1. ENGR 8-4, Lesson 4 Using Mathematics in Fluid Power
Written by Roland Williams

2. Big Idea
ENGR-TS-3: The students will develop an understanding of how humans interact with systems.

3. Critical Knowledge/Elements
Operate technological systems
Maintain technological systems
Constructing technological systems
Design technological systems

4. Essential Question
How are mathematics used to evaluate fluid power systems?

5. Word Wall Fluid Fluid Power Hydraulic Systems Pneumatic Systems
Boyle’s Law
Pascal’s Principle
Pressure
Actuators
Compressor
Mechanical Advantage

6. Earlier, we learned that an actuator is a device that converts fluid power into mechanical force and motion.

7. 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.

8. Area of a Circle If we know the radius: A = r2
If we know the diameter, we must divide the diameter by 2.

9. 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

10. 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.

11. 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)

12. 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 P = 50 lbs
A in2
P = pounds per square inch (psi)

13. 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.

14. Mechanical Advantage 10 inches diameter 1 inch 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

15. Mathematic Worksheet
Now let’s see if you can apply you mathematics skills to fluid power systems.
Complete the Mathematics Worksheet.

16. Mathematic Worksheet
Let’s see how well you did on the Mathematics Worksheet.

17. Essential Question
How are mathematics used to evaluate fluid power systems?

18. Fluid Power (conclusion)
ENGR 8-4, Lesson 1
Introduction to Fluid Power