1. Chapter 3: HYDRAULICS AND PNEUMATICS
Engineering Mathematics

2. Introduction/Description
Individually, and in teams, you will
build and evaluate a Stirling engine,
calculate hydraulic force multiple factor,
build linear, rotational, and lifting hydraulic systems,
build, design, and test a hydraulic arm that meets design criteria and accomplishes a given task, and
create a presentation about your hydraulic system, documentation the mathematics used and tested.

3. Chapter 3: Outline Introduction to Fluid Power
Pressure and Pascal’s Principle
Bernoulli’s Principle

4. Objectives and Results
Explain the Stirling engine heat cycle.
Explain and apply Pascal's Law.
Explain how linear, rotation, and lifting hydraulic systems are formed.
Explain and demonstrate how discrete hydraulic systems can be combined to form a more complex and functional system.
Calculate thermal efficiency of a Stirling engine.

5. Schedule of Assignments
Class Periods
Topic
Reading
Assignment
1-4
Vocabulary
Stirling Engines
Stirling Engine activity
Chapter
#1-Individual; Handout, vocabulary work; answer the questions posed at the end of the Stirling Engine activity.
5-9
Hydraulics and pneumatics
Pascal’s Law
Force multiplication introduction and activity
#2-Individual; Answer the evaluation questions posed at the end of the activity
10-14
Types of hydraulically driven motion
Hydraulic systems
Hydraulic motion activity
#3-In teams of 2-3; Apply the engineering design process to the scenario given; answer the questions posed at the end of the activity
15-30
Hydraulic arm design challenge
Background and team project
#4-In teams of 2-3; Apply the engineering design process to the scenario given; complete the mini engineering notebook (Daily)

6. Objectives, cont.
Calculate a system’s hydraulic force multiplication factor.
Graph and interpret data from experiments and tests,
Build a Stirling engine.
Build linear, rotational, and lifting hydraulic systems.
Practice the design process by designing and building a hydraulic arm that meets design criteria and accomplishes a given task.

7. Results Complete the various worksheets and projects.
Design, engineer, build, and troubleshoot hydraulic- pneumatic systems.
Write a research-based technical report on solar energy systems instructional design.
Present scenario, drawings, model, and other information for solar energy system design.

8. Vocabulary Actuator Alpha Stirling Engine Beta Stirling Engine
Constant volume process
Displacer piston
Gamma Stirling Engine
Flywheel
Force multiplication
Heat exchanger
Heat sink
Hydraulics
Isothermal
Linear motion
Master piston
Mechanical advantage
Pascal’s Law
Actuator: a device responsible for actuating a mechanical device
Alpha Stirling Engine: a Stirling engine that has two power pistons and two connected pressure chambers; one chamber is heated and one chamber is cooled
Beta Stirling Engine: a Stirling engine that has one power piston and a one displacer piston in the same chamber
Constant Volume Process: a process that is conducted in such a way that the volume of the system is held constant
Displacer Piston: a special piston that is used in beta and gamma Stirling engines; it moves the working fluid back and forth between the hot and cold side heat exchangers
Gamma Stirling Engine: a Stirling engine that has one hot pressure chamber with a displacer piston and one cold pressure chamber with a power piston
Flywheel: a heavy wheel that stores kinetic energy and allows for smooth operation of an engine by maintaining a constant speed of rotation over the whole cycle
Force multiplication: a phenomenon in fluid systems that arises from fluid behavior described by Pascal's Law; when a master of a certain area applies pressure to a body of fluid, the fluid exerts an equal pressure on the entire area of a slave piston; the force experienced by the slave piston is the original force multiplied by the ratio of the slave piston area to the master piston area
Heat Exchanger: a device, such as an automobile radiator, used to transfer heat from a fluid on one side of a barrier to a fluid on the other side without bringing the fluids into direct contact; in small, low-power systems the heat exchanger is simply the walls of the pressure chambers; in larger, higher power systems, more efficient heat exchanging is accomplished by increasing surface area through the use of fins
Heat Sink: an environment capable of absorbing heat from an object that shares thermal contact with it without a phase change or an appreciable change in temperature; in small, low-power systems this is the surrounding environment; for more powerful systems, a radiator is used to transfer heat to the surrounding environment
Hydraulics: is the branch of fluid power engineering that uses pressurized liquids to create mechanical motion
Isothermal: any process conducted so that the temperature of the system is held constant
Linear Motion: a continuous change of the position of a body so that every particle of the body follows a straight-line path.
Master Piston: the piston in a fluid system that applies the force to the fluid
Mechanical Advantage: the ratio of the working force exerted by a mechanism to the applied effort
Pascal’s Law: the pressure exerted anywhere in a mass of a confined liquid is transmitted in all directions throughout the liquid without the pressure being diminished

9. Vocabulary, cont. Piston Pneumatics Power piston Pressure chamber
Regenerator
Rotational motion
Slave piston
Stirling Engine
Piston: a solid cylinder or disk that fits snugly into a larger cylinder and moves under fluid pressure, or displaces or compresses fluids, as in pumps and compressors
Pneumatics: a branch of fluid power engineering that harnesses the potential energy in pressurized gas to create mechanical motion
Power Piston: the driving piston in a Stirling engine that drives the compression of the working fluid in the system
Pressure Chamber: a vessel designed for containing substances at pressures above atmospheric pressure
Regenerator: the component invented by Robert Stirling that distinguishes a Stirling engine from its competition; it connects the hot and cold pressure chambers and recycles the internal heat of the system; this conservation of heat energy increases the thermal efficiency of the engine; when designing a Stirling engine, the regenerator design is important as it can introduce too much internal volume and energy loss due to friction
Rotational Motion: the motion of a rigid body that takes place in such a way that all of its particles move in circles around an axis with a common angular velocity
Slave Piston: the piston in a fluid system that has a force applied to it by the fluid
Stirling Engine: an external combustion engine having an enclosed working fluid that is alternately compressed and expanded to operate a piston, thus converting heat from a variety of sources into mechanical energy

10. Stirling Engines
A Stirling engine is a heat engine that operates by expanding and compressing a working fluid, usually a gas-like air, in a cyclical fashion.
A Stirling engine has the following components:
Heat source
Hot side heat exchanger
Regenerator
Cold side heat exchanger
Heat sink
Displacer piston
Power piston
A Stirling engine is a heat engine that operates by expanding and compressing a working fluid, usually a gas-like air, in a cyclical fashion.
The expansion of the working fluid is driven by the introduction of heat energy into the system.
A Stirling engine has the following components:
Heat source-This is often provided by the combustion of fuel, but since the engine operation is not based on the type of fuel, any heat source will do. This can include greener sources of energy, such as solar and clean-burning renewable fuels.
Hot Side Heat Exchanger-In small, low-power systems the heat exchanger is simply the walls of the pressure chambers. In larger, higher power systems, more efficient heat exchanging is accomplished by increasing surface area through the use of fins.
Regenerator-This is the component that Robert Stirling invented that gives a Stirling engine its name. It connects the hot and cold pressure chambers and recycles the internal heat of the system. This conservation of heat energy increases the thermal efficiency of the engine. When designing a Stirling engine, the regenerator design is important since it can introduce too much internal volume and energy loss due to friction.
Cold side Heat Exchanger-In small, low-power systems the heat exchanger is simply the walls of the pressure chambers. In larger, higher power systems, more efficient heat exchanging is accomplished by cooling with water.
Heat Sink -In small, low-power systems the heat sink is the surrounding environment. For more powerful systems, a radiator is used to transfer heat to the surrounding environment.
Displacer Piston-This is a special piston that is used in a beta and gamma Stirling engines. It moves the working fluid back and forth between the hot and cold side heat exchangers.
Power Piston -This is the driving piston in a Stirling engine that drives the compression of the working fluid in the system.

11. Types of Stirling Engines
Alpha Stirling engine
Beta Stirling engine
Alpha Stirling Engine Beta Stirling Engine Gamma Stirling Engine
Stirling Engine Video Links
Alpha Stirling engine
Beta Stirling engine
Gamma Stirling engine
An Alpha Stirling engine has two power pistons and two connected pressure chambers. One chamber is heated and one chamber is cooled.
A Beta Stirling engine has one power piston and a one displacer piston in the same chamber.
A Gamma Stirling engine has one hot pressure chamber with a displacer piston and one cold pressure chamber with a power piston.
Gamma Stirling engine

12. Beta Stirling Engine Steps. 1. 2.
Isothermal expansion
Constant volume heat removal
Isothermal compression
Constant volume heat addition
Beta Stirling engine steps that match the Stirling engine cycle steps:
Isothermal expansion - the heated gas increases in pressure and pushes the power piston (black piston) to the farthest limit of the power stroke
Constant volume heat removal - the displacer piston (grey piston) now moves, shunting the gas to the cold end of the cylinder, cooling it
Isothermal Compression - the cooled gas is now compressed by the flywheel momentum. This takes less energy, since its pressure drops when it is cooled
Constant volume heat addition - power piston has compressed the gas, and the displacer piston has moved so that most of the gas is adjacent to the hot heat exchanger 3. 4.

13. Build Your Own Stirling Engine
Using the materials and instructions provided, construct Stirling engines in teams.
Record the temperature every 15 seconds for 5 minutes.
Calculate the kinetic energy of the flywheel and the heat energy added to the system. How do these compare? What is the efficiency of this engine with regards to transferring heat energy to rotational mechanical energy?
How else could you imagine heating the pressure chamber?
Building a Stirling Engine
Student Handout: Stirling Engine Introduction Project Activity Sheet
Student Activity: Students will build Stirling engines. (Alternative to having students build engines is for instructor to build a Stirling engine as a demonstration.)
Building a Stirling Engine video:
Using the materials and instructions provided, construct Stirling engines in teams.
Before placing your engine on the hotplate, record the starting temperature of your engine using the IR thermometer. Use the tachometer to measure the revolutions per minute of the flywheel (CD) and the IR thermometer to measure the temperature of the bottom pressure chamber. Record these measurements every 15 seconds for 5 minutes.
Calculate the kinetic energy of the flywheel and the heat energy added to the system. How do these compare? What is the efficiency of this engine with regards to transferring heat energy to rotational mechanical energy?
How else could you imagine heating the pressure chamber?

14. Questions/Discussions
What type of Stirling engine was created in the video? Identify the components.
Draw and identify the different parts of the Stirling engine cycle for this engine.
What are the design features of this engine that affect the thermal efficiency? How could you improve them?

15. Pneumatics and Hydraulics
Pneumatics is a branch of engineering that harnesses the potential energy in pressurized gas to create mechanical motion.
Hydraulics is the branch of engineering that uses pressurized liquids to create mechanical motion.
Pneumatic Aluminum Can Crusher
Medical Applications of Fluid Power
National Fluid Power Association (NFPA)
Pneumatic and Hydraulic Power Videos
Pneumatic Aluminum Can Crusher
Medical Applications of Fluid Power
National Fluid Power Association (NFPA) YouTube Channel
A Stirling engine is not technically a pneumatic system, but it uses pressurized gases (in part) to create mechanical motion. The gas compression and expansion is driven by the addition and removal of heat energy, which is why these systems fall under the category of heat engines.
Pneumatics is a branch of engineering that harnesses the potential energy in pressurized gas to create mechanical motion.
Hydraulics is the branch of engineering that uses pressurized liquids to create mechanical motion.

16. Pascal’s Law
The pressure exerted anywhere in a mass of a confined liquid is transmitted equally in all directions throughout the liquid without the pressure being diminished.
This is represented by the following equation:
Pascal’s Law (or Pascal’s principle) states that the pressure exerted anywhere in a mass of a confined liquid is transmitted in all directions throughout the liquid without the pressure being diminished.
This is represented by the following equation:
∆P = ρg(∆h)
In the equation, ∆P represents the change in pressure, ρ (rho) represents the density of the fluid, g represents the acceleration due to gravity, and ∆h represents the height difference between two points in a water column.

17. Hydraulic Force Multiplication
How Fluid Power Works
How Fluid Power Works Video:
The figure displays a hydraulic system with two pistons. Piston 1 is the master piston, the piston that pushes down on the liquid. Piston 2 is the slave piston, the piston that gets pushed by the liquid.
In hydraulics, force multiplication occurs when a master piston drives a slave piston. This force multiplication is the same as the mechanical advantage in simple machines and allows an operator to increase the applied force. Force multiplication arises due to physical phenomena described by Pascal’s Law.

18. Hydraulic Force Multiplication Example
Piston 1 = Master Piston
Piston 2 = Slave Piston
If r1 = 4 cm and r2 = 8 cm, then MA = 4.
As stated by Pascal’s Law, the force applied on the slave piston (F2) is equal to the force applied at the master piston (F1) times the ratios of the piston areas. The ratio of the slave piston area to the master piston area is the mechanical advantage. If the radius of the master piston is 4 cm and the radius of the slave piston is 8 cm the mechanical advantage would be 4.
What would the MA be, if Piston 2 was the Master Piston?

19. Evaluate Hydraulic Force Multiplication
Using the materials and instructions provided, construct the four hydraulic systems as directed in the activity procedure.
Test each assembly by adding weights to the metal plate. When the syringe can no longer support a weight, the slave plunger will depress after the master syringe raises it. Record the weight at which this happens for each assembly.
Calculate the force multiplication factor for each assembly system. Compare the trend in force multiplication factors to the trend in the maximum weight each assembly held.
How do these trends compare? Does your data make sense?
Student Handout: Force Multiplication Student Activity Sheet
Student Activity: Students will build and test hydraulic systems and calculate force multiplication factor for each system.

20. Questions/Discussions
Assuming you applied the same force to the master 12 cc syringe in each trial, which syringe had the most force applied to it?
Which had the least?
How could you use this principle to do work in the real world?
Questions/Discussion
Assuming you applied the same force to the master 12 cc syringe in each trial, which syringe had the most force applied to it?
Solution: the 100 cc slave syringe
Which syringe had the least force applied to it?
Solution: the 12 cc slave syringe
How could you use this principle to do work in the real world?
Solution: answers will vary.

21. Linear Hydraulic Motion
Linear hydraulic motion is created by attaching the end of a slave piston to an actuator that can only move in one direction.
When the master piston is depressed, the slave piston will drive the actuator linearly in one direction.
Three linear hydraulic assemblies can be combined to give motion along the x, y, and z axes.
NFPA Hydraulic Motion Instructions
NFPA Hydraulic
Motion Instructions

22. Rotational Hydraulic Motion
Rotational hydraulic motion is created by attaching the end of a slave piston to one side of an actuator that is attached to a wheel.
It is important that the end of the slave piston is attached away from the center of the wheel.
When the master piston is depressed, the slave piston will drive the actuator, which translates the force to the wheel. This force causes the wheel to turn.

23. Lifting Hydraulic Motion
Lifting hydraulic motion is created by attaching the end of a slave piston to an actuator that is hinged.
It is important that the end of the slave piston is attached away from the actuator’s hinge.
The closer the piston is to the hinge, the more height the actuator arm can achieve.

24. Lifting Hydraulic Motion, cont.
If there is a weight on the end of the arm, more force will be needed to lift the weight.
The farther away the piston is from the end of the arm, the more force is needed to lift the weight.

25. Building Hydraulic Systems
Using the materials provided, construct linear, rotational, and lifting hydraulic systems.
Identify the slave and master pistons in each assembly. Test each assembly by adding water to the systems. Next add a small amount of weight to the actuators. What happens?
Try combining your rotation and linear systems. Is it possible? What sort of motion is created?
Linear, Rotational, and Lifting Hydraulic Systems Instructions
Student Handout: Building Linear, Rotational, & Lifting Hydraulic Systems
Student Activity: Students will build linear, rotational, and lifting hydraulic systems.
Linear Hydraulic Motion Instructions

26. Questions/Discussions
How could you use the principles of force multiplication and/or a system redesign to enable the three hydraulic systems to translate more weight?
Sketch a design of a system that uses at least one of each type of hydraulic system. What does your system do?
Choose a design from the class that would be possible to build with the number of systems currently in the room, then build it.
Discuss the hardest part of the process.

27. Hydraulic Arm Design Challenge
In teams of 2-3 students, you will
use your knowledge and experience gained in the previous activities to build a hydraulic arm, and
prepare a 45-minute presentation of your hydraulic arm to the class.
Student Handout: Hydraulic Arm Design Project
Student Activity: Students will participate in the Hydraulic Arm Design Challenge.

28. Criteria for Your Hydraulic Arm
The hydraulic arm must be able to lift an object over a wall 20 cm high and place the object on the other side within the designated area 15 cm from the wall.
The arm will be secured to the testing table with a vise, so each arm must have a base that allows it to be clamped to the table.
The arm can only be constructed from the given materials and have at least hydraulically controlled joints.

29. Credits ClipArt; http://www.clipart.com/en/
Images;
Slide 11
Alpha Stirling Engine video; from YouTube user; GREENPOWERSCIENCE;

30. Credits, cont. Slide 11, cont.
Beta Stirling Engine video; from YouTube user; PullTab; eature=fvwrel
Gamma Stirling Engine video; from YouTube user; Sawerrt;
Gamma Stirling Engine graphic

31. Credits, cont.
Slide 13
Building a Stirling Engine video; from YouTube user; Jim Larsen; 49E86CC4&feature=plpp
Slide 15
Pneumatic Aluminum Can Crusher video; from YouTube user; Kedge24
Medical Applications of Fluid Power video; from YouTube user; National Fluid Power Association;

32. Credits, cont. Slide 15, cont.
National Fluid Power Association (NFPA) YouTube Channel video; from YouTube user; National Fluid Power Association; ature=results_mainraulics.aspx
Slide 17
How Fluid Power Works video; from YouTube user; CCEFP;