluid Power
ENGR 8-4, Lesson 4
Using Mathematics in Fluid Power
Written by Roland Williams
Big Idea
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ENGR-TS-3: The students will
develop an understanding of how
humans interact with systems.
Critical Knowledge/Elements
a)
Operate technological systems
b)
Maintain technological systems
c)
Constructing technological systems
d)
Design technological systems
Essential Question
How are mathematics used
to evaluate fluid power
systems?
Word Wall
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Fluid
Fluid Power
Hydraulic Systems
Pneumatic Systems
Boyle’s Law
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Pascal’s Principle
Pressure
Actuators
Compressor
Mechanical
Advantage
Earlier, we learned that an
actuator is a device that converts
fluid power into mechanical force
and motion.
The Piston is a round plunger inside of an
actuator that transmits force to the fluid or
transmits the force of the fluid to an object.
To find the pressure of the fluid inside
of a mechanical device, we must know
the area of the piston. This is done by
using the formula used to determine
the area of a circle.
Area of a Circle
If we know the radius:
A=
r2
If we know the diameter,
we must divide the
diameter by 2.
If the diameter of a piston is 1 inch, we
would do the following:
diameter 1” ÷ 2 = .5 radius
A=
r2
A = 3.14 x .25
A = .785 square inches
Pascal’s Law
Recall from the earlier lesson
that the foundation of modern
hydraulics was established
when Pascal discovered that
pressure in a fluid acts equally
in all directions. This pressure
acts at right angles to the
containing surfaces.
Pressure
In the last lesson, we learned that
pressure is the amount of force
distributed over a unit of area,
usually expressed in pounds per
square inch. And the formula to find
pressure was:
Pressure = Force (F)
Area (A)
Earlier we determined the area of the piston
was .785 square inches.
To find the pressure we would:
50 lbs of
force
63.69 psi
P=
F
A
P=
50 lbs
.785 in2
P = 63.69 pounds per square inch (psi)
Mechanical Advantage
In the previous lesson, we learned that
mechanical advantage was the increase
in force gained by using a machine.
Using mathematics we can evaluate the
amount of mechanical advantage we
would gain by using a fluid power
system.
Mechanical Advantage
1 inch diameter
50 lbs force
10 inches diameter
5000 lbs force
63.69 PSI
If we know the PSI and Area, we can find the Force to
determine mechanical advantage: F = P x A
Mathematic Worksheet
Now let’s see if you can
apply you mathematics skills
to fluid power systems.
Complete the Mathematics
Worksheet.
Mathematic Worksheet
Let’s see how well you did on
the Mathematics Worksheet.
Essential Question
How are mathematics used
to evaluate fluid power
systems?
Fluid Power (conclusion)
ENGR 8-4, Lesson 1
Introduction to Fluid Power