mechanicalmechanical pe - engproguides.comengproguides.com/thermalguidesample.pdf5.3 schaum's...

Justin Kauwale, P.E.

Creates an understanding of the key exam concepts and skills

MechanicalMechanicalPE

Follows the exam outline and teaches the main topics.Simplifies and focuses your studying

ProEngineering Guides

Covers Fluids, Heat Transfer, Mass Balance, Thermodynamics

Thermal & FluidsThermal & Fluids

How to pass the examHow to pass the exam

Hydraulic/Fluid & Energy/Power Applications and Support.

Technical Study GuideTechnical Study Guide

i http://www.engproguides.com

THERMAL & FLUIDS TECHNICAL STUDY GUIDE HOW TO PASS THE PE EXAM

Table of Contents

Section 1.0 ..................................................................................................... Introduction

Section 2.0 ........................................................... Principles - Basic Engineering Practice

Section 3.0 ............................................................................ Principles - Fluid Mechanics

Section 4.0 ................................................................................ Principles - Heat Transfer

Section 5.0 ............................................................................... Principles - Mass Balance

Section 6.0 .......................................................................... Principles - Thermodynamics

Section 7.0 .................................................................. Principles - Supportive Knowledge

Section 8.0 ............................................... Applications - Hydraulic and Fluid Applications

Section 9.0 ....................................................... Applications - Energy/Power Applications

Section 10.0 .................................................................................................... Conclusion

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SECTION 1

INTRODUCTION

Introduction-1 http://www.engproguides.com

Introduction Table of Contents 1.0 Introduction ............................................................................................................................. 2

1.1 Key Concepts and Skills ...................................................................................................... 2

1.2 Units .................................................................................................................................... 5

2.0 Disclaimer ............................................................................................................................... 5

3.0 How to use this Book .............................................................................................................. 5

4.0 Sample exam tips ................................................................................................................... 6

5.0 Recommended References .................................................................................................... 9

5.1 Mechanical Engineering Reference Manual ........................................................................ 9

5.2 Engineering Unit Conversions Book .................................................................................... 9

5.3 Schaum's Outline of Thermodynamics for Engineers, 3rd Edition ...................................... 9

5.4 Schaum's Outline of Fluid Mechanics and Hydraulics, 4th Edition .................................... 10

5.5 ASHRAE Handbooks ........................................................................................................ 10


1.0 INTRODUCTION One of the most important steps in an engineer's career is obtaining the professional engineering (P.E.) license. It allows an individual to legally practice engineering in the state of licensure. This credential can also help to obtain higher compensation and develop a credible reputation. In order to obtain a P.E. license, the engineer must first meet the qualifications as required by the state of licensure, including minimum experience, references and the passing of the National Council of Examiners for Engineering and Surveying (NCEES) exam. Engineering Pro Guides focuses on helping engineers pass the NCEES exam through the use of free content on the website, http://www.engproguides.com and through the creation of books like sample exams and guides that outline how to pass the PE exam.

The key to passing the PE exam is to learn the key concepts and skills that are tested on the exam. There are several issues that make this key very difficult. First, the key concepts and skills are unknown to most engineers studying for the exam. Second, the key concepts and skills are not contained in a single document. This technical guide teaches you the key concepts and skills required to pass the Mechanical - Thermal & Fluids Mechanical P.E. Exam.

1.1 KEY CONCEPTS AND SKILLS How are the key concepts and skills determined?

The key concepts and skills tested in this sample exam were first developed through an analysis of the topics and information presented by NCEES. NCEES indicates on their website that the P.E. Exam will cover an AM exam (4 hours) followed by a PM exam (4 hours) and that the exam will be 80 questions long, 40 questions in the morning and 40 questions in the afternoon. The Thermal & Fluids Mechanical PE exam will focus on the following topics as indicated by NCEES. (http://ncees.org/engineering/pe/):

I. Principles (32 questions)

A) Basic Engineering Practice (6 questions) 1 Engineering terms and symbols 2 Economic analysis 3 Units and conversions

B) Fluid Mechanics (6 questions) 1 Fluid properties (e.g., density, viscosity) 2 Compressible flow (e.g., Mach number, nozzles, diffusers) 3 Incompressible flow (e.g., friction factor, Reynolds number, lift, drag)

C) Heat Transfer Principles (e.g., convection, conduction, radiation) (6 questions) D) Mass Balance Principles ((e.g., evaporation, dehumidification, mixing)) (4 questions)

E) Thermodynamics (7 questions)

1 Thermodynamic properties (e.g., enthalpy, entropy) 2 Thermodynamic cycles (e.g., Combined, Brayton, Rankine) 3 Energy Balances (e.g., 1st and 2nd laws)


4 Combustion (e.g., stoichiometrics, efficiency) F) Support Knowledge (4 questions)

1 Pipe system analysis (e.g., pipe stress, pipe supports, hoop stress) 2 Joints (e.g., welded, bolted, threaded) 3 Psychrometrics (e.g., dew point, relative humidity) 4 Codes and Standards

II. Hydraulic and Fluid Applications

A. Hydraulic and Fluid Equipment (15 questions) 1. Pumps and fans (e.g., cavitation, curves, power, series, parallel) 2. Compressors (e.g., dynamic head, power, efficiency) 3. Pressure vessels (e.g., design factors, materials, pressure relief) 4. Control valves (e.g., flow characteristics, sizing) 5. Actuators (e.g., hydraulic, pneumatic) 6. Connections (e.g., fittings, tubing)

B. Distribution Systems (e.g., pipe flow) (9 questions)

III. Energy/Power System Applications

A. Energy/Power Equipment (8 questions) 1. Turbines (e.g., steam, gas) 2. Boilers and steam generators (e.g., heat rate, efficiency) 3. Internal combustion engines (e.g., compression ratio, BMEP) 4. Heat exchangers (e.g., shell and tube, feedwater heaters) 5. Cooling towers (e.g., approach, drift, blowdown) 6. Condensers (e.g., surface area, materials)

B. Cooling/Heating (e.g., capacity, loads, cycles) (6 questions) C. Energy Recovery (e.g., waste heat, storage) (5 questions) D. Combined Cycles (e.g., components, efficiency) (5 questions


Next, each of these broad topics were investigated and filtered for concepts and skills that met the following criteria:

(1) First, the concept and skill must be commonly encountered in the Thermal & Fluids field of study. For example, in the Thermal & Fluids field: Power cycles, steam properties, pump sizing, fan sizing, determining friction losses and calculating net positive suction head are regular occurrences in the Thermal & Fluids field.

(2) Second, the skill and concept must be testable in roughly 6 minutes per problem. There are (40) questions on the morning exam and you will be provided with 4 hours to complete the exam. The same is true for the afternoon portion of the exam. This results in an average of 6 minutes per problem. This criterion limits the complexity of the exam problems and the resulting solutions. For example, pressure drop calculations are common in the Thermal & Fluids field, but the calculation is often very lengthy because of the number of steps involved, especially if a unique fluid and flow condition is used. Thus, common fluids like water/air and common pipe/duct materials are used.

(3) Third, the key concepts and skills must be used or be known by practicing Mechanical engineers in the Thermal & Fluids field. This criterion is similar to the first criterion. However, this criterion filters the concepts and skills further by limiting the field to material encountered and used by practicing engineers. The HVAC & Refrigeration, Thermal & Fluids and Mechanical Systems & Materials fields are vast and there are many different avenues an engineer can take. Two diverging paths are those engineers involved in research and those who practice. Research engineers are pushing the boundaries of the field and are highly focused in their specific area of the field. The Professional Engineering exam does not cover emerging technologies or highly focused material.

(4) The P.E. Exam must test the principle or application of the skill and concept and not the background knowledge of the topic or concept. The exam also does not cover background information on the NCEES topics. The P.E. Exam is meant to prove that the test taker is minimally competent to practice in the Mechanical Engineering field. The exam is less concerned with theory and more with the principle or application of the theory, skill or concept. For example, the P.E. exam is less concerned with the theory of evaporation in a cooling tower and more with the performance and selection of a cooling tower.

In summary, this book is intended to teach the necessary skills and concepts to develop a minimally competent, practicing professional engineer in the Mechanical Engineering – Thermal & Fluids field, capable of passing the P.E. exam.


1.2 UNITS The primary units that are used in the P.E. Exam are United States Customary System Units (USCS). As such, this guide focuses exclusively on the USCS. However, it is recommended that the test taker have a conversion book, because certain areas of the P.E. Exam may use the International System of Units (SI).

2.0 DISCLAIMER In no event will Engineering Pro Guides be liable for any incidental, indirect, consequential, punitive or special damages of any kind, or any other damages whatsoever, including, without limitation, those resulting from loss of profit, loss of contracts, loss of reputation, goodwill, data, information, income, anticipated savings or business relationships, whether or not Engineering Pro Guides has been advised of the possibility of such damage, arising out of or in connection with the use of this document or any referenced documents and/or websites.

This book was created on the basis of determining an independent interpretation of the minimum required knowledge and skills of a professional engineer. In no way does this document represent the National Council of Examiners for Engineers and Surveying views or the views of any other professional engineering society.

3.0 HOW TO USE THIS BOOK This book is organized into the topics as designated by the NCEES. These topics include:

1. Basic Engineering Practice 2. Fluid Mechanics 3. Heat Transfer 4. Mass Balance 5. Thermodynamics 6. Supportive Knowledge 7. Hydraulics and Fluid Applications 8. Energy/Power System Applications

First, it is recommended that the engineer in training gather the recommended references presented in the following section.

Second, proceed through the book in the order designated. Go through and first read the material of the section, then complete the practice problems designated for that section. If you have trouble with the practice problems, review the material and then read the solutions. The problems at the end of each section are slightly easier and more straightforward than the typical problems you would find in an actual P.E. Exam. These problems are meant only to practice the application of the skill or concept presented in the section.


Following the completion of each of the sections, it is recommended that you determine if you are unconfident with any of the NCEES topics. If you are not confident then please go back and revisit the section.

Finally, set aside an eight-hour block of uninterrupted time to complete a sample exam. Gather your references and calculator and create a test-like environment. Set a timer and proceed to take the sample exam presented at the end of this book. Remember that the exam is only 40 problems for the morning and afternoon sessions and does not encompass all the possible items that can appear on an exam, but it should give you an idea of your level of readiness for the exam.

4.0 SAMPLE EXAM TIPS Sample exams are not provided in this book, please see the engineering pro guides

website for sample exams.

Engineering Pro Guides sample exams can be used in multiple ways, depending on where you are in your study process. If you are at the beginning or middle, it can be used to test your competency, gain an understanding and feel for the test format, and help to highlight target areas to study. If you are at the end, it can be used to determine your preparedness for the real exam. Remember that the questions are a sample of the many topics that may be tested and are limited to fit a full exam length and therefore is not comprehensive of all concepts.

Because the exam is written to be similar to the difficulty and format of the NCEES exam, it is recommended that the test be completed in one sitting and timed for four hours to simulate the real exam. This will give you a better indication of your status of preparation for the exam. If you are at the ending of your studying, it is recommended to couple this exam with the PM section to simulate the full exam test day.

Review the exam day rules and replicate the environment for the real test as much as possible, including the type of calculator you may use and the acceptable references. Keep a watch or clock next to you to gauge your pace for 40 questions in 4 hours.

Based on the NCEES website, the following are general rules for exam day.

Allowed:

1. Snacks that are not disruptive to others 2. Watches and small clocks 3. Religious head coverings 4. Two straight edges: e.g. ruler, scale, protractor, triangle 5. Approved references 6. Approved calculator (2 recommended for backup) 7. Eyeglasses 8. Non electronic magnifying glass 9. (Units conversion book is also recommended)

Prohibited:


1. Cell phones 2. Hats and hoods 3. Slide charts, wheel charts, drafting compasses 4. Weapons 5. Tobacco 6. Personal Chairs 7. Eyeglass/Magnifying glass cases 8. Scratch Paper (all writing must be done in the exam booklet)

For additional references on exam day policies, exam day processes, and items to bring on your exam day, review the NCEES Examinee Guide:

http://ncees.org/exams/examinee-guide/

Similar to the NCEES exam, the tested topics are presented in a random order. For best use of your time, answer the questions that you know first and return to the questions that you are unfamiliar with later. Once all the known questions are answered, go through the test again and attempt to answer the remaining questions by level of difficulty. If time allots, review your answers.

If you are stuck on a question, seek the following avenues.

1. Study Guide: It is important to understand your study guides and indices. During times of uncertainty, these will likely lead you to your answers. Determine the key concept that is being asked in the question and refer to your indices or pre-tabbed sections. The concepts will likely be found in the Mechanical Engineering Reference Manual (MERM) or one of the other references, listed below.

2. Process of Elimination: There are only four possible choices for each question. Ask yourself if there is an answer that does not make sense and eliminate it. Further narrow down the answer that are derived from equations or concepts that you know are not right and are instead meant to deceive the test taker. See if there are answers that are similar or separated by something like a conversion error. This may be an indication that the correct equation was used.

3. Educated Guess: Remember that there is no penalty for wrong answers. Hopefully with the process of elimination you are able to narrow down as many answers as possible and are able to create an educated guess.

4. Rules of Thumb: Rules of thumb can be used to not only speed up time, but to help lead you in the right direction.

5. If the time is almost up and there are still unanswered questions remaining, determine whether it makes sense to check for mistakes on the problems you do know how to solve, or to tackle the unanswered problems.

Typical Exam Verbiage/Design:


1. Most Nearly: Due to rounding differences, the exam answers will not match yours exactly and in fact may not closely resemble your answer. NCEES uses the term “most nearly” to test your confidence in your solution. When the question prompts you with “most nearly”, choose the answer that most closely matches yours, whether it be greater than or lesser to your value.

2. Irrelevant Information: The exam is intended to test your overall understanding of concepts. At times the question will include unnecessary information that is meant to misdirect you.

3. Deceiving Answers: NCEES wants to know that you are able to determine the appropriate methods for the solutions. There are answers that were intentionally produced from wrong equations to mislead the test taker. For example, you may forget a 1/2 in the formula, KE = (1/2)MV2 and there would be two answers each off by a factor of 1/2.

4. Do Not Overanalyze: The exam questions are meant to be completed in 6 minutes. Therefore, they are intended to be written as straight forward as possible. Do not be tempted to overanalyze the meaning of a question. This will only lead you down the wrong path.

Review the Solutions:

Once the sample test is completed, grade your results. Measure your aptitude in speed, concept comprehension, and overall score. If you score is above the 75% range then you are in good shape. This 75% score is only applicable if you have prepared completely for the exam. If you are just starting out, then please do not be worried about a low score. This is number is also just a range; there is no finite score to determine passing the test. Instead, NCEES calibrates the results against practicing professional engineers. See this page http://ncees.org/exams/scoring-process/ for a better understanding of how NCEES grades the scores.

Review the answers that you got wrong and use the solutions as a learning tool on how to address these types of problems. Compare the types of questions you are missing with the NCEES outline of topics and determine where you should focus your studying. Finally repeat as many practice problems as you can to get a better grasp of the test and to continually improve your score.


5.0 RECOMMENDED REFERENCES The following references are recommended to be reviewed prior to the exam and should be used during the exam. When reviewing these references, make sure you first understand the content. These references do not go into depth on explaining the equations or concepts but are simply references. If you require more background information on any of the information in these references, then you may need to research the information on the internet. Secondly, you should be very familiar with the indices of these references and should be able to navigate the references to find information quickly. This may require you to insert tabs into the references. Once you have completed these two tasks then you should be ready to use these references during the exam. (Tip: It is helpful to have the indices of your references printed separately to allow you to have both the index and the reference material open at the same time, making for quicker searches.)

5.1 MECHANICAL ENGINEERING REFERENCE MANUAL By Michael Lindeburg PE

The Mechanical Engineering Reference Manual or MERM is the most popular and most comprehensive manual designed for the Mechanical Professional Engineering exam. It is recommended that the engineer be very familiar with the contents of this book and to bring this book to the exam. This book and the engineering unit conversions book should allow you to answer a good portion of the exam questions.

Amazon Linki: Mechanical Engineering Reference Manual for PE Exam, 13th Edition

5.2 ENGINEERING UNIT CONVERSIONS BOOK By Michael Lindeburg PE

Another book related to the MERM is the Engineering Unit Conversions book. This is also another recommended book to use during the exam and while studying for the exam.

Amazon Linki: Engineering Unit Conversions

5.3 SCHAUM'S OUTLINE OF THERMODYNAMICS FOR ENGINEERS, 3RD EDITION By Merle Potter, Craig W. Somerton

This book covers the Energy/Power Systems section. Although it is not as concise as the previous two references, it does provide a little explanation and background information on concepts.

Amazon Linki: Schaum's Outline of Thermodynamics for Engineers, 3rd Edition


5.4 SCHAUM'S OUTLINE OF FLUID MECHANICS AND HYDRAULICS, 4TH EDITION By Cheng Liu, Giles Ranald, Jack Evett

This book covers the Hydraulics and Fluids section. This reference is similar to the previous reference. It provides the key equations and concepts but also provides a little background information on concepts.

Amazon Linki: Schaum's Outline of Fluid Mechanics and Hydraulics, 4th Edition

5.5 ASHRAE HANDBOOKS By ASHRAE

The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) is the guiding source for primarily the HVAC engineer, however based on input from examinees from the April 2017 exam these books may also be required as references.

The society publishes four handbooks that contain the essential topics and knowledge for practicing engineer: HVAC Systems and Equipment, HVAC Applications, Refrigeration, Fundamentals. Each of these handbooks is updated in a four year rotation. Only the HVAC Systems and Equipment and the Fundamentals book are needed for the Thermal and Fluids exam. The handbooks are comprehensive and detailed. It is not necessary to know the extensive details of these books, but it is essential to understand their layout and know how to navigate them. If there is a question that you are unsure of in the test, these books will likely have the solution. But because there is so much information, it will be difficult to find the necessary references without at least having a familiarity with these resources.

These books will help with the Cooling/Heating, Pumps/Fans, Compressors, Control Valves, Boilers, Heat Exchangers, Cooling Towers and Condensers topics.

Amazon Linki: 2016 ASHRAE Handbook: HVAC Systems and Equipment

Amazon Linki: 2013 ASHRAE Handbook: Fundamentals

i Justin Kauwale is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com


SECTION 2

BASIC ENGINEERING PRACTICE

Section 2.0 - Basic Engineering Practice Table of Contents 1.0 Introduction ........................................................................................................................ 2

2.0 Important Terms & Equations ............................................................................................ 3

3.0 Engineering terms, symbols and technical drawings ......................................................... 4

3.1 Terms & Symbols ........................................................................................................... 4

3.2 Technical Drawings ........................................................................................................ 4

4.0 Economic Analysis ............................................................................................................. 7

4.1 Interest Rate & Time value of Money ............................................................................. 7

4.2 Annual value/Annuities ................................................................................................... 8

4.3 Equipment Type Questions .......................................................................................... 10

4.4 Convert to Present Value ............................................................................................. 11

4.5 Convert to Future Value ............................................................................................... 12

4.6 Convert to Annualized Value ........................................................................................ 12

4.7 Convert to Rate of Return ............................................................................................. 13

4.8 Factor Tables ................................................................................................................ 14

5.0 Units and conversions ...................................................................................................... 15

6.0 Practice Problems ............................................................................................................ 16

6.1 Problem 1 - Economics ................................................................................................ 16

6.2 Solution 1 - Economics ................................................................................................. 17









1.0 INTRODUCTION Basic Engineering Practice accounts for approximately 6 questions on the Thermal & Fluids Mechanical PE exam.

The Thermal & Fluids Mechanical PE exam is designed to ensure that a passing engineer is minimally competent to practice engineering. Being minimally competent does include understanding engineering terms, symbols and technical drawings, unit conversions and economic analysis. However, many of these tasks can be completed without an engineering background and thus the PE exam should provide questions that are more complex than just questions in one of these topics. The questions may include an economic analysis but also with thermodynamics. You may also have to decipher a technical drawing and use the information to complete a heat transfer question or you will complete a power cycle question and need to convert units to match the selected answers.

Based on the above reasoning, you should focus your studying on other sections of this book, with the exception of the Economic Analysis section. The skills learned in the Economic Analysis section are necessary of an engineer.

Basic Engineering Practice 6 questions

Engineering terms, symbols and technical

drawings

Economic Analysis Units & Conversions

• Present value • Future value • Annual value • Rate of return • Interest rate • Factor tables

4.3 EQUIPMENT TYPE QUESTIONS In the Thermal & Fluids field, often times the engineer must develop an economic analysis on purchasing one piece of equipment over another. In this event the engineer will use terms like present value, annualized cost, future value, initial cost and other terms like salvage value, equipment lifetime and rate of return.

Salvage value is the amount a piece of equipment will be worth at the end of its lifetime. Lifetime is typically given by a manufacturer as the average lifespan (years) of a piece of equipment. Looking at the figure below, initial cost is shown as a downward arrow at year 0. Annual gains are shown as the upward arrow and maintenance costs and other costs to run the piece of equipment are shown as downward arrows starting at year 1 and proceeding to the end of the lifetime. Finally, at the end of the lifetime there is an upward arrow indicating the salvage value.

As previously stated, the most important thing in engineering economic analysis is to convert all monetary gains and costs to like terms, whether it is present value, future value, annual value or rate of return. Each specific conversion will be discussed in the following sections.

Each of the sections will use the same example, in order to illustrate the difference in converting between each of the different terms.

6.6 SOLUTION 3 - ECONOMICS Background: An existing A/C control system is inefficient and you are researching whether or not to replace system. You develop a new system that will cost $30,000 and require an ongoing maintenance of $1,000 per year, but it will save $4,000 per year in energy savings. The new A/C control system will have a lifetime of 30 years.

Problem: If the minimum rate of return is 8%, what will be the annual cost of the new system? Economically, should the new system be installed?

First convert all terms to annual values.

Maintenance cost and energy savings are already annual values.

𝐴𝑚𝑎𝑖𝑛𝑡 = −$1,000

𝐴𝑠𝑎𝑣𝑖𝑛𝑔𝑠 = $4,000

Convert initial cost (present value) to annual value.

𝐴𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡 = −$30,000 ∗ (𝐴𝑃

, 8%, 30)

Refer to economics tables for value.

𝐴𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡 = −$30,000 ∗ (.08883)

𝐴𝑡𝑜𝑡𝑎𝑙 = 𝐴𝑚𝑎𝑖𝑛𝑡 + 𝐴𝑠𝑎𝑣𝑖𝑛𝑔𝑠 + 𝐴𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡

𝐴𝑡𝑜𝑡𝑎𝑙 = $4,000 − $1,000 − $2,664.90

𝐴𝑡𝑜𝑡𝑎𝑙 = $335

Correct Answer: C) $335; Yes, it provides a positive annual cost at the minimum rate of return.


SECTION 3

FLUID MECHANICS

Fluid Mechanics-1 http://www.engproguides.com

Section 3.0 – Fluid Mechanics Table of Contents 1.0 Introduction ........................................................................................................................ 3


3.0 Fluid Properties .................................................................................................................. 7

3.1 Density ............................................................................................................................ 7

3.2 Viscosity ......................................................................................................................... 7

3.3 Specific gravity ............................................................................................................... 8

4.0 Compressible Fluids ........................................................................................................... 9

4.1 Compressible Fluid ......................................................................................................... 9

4.1 Mach Number ................................................................................................................. 9

4.1.1 Speed of Sound ....................................................................................................... 9

4.2 Nozzles ......................................................................................................................... 10

4.2.1 Conservation of energy & mass ............................................................................ 10

4.2.2 Converging-Diverging Nozzle ................................................................................ 11

4.3 Diffusers ....................................................................................................................... 12

4.4 Bulk modulus ................................................................................................................ 12

5.0 Incompressible Fluids ...................................................................................................... 13

5.1 Finding Friction Loss .................................................................................................... 13

5.1.1 Inner diameter tables of common pipe materials and sizes .................................. 13

5.1.2 Flow unit conversions. ........................................................................................... 14

5.1.3 Inner Area table of common pipe materials and sizes. ........................................ 14

5.1.4 Kinematic viscosity tables of common fluids at various temperatures ................... 14

5.1.5 Moody Diagram. .................................................................................................... 14

5.1.6 Pipe Roughness .................................................................................................... 15

5.1 Lift ................................................................................................................................. 20

5.2 Drag .............................................................................................................................. 20

5.3 Buoyancy ...................................................................................................................... 20

5.4 Fluid Power ................................................................................................................... 22


6.1 Problem 1 - Reynolds number ...................................................................................... 24

6.2 Solution 1 - Reynolds number ...................................................................................... 25

6.3 Problem 2 - Mach number ............................................................................................ 26

6.4 Solution 2 - Mach number ............................................................................................ 27


6.5 Problem 3 – Friction loss .............................................................................................. 28

6.6 Solution 3 - Friction loss ............................................................................................... 29

6.7 Problem 4 - Buoyancy .................................................................................................. 30

6.8 Solution 4 - Buoyancy ................................................................................................... 31


6.10 Solution 5 – Friction loss .............................................................................................. 33

6.11 Problem 6 - Reynolds number ...................................................................................... 34

6.12 Solution 6 - Reynolds number ...................................................................................... 35


1.0 INTRODUCTION Fluid Mechanics accounts for approximately 6 questions on the Thermal & Fluids Mechanical PE Exam portion of the exam.

The fluid mechanics principles section accounts for 6 questions. These questions can cover any of the topics below. Fluid properties describe the density, viscosity, kinematic viscosity, specific gravity and much more. Other properties are described in other sections of this book. In order to be prepared for questions on Fluid properties you need to understand what these properties describe, its units and where to find the properties of common fluids. Finally in this section you need to understand the difference between compressible and incompressible flow and when you can use compressible equations versus incompressible equations. The majority of the exam, which basically includes all sections in this book except for the compressible flow section, will assume incompressible flow.

Fluid Mechanics 6 questions

Fluid Properties Compressible Flow Incompressible Flow

• Density • Viscosity • Kinematic viscosity • Specific gravity

• Mach number • Nozzles • Diffusers

• Friction factor • Reynolds number • Lift • Drag


2.0 IMPORTANT TERMS & EQUATIONS

Kinematic and Dynamic Viscosity

𝒗 = 𝝁 [ 𝒍𝒃𝒇𝒕 ∗ 𝒔 ]

𝝆 [ 𝒍𝒃𝒇𝒕𝟑]= [

𝒇𝒕𝟐

𝒔]

𝒘𝒉𝒆𝒓𝒆 𝝆 = 𝒅𝒆𝒏𝒔𝒊𝒕𝒚,𝝁 = 𝒅𝒚𝒏𝒂𝒎𝒊𝒄 𝒗𝒊𝒔𝒄𝒐𝒔𝒊𝒕𝒚;𝒗 = 𝒌𝒊𝒏𝒆𝒎𝒂𝒕𝒊𝒄 𝒗𝒊𝒔𝒄𝒐𝒔𝒊𝒕𝒚

Specific Gravity

𝑺𝑮 =𝝆𝒇𝒍𝒖𝒊𝒅𝝆𝒘𝒂𝒕𝒆𝒓

𝑫𝒆𝒏𝒔𝒊𝒕𝒚 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓,𝝆𝒘𝒂𝒕𝒆𝒓 = 𝟔𝟐.𝟒 𝒍𝒃

𝒇𝒕𝟑@ 𝟔𝟎℉

Mach Number

𝑴 =𝒖𝒄

𝑴 = 𝑴𝒂𝒄𝒉 𝒏𝒖𝒎𝒃𝒆𝒓 [𝒖𝒏𝒊𝒕𝒍𝒆𝒔𝒔];𝒖 = 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 �𝒇𝒕𝒔𝒆𝒄

� ; 𝒄 = 𝒔𝒑𝒆𝒆𝒅 𝒐𝒇 𝒔𝒐𝒖𝒏𝒅

Speed of Sound

𝒄 = �𝒌 ∗ 𝑹𝒔 ∗ 𝑻 �𝒇𝒕𝒔𝒆𝒄

� 𝑴 = 𝑴𝒂𝒄𝒉 𝒏𝒖𝒎𝒃𝒆𝒓;𝑹𝒔 = 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒈𝒂𝒔 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕;

𝑻 = 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 𝒊𝒏 𝑹𝒂𝒏𝒌𝒊𝒏𝒆 𝒌 = 𝒓𝒂𝒕𝒊𝒐 𝒐𝒇 𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒉𝒆𝒂𝒕𝒔 =

𝒄𝒑𝒄𝒗

,

𝒘𝒉𝒆𝒓𝒆 𝒄𝒑 = 𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒉𝒆𝒂𝒕 𝒐𝒇 𝒈𝒂𝒔 𝒂𝒕 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆 𝒂𝒏𝒅 𝒄𝒗 = 𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄𝒆 𝒉𝒆𝒂𝒕 𝒐𝒇 𝒈𝒂𝒔 𝒂𝒕 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒗𝒐𝒍𝒖𝒎𝒆

Air Properties Units

𝑅𝑠 53.35 �𝑓𝑡 − 𝑙𝑏𝑓𝑙𝑏𝑚 − °𝑅

�

𝑘 1.4 N/A Nozzles & Diffusers

Conservation of energy 𝒒𝒊𝒏 + 𝒉𝒊𝒏 +

𝟏𝟐𝒗𝒊𝒏𝟐 = 𝒒𝒐𝒖𝒕 + 𝒉𝒐𝒖𝒕 +

𝟏𝟐𝒗𝒐𝒖𝒕𝟐

𝒘𝒉𝒆𝒓𝒆 𝒒𝒊𝒏/𝒐𝒖𝒕 = 𝒂𝒏𝒚 𝒉𝒆𝒂𝒕 𝒆𝒏𝒕𝒆𝒓𝒊𝒏𝒈 𝒐𝒓 𝒆𝒙𝒊𝒕𝒊𝒏𝒈 𝒕𝒉𝒆 𝒔𝒚𝒔𝒕𝒆𝒎 𝒉𝒊𝒏/𝒐𝒖𝒕 = 𝒆𝒏𝒕𝒉𝒂𝒍𝒑𝒚 𝒂𝒕 𝒕𝒉𝒆 𝒆𝒏𝒕𝒓𝒂𝒏𝒄𝒆 𝒂𝒏𝒅 𝒆𝒙𝒊𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒏𝒐𝒛𝒛𝒍𝒆 𝒗𝒊𝒏/𝒐𝒖𝒕 = 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒂𝒕 𝒕𝒉𝒆 𝒆𝒏𝒕𝒓𝒂𝒏𝒄𝒆 𝒂𝒏𝒅 𝒆𝒙𝒊𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒏𝒐𝒛𝒛𝒍𝒆


3.0 FLUID PROPERTIES During the exam you will need to be able to find and use fluid properties to complete many problems. You should be very familiar with your resources and where to find these fluid properties. As you go through these descriptions of the important fluid properties, look through your Mechanical Engineering Reference Manual and your Schaum’s Thermodynamic Fluid Mechanics. Tag the appendices that contain these properties and recognize the units. The key is to not waste time looking for fluid properties and to not make mistakes when solving a problem due to incorrect units.

3.1 DENSITY The density of a substance is its mass per unit volume, basically how heavy is something in one cubic foot or one cubic meter.

The density of a fluid is measured as a weight per unit volume. Specific volume is the inverse of density and is measures as a volume per unit mass.

3.2 VISCOSITY

Figure 1: Varying liquids and their viscosities

The viscosity of a fluid describes the fluids resistance to flow. Viscosity is measured in 𝑐𝑃 or centipoises and is represented by the variable, µ or mu. Viscosity is measured with a device called a viscometer. There are many different types of viscometers, but each typically has the fluid moving past/through an object or it has the object moving through the fluid. The time of travel will vary based on the viscosity of the fluid. For example, water has a viscosity of ~1.00 cP (centipoises) at 68° F, while syrup has a viscosity of ~1400 cP and air has a viscosity of ~.01827 cP.

µ (𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦) = �𝑔

𝑐𝑚 ∗ 𝑠�


When an object is submerged, the buoyancy force is found through the above equation. Notice that the object’s mass is not in this equation, thus when an object is submerged, the buoyancy force is only dependent on the volume of the object and the density of the fluid.

Figure 9: This shows an object in a fluid, where the object’s weight is greater than the buoyancy force. This causes the object to sink.

𝐵𝑠𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 = 𝜌𝑓𝑙𝑢𝑖𝑑 ∗ 𝑉𝑓𝑙𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑡𝑒𝑑 ∗ 𝑔 = 𝜌𝑓𝑙𝑢𝑖𝑑 ∗ 𝑉𝑜𝑏𝑗𝑒𝑐𝑡 ∗ 𝑔

When the buoyancy force is equal to the weight of the object, then the object will float.

Figure 10: This shows an object in a fluid, where the object’s weight is equal to the buoyancy force. This causes the object to float.

𝐵𝑓𝑙𝑜𝑎𝑡𝑖𝑛𝑔 𝑤ℎ𝑒𝑛, 𝜌𝑓𝑙𝑢𝑖𝑑 ∗ 𝑉𝑓𝑙𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑡𝑒𝑑 ∗ 𝑔 = 𝜌𝑜𝑏𝑗𝑒𝑐𝑡 ∗ 𝑉𝑜𝑏𝑗𝑒𝑐𝑡 ∗ 𝑔

When the buoyancy force is greater than the weight of the object, then the object will rise.

Figure 11: This shows an object in a fluid, where the object’s weight is greater than the buoyancy force. This causes the object to rise, until it reaches equilibrium, where the object will

float.

𝐵𝑟𝑖𝑠𝑖𝑛𝑔 𝑤ℎ𝑒𝑛, 𝜌𝑓𝑙𝑢𝑖𝑑 ∗ 𝑉𝑓𝑙𝑢𝑖𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑡𝑒𝑑 ∗ 𝑔 > 𝜌𝑜𝑏𝑗𝑒𝑐𝑡 ∗ 𝑉𝑜𝑏𝑗𝑒𝑐𝑡 ∗ 𝑔


5.4 FLUID POWER A large portion of the Thermal & Fluids field is using fluids to transmit power in hydraulic and pneumatic industrial systems. Pneumatics is the transfer of energy via compressed air and hydraulics is the transfer of energy via hydraulic fluid like oil. For example, pneumatics is used in the medical field, construction, manufacturing and packaging. Hydraulic fluids are used heavily in the construction and industrial industries to power large equipment like tractors, cranes, excavators, etc. This section of the book provides you a basic understanding of the engineering principles behind both hydraulics and pneumatics.

The first principle is Pascal’s Law. This law states that pressure is transmitted undiminished in all directions and exerts equal force on all areas for a confined fluid at rest. This means that anywhere within this circuit, the fluid’s pressure is equal. Also be sure that the fluid is confined at rest. If the fluid is moving, then friction losses will occur.

Figure 12: The pressure acting upon all surfaces by the fluid in pink is equal, in accordance with Pascal’s law.

𝑝 =𝐹𝐴

𝑝 = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑙𝑏𝑠𝑖𝑛2

); 𝐹 = 𝑓𝑜𝑟𝑐𝑒 (𝑙𝑏𝑠); 𝐴 = 𝜋𝑟2 = 𝑎𝑟𝑒𝑎 (𝑖𝑛2)

Here are some conversions that you should be familiar with.

Pascal (Pa) Megapascal (Mpa) Bar Lbs-sq-in (psi)

1 Pa 1 10−6 10−5 145.04 x 10−6 1 Mpa 106 1 10 145 1 Bar 105 0.1 1 14.5 1 Psi 6,895 6.895 x 10−3 .06895 1


6.12 SOLUTION 6 - REYNOLDS NUMBER A 3” Schedule 80 steel pipe has 100 GPM of 50 F water flowing through it. What is the Reynolds number?

For this equation use the Reynolds Number equation below:

𝑅𝑒 =𝑉 [ 𝑓𝑡𝑠𝑒𝑐] ∗ 𝑑[𝑓𝑡]

𝜈[𝑓𝑡2

𝑠𝑒𝑐]

First find the velocity, which requires the inner diameter of Schedule 80 pipe. Refer to your Mechanical Engineering Reference Manual (MERM) to find the inner diameter.

𝐷 = 0.2417 𝑓𝑡

Next find the inner area, which is also shown in the MERM.

𝐴 = 0.04587 𝑓𝑡2

Next convert GPM to ft^3.

100 GPM ∗ 1

448.83= 0.223

FT3

sec.

Next find the velocity.

V =0.223 FT3

sec0.04587 ft2

= 4.86 𝑓𝑡/𝑠𝑒𝑐

Next find the kinematic viscosity for water at 50 F which is also found in the MERM.

𝜈 = .0000141 𝑓𝑡2/𝑠𝑒𝑐

Plug the values in to the equation.

𝑅𝑒 =4.86 ∗ 0.2417

. 0000141 = 83,343


SECTION 4

HEAT TRANSFER

Heat Transfer-1 http://www.engproguides.com

Section 4.0 – Heat Transfer Table of Contents 1.0 Introduction ........................................................................................................................ 2


3.0 Conduction ......................................................................................................................... 8

3.1 Thermal Conductivity ...................................................................................................... 9

3.2 U-Factor .......................................................................................................................... 9

3.3 R-Value ........................................................................................................................... 9

3.4 Thermal Conduction Through Pipes ............................................................................. 10

4.0 Convection ....................................................................................................................... 12

4.1 Heat Transfer For Pipes ............................................................................................... 12

4.2 Forced convective heat transfer in pipe flow ................................................................ 12

4.2.1 Turbulent flow inside circular pipe (heating) .......................................................... 13

4.2.2 Turbulent flow inside circular pipe (cooling) .......................................................... 13

4.2.3 Laminar flow inside circular pipe (heating) ............................................................ 13

4.2.4 Laminar flow inside circular pipe (cooling) ............................................................ 14

4.2.4 Other situations ..................................................................................................... 14

5.0 Radiation .......................................................................................................................... 14

5.1 Emissivity ...................................................................................................................... 15

5.2 Temperature difference between two objects ............................................................... 15

6.0 Calculating Overall Heat Transfer Coefficient .................................................................. 15

7.0 Cooling/Heating Air .......................................................................................................... 18

8.0 Practice Problems ................................................................................................................. 19

8.1 Problem 1: Calculate Overall Heat Transfer Coefficient ............................................... 19

8.2 Solution 1: Calculate Overall Heat Transfer Coefficient ............................................... 20

8.3 Problem 2: Calculate Overall Heat Transfer Coefficient ............................................... 21

8.4 Solution 2: Calculate Overall Heat Transfer Coefficient ............................................... 22

8.5 Problem 3: Calculate the Reynolds number ................................................................. 23

8.6 Solution 3: Calculate the Reynolds Number ................................................................. 24

8.7 Problem 4: Calculate the Convective Heat Transfer Coefficient................................... 25

8.8 Solution 4: Calculate the Convective Heat Transfer Coefficient ................................... 26


1.0 INTRODUCTION Heat Transfer accounts for approximately 6 questions on the Thermal & Fluids Mechanical PE exam.

The heat transfer principles tested on the Thermal & Fluids exam are used throughout other sections of the exam, specifically in heat exchangers, cooling/heating cycles and distribution systems. There are three main areas of heat transfer: conduction, convection and radiation. Conduction is the transfer of heat through contact. In this type of heat transfer, common skills needed include finding overall heat transfer coefficients, finding insulation values and temperature transitions through materials. Convection is the transfer of heat through a moving fluid. This is most commonly seen in heat exchangers as moving hot fluids transfer heat to cool fluids. The main skill needed in this area include finding the convective heat transfer coefficient. The final type is radiation, which will require finding the radiative heat transfer coefficient and finding the temperature difference between two objects.

Heat Transfer 6 questions

Conduction

• U-value • R-value • Overall heat transfer

coefficient • Temperature

transitions through materials

• Required insulation • Conductive heat

Convection

• Find convective heat transfer coefficient

• Convective heat

Radiation

• Radiative heat • Radiative heat

between objects


𝑇𝑖𝑛𝑛𝑒𝑟 = 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑛𝑛𝑒𝑟 𝑝𝑖𝑝𝑒 𝑤𝑎𝑙𝑙 [℉] 𝑇𝑜𝑢𝑡𝑒𝑟 = 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 [℉]

𝑟𝑖𝑛𝑛𝑒𝑟 = 𝑖𝑛𝑛𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑝𝑖𝑝𝑒 [𝑓𝑡] 𝑟𝑜𝑢𝑡𝑒𝑟 = 𝑜𝑢𝑡𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑝𝑖𝑝𝑒 [𝑓𝑡]

𝐿 = 𝑝𝑖𝑝𝑒 𝑙𝑒𝑛𝑔𝑡ℎ [𝑓𝑡]

For a pipe with multiple layers of different materials, the equation becomes:

𝑄 =2𝑘𝜋𝐿 ∗ (𝑇𝑖𝑛𝑛𝑒𝑟 − 𝑇𝑜𝑢𝑡𝑒𝑟)

ln � 𝑟2𝑟𝑖𝑛𝑛𝑒𝑟

�𝑘𝑖

+ln �𝑟3𝑟2

�𝑘𝑖𝑖

+ ⋯+ln �𝑟𝑜𝑢𝑡𝑒𝑟𝑟𝑛

�𝑘𝑚

Figure 2: Heat transfer takes place from the fluid to the exterior through the various layers around the pipe.


8.2 SOLUTION 1: CALCULATE OVERALL HEAT TRANSFER COEFFICIENT

The overall heat transfer coefficient is found by first converting all values to R-values.

𝑅𝑜𝑎𝑖𝑟 =1

ℎ𝑜𝑎𝑖𝑟=

13

= 0.33ℎ𝑟 ∗ 𝑓𝑡2 ∗ ℉

𝐵𝑡𝑢

𝑅𝑖𝑛𝑠 =𝑡

𝑘𝑖𝑛𝑠=

20.3

= 6.67ℎ𝑟 ∗ 𝑓𝑡2 ∗ ℉

𝐵𝑡𝑢

𝑅𝑏𝑟𝑖𝑐𝑘 =𝑡

𝑘𝑏𝑟𝑖𝑐𝑘=

89

= 0.89ℎ𝑟 ∗ 𝑓𝑡2 ∗ ℉

𝐵𝑡𝑢

Sum up all R-values that are in series.

𝑅𝑡𝑜𝑡𝑎𝑙 = 𝑅𝑜𝑎𝑖𝑟 + 𝑅𝑏𝑟𝑖𝑐𝑘 + 𝑅𝑖𝑛𝑠 + 𝑅𝑔𝑦𝑝

𝑅𝑡𝑜𝑡𝑎𝑙 = 0.33 + 0.89 + 6.67 + 0.8

𝑅𝑡𝑜𝑡𝑎𝑙 = 8.69ℎ𝑟 ∗ 𝑓𝑡2 ∗ ℉

𝐵𝑡𝑢

The overall heat transfer coefficient is simply the inverse of the total resistance.

𝑈𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =1

𝑅𝑡𝑜𝑡𝑎𝑙=

18.69

𝑈𝑜𝑣𝑒𝑟𝑎𝑙𝑙 = 0.12𝐵𝑡𝑢

ℎ𝑟 ∗ 𝑓𝑡2 ∗ ℉


SECTION 5

MASS BALANCE

Mass Balance-1 http://www.engproguides.com

Section 5.0 – Mass Balance Table of Contents 1.0 Introduction ........................................................................................................................ 2


3.0 Conservation of Mass ........................................................................................................ 4

3.0 Evaporation ........................................................................................................................ 5

3.1 Latent heat of evaporation .............................................................................................. 5

3.2 Convert liquid to vapor .................................................................................................... 6

4.0 Condensation ..................................................................................................................... 6

5.0 Dehumidification & Humidification ...................................................................................... 7

6.0 Mixing ................................................................................................................................. 8

6.1 Gas-gas mixing mass balance ....................................................................................... 8

6.2 Liquid-liquid mixing mass balance ................................................................................ 10

7.0 Practice Problems ................................................................................................................. 11

7.1 Problem 1 - Humidifier .................................................................................................. 11

7.2 Solution 1 - Humidifier .................................................................................................. 12

7.3 Problem 2 – Dehumidifier ............................................................................................. 13

7.4 Solution 2 - Dehumidifier .............................................................................................. 14

7.5 Problem 3 – Air Mixtures .............................................................................................. 15

7.6 Solution 3 – Air Mixtures ............................................................................................... 16

7.7 Problem 4 – Condensation ........................................................................................... 17

7.8 Solution 4 – Condensation ........................................................................................... 18


SECTION 6

THERMODYNAMICS

Thermodynamics-1 http://www.engproguides.com

Section 6.0 – Thermodynamics Table of Contents 1.0 Introduction ........................................................................................................................ 4


3.0 Thermodynamics Properties .............................................................................................. 9

3.1 Pressure ......................................................................................................................... 9

3.2 Temperature ................................................................................................................. 10

3.2 Enthalpy ........................................................................................................................ 11

3.3 Entropy ......................................................................................................................... 11

3.4 Specific Heat ................................................................................................................ 12

4.0 Thermodynamic Cycles .................................................................................................... 14

4.1 Pressure-Enthalpy Diagrams ........................................................................................ 14

4.2 Thermodynamic Tables ................................................................................................ 19

4.3 Enthalpy-Entropy Diagrams .......................................................................................... 23

4.4 Finding Thermodynamic Properties .............................................................................. 24

4.5 Thermodynamic Transitions ......................................................................................... 26

4.5.1 Isentropic Transition from Pressure State 1 to Pressure State 2 .......................... 26

4.5.2 Isobaric transition with heat gain or heat rejection ................................................ 27

4.5.3 Other transitions .................................................................................................... 28

4.6 Ideal open gas turbine cycle ......................................................................................... 29

4.6.1 Step 1: Compressor ............................................................................................. 30

4.6.2 Step 2: Combustion chamber ............................................................................... 30

4.6.3 Step 3: Turbine ..................................................................................................... 30

4.6.4 Step 4: Exhaust .................................................................................................... 30

4.6.5 Brayton cycle efficiency ......................................................................................... 30

4.7 Ideal Brayton cycle - closed gas turbine cycle .............................................................. 31

4.7.1 Step 1 to 2: Compressor ...................................................................................... 31

4.7.2 Step 2 to 3: Combustion chamber and heat exchanger ....................................... 32

4.7.3 Step 3 to 4: Turbine .............................................................................................. 32

4.7.4 Step 4 to 1: Heat exchanger ................................................................................. 32

4.7.5 Efficiency ............................................................................................................... 32

4.8 Ideal Brayton cycle - closed gas turbine cycle with heat recovery................................ 33

4.9 Actual Brayton cycle - closed gas turbine cycle ........................................................... 33

4.9.1 Step 1: Compressor ............................................................................................. 33


4.9.2 Step 2: Combustion chamber and heat exchanger .............................................. 33

4.9.3 Step 3: Turbine ..................................................................................................... 33

4.9.4 Step 4: Heat exchanger ........................................................................................ 34

4.10 Rankine Cycle .............................................................................................................. 35

4.10.1 Rankine cycle (yellow) ........................................................................................... 35

4.10.2 Boiler-combustion system (red-blue) ..................................................................... 35

4.10.3 Electric generator (green) ...................................................................................... 36

4.10.4 Cooling tower-condenser water system (blue) ...................................................... 36

5.0 Energy Balances .............................................................................................................. 39

5.1 Turbines, Pumps & Compressors: ................................................................................ 39

5.2 Boilers, Condensers, Evaporators: ............................................................................... 39

5.3 Nozzles & diffusers ....................................................................................................... 39

5.4 Heat exchangers .......................................................................................................... 40

5.5 Mixing ........................................................................................................................... 40

6.0 Combustion ...................................................................................................................... 41

6.1 Fuel ............................................................................................................................... 41

6.2 Air ................................................................................................................................. 41

6.3 Stoichiometry ................................................................................................................ 41

6.4 Air to Fuel Ratio ............................................................................................................ 42

6.5 Excess Air ..................................................................................................................... 43

7.0 Steam ............................................................................................................................... 44

7.1 Pressure-Enthalpy Diagram ......................................................................................... 44

7.2 Steam Tables ............................................................................................................... 50

7.3 Mollier Diagram ............................................................................................................ 53

7.4 Determining Properties of Steam ................................................................................. 54

8.0 Vapor Compression Cycle ............................................................................................... 56

8.1 Evaporator .................................................................................................................... 57

8.2 Compressor .................................................................................................................. 59

8.3 Condenser .................................................................................................................... 61

8.4 Expansion Device ......................................................................................................... 62

9.0 Refrigeration Cycle ........................................................................................................... 63

9.1 Step 1 Evaporator ............................................................................................................. 64

9.2 Step 2 Compressor ........................................................................................................... 68

9.3 Step 3 Condenser ............................................................................................................. 70

9.4 Step 4 Expansion Device .................................................................................................. 72


9.5 Net Refrigeration/Condenser, Work and COP: ................................................................. 73

10.0 Practice problems ............................................................................................................ 76

10.1 Problem 1 – Rankine cycle ........................................................................................... 76

10.2 Solution 1 – Rankine cycle ........................................................................................... 77

10.3 Problem 2 – Rankine cycle ........................................................................................... 79

10.4 Solution 2 – Rankine cycle ........................................................................................... 80

10.5 Problem 3 – Brayton cycle ............................................................................................ 81

10.6 Solution 3 – Brayton cycle ............................................................................................ 82

10.7 Problem 4 – Brayton cycle ............................................................................................ 83

10.8 Solution 4 – Brayton cycle ............................................................................................ 84

10.9 Problem 5 – COP ......................................................................................................... 85

10.10 Solution 5 – COP ...................................................................................................... 86

10.11 Problem 6 – Combustion .......................................................................................... 89

10.12 Solution 6 – Combustion ........................................................................................... 90


Entropy is mostly known for its use in the 2nd law of thermodynamics, which states that a system’s entropy never decreases. Also entropy is used to describe thermodynamic transitions. If there is no change in entropy then the process is determined to be isentropic. Also a process is reversible if the entropy is not increased and the process is irreversible if the entropy increases.

3.4 SPECIFIC HEAT The specific heat describes the ease of a fluid or solid to increase in temperature when heat is applied. Specific heat is also known as heat capacitance and can be thought of as an object’s ability to hold and gain heat. For solids and liquids, specific heat is shown as the variable, cp.

ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 𝑐𝑝 �𝐵𝑡𝑢𝑙𝑏𝑚 ℉

�

Water has a specific heat of 1.0 � 𝐵𝑡𝑢𝑙𝑏𝑚 ℉

�, while aluminum has a specific heat of 0.23 � 𝐵𝑡𝑢𝑙𝑏𝑚 ℉

�. As heat is added to water, water will increase in temperature at a slow rate. Since aluminum has a lower specific heat, it needs less energy to raise its temperature.


4.6 IDEAL OPEN GAS TURBINE CYCLE The two major application areas of the open gas turbine cycle are for aircrafts and electric power generation. In an open cycle the working fluid (air) only passes through the cycle once and is then exhausted to the atmosphere. In a closed cycle, the working fluid (air) is recycled through the cycle. One assumption that you should be aware of is that the mass flow rate through both the open and closed cycles are assumed to be constant. Although fuel does enter the cycle, it is assumed that the only mass flow rate to be considered in doing problems is the mass flow rate of the air. This is typically a safe assumption because the ratio of air to fuel is quite large, typically fuel can be around 2% of the total mass flow rate.

Figure 16: The above figure shows the components of an open Brayton cycle. Step 1 to 2 is the isentropic compressor. Step 2 to 3 is a constant pressure combustion chamber. Step 3 to 4

is the isentropic turbine.

Figure 17: These figures show the constant entropy and constant pressure paths in the Brayton cycle. Use these figures with the previous figure to match each point to each piece of

equipment.

S


10.10 SOLUTION 5 – COP First find point H1, which is the enthalpy entering the compressor. Follow the suction pressure

line to a superheat temperature of 15 F.

𝐻1 = 110𝐵𝑡𝑢𝑙𝑏

Second find point H2, which is the enthalpy leaving the compressor. Follow the constant

entropy line from the “entering compressor” point B to the intersection of the discharge

pressure.

𝐻2 = 125𝐵𝑡𝑢𝑙𝑏

Third find point H4, which is the enthalpy entering the evaporator. Follow the constant enthalpy

line to the discharge pressure horizontal line, which is located at a sub-cooled temperature of

10F.

𝐻4 = 50.5𝐵𝑡𝑢𝑙𝑏


SECTION 7

SUPPORT KNOWLEDGE

Support Knowledge-1 http://www.engproguides.com

Section 7.0 – Support Knowledge Table of Contents 1.0 Introduction ........................................................................................................................ 3


3.0 Pipe System Analysis ......................................................................................................... 6

3.1 Pipe Stress ..................................................................................................................... 6

3.2 Pipe Supports ................................................................................................................. 7

3.2.1 Beam diagrams ....................................................................................................... 7

3.2.2 Pipe support types ................................................................................................. 12

3.3 Hoop Stress .................................................................................................................. 12

3.3.1 Thin walled assumption ......................................................................................... 13

4.0 Joints ................................................................................................................................ 13

4.1 Welded joints ................................................................................................................ 13

4.2 Flanged, bolted and grooved joints .............................................................................. 14

4.3 Threaded joints ............................................................................................................. 14

5.0 Psychrometrics ................................................................................................................. 15

5.1 Properties of Moist Air .................................................................................................. 16

5.1.1 Dry Bulb Temperature ........................................................................................... 16

5.1.2 Wet Bulb Temperature .......................................................................................... 18

5.1.3 Relative Humidity .................................................................................................. 18

5.1.4 Humidity Ratio ....................................................................................................... 20

5.1.5 Enthalpy ................................................................................................................ 21

5.1.6 Specific Volume ..................................................................................................... 22

5.1.7 Dew Point .............................................................................................................. 23

5.2 Movement on Psychrometric Chart .............................................................................. 24

5.2.1 Sensible Heating/Cooling ...................................................................................... 24

5.2.2 Latent Heating/Cooling .......................................................................................... 27

5.2.3 Sensible Heat Ratio ............................................................................................... 32

5.2.4 Mixing of Two Air Streams .................................................................................... 35

6.0 Codes and Standards ...................................................................................................... 37

6.1 ASTM ............................................................................................................................ 37

6.2 ASME ........................................................................................................................... 39

6.3 UL ................................................................................................................................. 39

6.4 NFPA ............................................................................................................................ 40


6.5 ASHRAE ....................................................................................................................... 41


7.1 Problem 1 - Navigating Psychrometric Chart ............................................................... 42

7.2 Solution 1 - Navigating Psychrometric Chart ................................................................ 43

7.3 Problem 2 - Air Mixtures ............................................................................................... 44

7.4 Solution 2 - Air Mixtures ............................................................................................... 45

7.5 Problem 3 - Electric Heater .......................................................................................... 46

7.6 Solution 3 - Electric Heater ........................................................................................... 47

7.7 Problem 4 - Cooling Coil ............................................................................................... 48

7.8 Solution 4 - Cooling Coil ............................................................................................... 49


1.0 INTRODUCTION This book is intended to be a focus on ONLY the application of the key concepts and skills of the Thermal & Fluids Systems Mechanical PE Exam, specifically the Support Knowledge topic of the Mechanical P.E. Exam. This book does not provide a broad overview of all possible topics on the P.E. exam.

Support Knowledge accounts for approximately 6 questions on the Thermal & Fluids Mechanical PE exam.

The support knowledge section includes any principle that did not fit in the principle categories in the previous sections, but might be used in the application section. Pipe system analysis could be used in the Hydraulic and Fluid Applications – Distribution Systems section. This part covers the supports and stresses in a piping system. Similarly, different types of joints could also be included in this section. Psychrometrics are building blocks to air properties in cooling/heating air and also in air heat exchangers. Finally, codes and standards that govern the minimum safety and efficiency requirements for practicing engineers are mentioned here.

Support Knowledge 6 questions

Pipe System Analysis Joints Psychrometrics

• Pipe stress • Pipe supports • Hoop stress

• Welded • Bolted • Threaded

• Dry bulb • Wet bulb • Relative humidity • Humidity ratio • Enthalpy • Specific volume • Dew point • Sensible

heating/cooling • Latent

heating/cooling • Sensible heat ratio • Mixing air streams

Codes & Standards

• ASTM • ASME • UL • NFPA • ASHRAE


3.3.1 Thin walled assumption This above equation only works if the thin walled assumption is true. For the thin-walled assumption to be true, the cylinder must have a wall thickness of no more than about one-tenth of its radius.

𝑡 <1

10𝑟 → 𝑡ℎ𝑖𝑛 𝑤𝑎𝑙𝑙𝑒𝑑 𝑎𝑠𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛

4.0 JOINTS Pipes are joined through the use of joints. There are multiple types of joining methods and these include:

• Welded joints • Bolted joints • Threaded joints

These various joining methods are used based on the pipe material, the fluid within the pipe, size of pipe and the pressure within the pipe. For example, copper pipe is typically soldered together and high pressure pipe uses welding. Bolted and threaded joints have a limit on the pressure it can withstand. The welding of large pipes may sometimes be financially infeasible and thus another joining method may be used.

4.1 WELDED JOINTS A welded pipe joint is formed by melting the pipe material between two pipes and filling the gap with a filler material. As the two sides of the pipe and material cool together, the two pipes become a continuous piece. The joint is often just as strong as the actual pipe material. Welding can be completed with both metal and plastic pipes.

Figure 5: Welded joints are shown in black


• NFPA 99 Healthcare Facilities: This standard applies a higher level of fire safety

based on the unique operation of a healthcare facility.

• NFPA 101 Life Safety Code: This code is used to protect people in buildings, based on the construction and occupancy of the building.

• NFPA 231 Standard for General Storage: This standard applies to the storage of combustibles in a building up to 30 feet in height.

• NFPA 13 Standard for the Installation of Sprinkler Systems: This standard applies to the selection, installation, inspection, maintenance and testing of sprinklers systems in a building.

• NFPA 20 Standard for the Installation of Stationary Pumps for Fire Protection: This standard applies to the selection and installation of fire pumps, so they may reliably deliver water to critical fire suppression systems.

6.5 ASHRAE ASHRAE stands for American Society of Heating, Refrigeration and Air Conditioning Engineers. This organization and its standards play a more important role in the HVAC & Refrigeration exam. For the Thermal & Fluids exam, you simply need to know of this organization and some of its common standards.

For example, here is a list of some of the commonly used ASHRAE codes.

Do not purchase these standards for the exam.

• ASHRAE 15 Safety Code for Mechanical Refrigeration: This standard applies to refrigerant classification and the safe handling of refrigerants.

• ASHRAE 55 Thermal Environmental Conditions for Human Occupancy: This standard applies to the acceptable thermal range for indoor environments.

• ASHRAE 62.1 Ventilation for Acceptable Indoor Air Quality: This standard provides the minimum outside air requirements and exhaust air requirements for various occupancies and uses.

• ASHRAE 90.1 Energy Standard for Buildings except Low-Rise Residential Buildings: This standard sets the minimum efficiency standards for HVAC systems, its equipment and other energy using equipment like lights.

1 http://www.engproguides.com

SECTION 8 HYDRAULIC & FLUID APPLICATIONS

Hydraulic/Fluid Applications-1 http://www.engproguides.com

TABLE OF CONTENTS 1.0 Introduction ........................................................................................................................ 4

2.0 Outline of hydraulic and fluid applications .......................................................................... 5


4.0 Pumps .............................................................................................................................. 10

4.1 Types of pumps ............................................................................................................ 10

4.2 Determining Total Head ................................................................................................ 12

4.3 Determining Net Positive Suction Head Available ........................................................ 17

4.4 Reading Pump Curves ................................................................................................. 20

4.5 Using the Affinity Laws ................................................................................................. 21

4.6 Multiple pumps ............................................................................................................. 21

5.0 Fans ................................................................................................................................. 22

5.1 Important Terms ........................................................................................................... 22

5.2 Types of Fans ............................................................................................................... 23

5.2.1 Axial Fans .............................................................................................................. 23

5.2.2 Propeller Fans ....................................................................................................... 23

5.2.3 Tube-Axial Fans .................................................................................................... 23

5.2.4 Centrifugal Fans .................................................................................................... 24

5.3 Fan Sizing ..................................................................................................................... 26

5.3.1 Determining Volumetric Flow Rate [CFM] ............................................................. 26

5.3.2 Determining Total Static Pressure [in. wg] ............................................................ 26

5.4 Fan Curves ................................................................................................................... 29

5.5 Fan Affinity Laws .......................................................................................................... 31

5.6 Multiple Fans ................................................................................................................ 31

5.6.1 Fans in parallel ...................................................................................................... 32

5.6.2 Fans in series ........................................................................................................ 32

6.0 Compressors .................................................................................................................... 34

6.1 ACFM vs SCFM ............................................................................................................ 36

6.2 Compressor work ......................................................................................................... 36

6.3 Compressor efficiency .................................................................................................. 37

6.3 Compressor dynamic head ........................................................................................... 38

6.3.1 Compressed air pressure loss in piping .................................................................... 38

6.3.2 Compressed air pressure loss at devices and fittings ............................................... 38

7.0 Pressure Vessels ............................................................................................................. 40


7.1 Design factor ................................................................................................................ 40

7.2 Materials ....................................................................................................................... 40

7.3 Pressure relief .............................................................................................................. 41

7.4 Receiver ....................................................................................................................... 42

8.0 Control Valves .................................................................................................................. 43

8.1 Flow characteristics ...................................................................................................... 44

8.2 Sizing for liquids ........................................................................................................... 45

8.3 Sizing for gases ............................................................................................................ 46

8.4 Critical point .................................................................................................................. 46

9.0 Actuators .......................................................................................................................... 47

9.1 Cylinder force ............................................................................................................... 47

9.2 Fluid pressure ............................................................................................................... 47

9.3 Cylinder speed .............................................................................................................. 47

9.4 Fluid flow ...................................................................................................................... 47

10.0 Connections ..................................................................................................................... 48


11.1 Problem 1 – Pressure vessel ........................................................................................ 49

11.2 Solution 1 – Pressure vessel ........................................................................................ 50

11.3 Problem 2 – ACFM ....................................................................................................... 51

11.4 Solution 2 – ACFM ....................................................................................................... 52

11.5 Problem 3 – Compressor .............................................................................................. 53

11.6 Solution 3 – Compressor .............................................................................................. 54

11.7 Problem 4 – Orifice/Valve ............................................................................................. 55

11.8 Solution 4 - Orifice/Valve .............................................................................................. 56


11.10 Solution 5 – Friction loss ........................................................................................... 58

11.11 Problem 6 - Hydraulics .............................................................................................. 59

11.12 Solution 6 - Hydraulics .............................................................................................. 60

11.13 Problem 7 - Compressor ........................................................................................... 61

11.14 Solution 7 - Compressor ........................................................................................... 62

11.15 Problem 8 - Hydraulics .............................................................................................. 63

11.16 Solution 8 – Hydraulics ............................................................................................. 64

11.17 Problem 9 - Pressure loss fittings ............................................................................. 65

11.18 Solution 9 – Pressure loss fittings ............................................................................. 66

11.19 Problem 10 – Pumps/Distribution ............................................................................. 67


11.20 Solution 10 - Pumps/Distribution ............................................................................... 68

11.21 Problem 11 – Net positive suction head ................................................................... 69

11.12 Solution 11 - Net positive suction head ..................................................................... 70

11.23 Problem 12 - Pumps ................................................................................................. 71

11.24 Solution 12 - Pumps .................................................................................................. 72

11.25 Problem 13 - Pumps ................................................................................................. 73

11.26 Solution 13 - Pumps .................................................................................................. 74

11.27 Problem 14 - Fans .................................................................................................... 75

11.28 Solution 14 - Fans ..................................................................................................... 76


1.0 INTRODUCTION “Hydraulic and Fluid Applications” accounts for approximately 24 questions on the Thermal & Fluids Mechanical PE exam.

Hydraulic and Fluid Applications is broken up into two parts

1. Hydraulic and Fluid Equipment 2. Hydraulic and Fluid Distribution Systems

Both topics, Equipment and Systems, point towards the topics of Hydraulics and Pneumatics.

Hydraulics includes the equipment necessary to do work with liquid. This includes pumps, pipes, pressure vessels, control valves, actuators and connections, as shown in the simply hydraulic system.

Figure 1: A simple hydraulic system consists of a reservoir that holds the hydraulic fluid, followed by a pump that pressurizes the fluid. The pressurized fluid in pink is then used to power an

actuating cylinder to conduct mechanical work. In order to avoid over pressurization, there is a relief valve in the system. The green line shows the hydraulic fluid returning back to the reservoir when not

needed

Pneumatics includes the equipment necessary to do work with air. This includes compressors, tubing, pressure vessels, control valves, actuators and connections, as shown in the simply pneumatic system.


Figure 2: A simple pneumatic system consists of a receiver that holds the compressed gas, followed by a compressor that pressurizes the gas. The pressurized gas then goes through a dehumidifier, air dryer filters and drains, before it finally reaches the actuator. The actuator is used to conduct mechanical work.

2.0 OUTLINE OF HYDRAULIC AND FLUID APPLICATIONS The blue indicates the topics that are covered under Equipment and the green indicates the topics that are covered under Distribution Systems.

Hydraulic and Fluid Equipment

15 questions

Pumps & Fans

• Cavitation • Curves • Power • Series • Parallel

• Dynamic head

• Power • Efficiency

• Flow • Sizing

• Design • Material • Pressure

relief

Pressure Vessels

Compressors Control Valves

Actuators Connections

• Fittings • Tubing

• Hydraulic • Pneumatic

Hydraulic and Fluid Distribution 9 questions

• Pipes • Ducts • Open

/closed systems

• Pipes • Tubing

• N/A • N/A • Tubing • Fittings • Tubing


11.10 SOLUTION 5 – FRICTION LOSS 20 GPM of water at 50 F is flown through a 2” plastic pipe (2.067” ID). The Moody friction factor is .025. What is the pressure drop (PSI) through 50’ of pipe?

For this equation use the Darcy Weisbach Equation below:

ℎ =𝑓𝐿𝑣2

2𝐷𝑔 [𝐷𝑎𝑟𝑐𝑦 𝑊𝑒𝑖𝑠𝑏𝑎𝑐ℎ 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛]

𝑤ℎ𝑒𝑟𝑒 ℎ = 𝑓𝑡 𝑜𝑓 ℎ𝑒𝑎𝑑; 𝑓 = 𝐷𝑎𝑟𝑐𝑦 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟; 𝑣 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 �𝑓𝑡𝑠𝑒𝑐

�,

𝐷 = 𝑖𝑛𝑛𝑒𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑓𝑡],𝑔 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 [32.2𝑓𝑡𝑠𝑒𝑐2

]

Prepare each term to be plugged into the equation. First, find velocity. Convert 20 GPM to velocity [ft/sec].

Multiply GPM by 1

448.83 to get

FT3

sec.

20 GPM ∗ 1

448.83= 0.04456

FT3

sec.

Area = PI ∗�2.067

12 �2

4= 0.0233 ft2

Velocity = .04456 ft3/sec

0.0233 ft2= 1.91

𝑓𝑡𝑠𝑒𝑐

Plug in the variables to the equation.

ℎ =. 025 ∗ 50 ∗ 1.912

2 ∗ (2.06712 )32.2

[𝑓𝑡 𝑜𝑓 ℎ𝑒𝑎𝑑]

ℎ =. 025 ∗ 50 ∗ 1.912

2 ∗ (2.06712 )32.2

[𝑓𝑡 𝑜𝑓 ℎ𝑒𝑎𝑑]

ℎ = 0.41 [𝑓𝑡 𝑜𝑓 ℎ𝑒𝑎𝑑]

Next convert to PSI ℎ = 0.41 𝑓𝑡 𝑜𝑓 ℎ𝑒𝑎𝑑 ∗ 0.433 𝑝𝑠𝑖1 𝑓𝑡 𝑜𝑓 ℎ𝑒𝑎𝑑

= 0.18 𝑃𝑆𝐼

The answer is most nearly, A, 0.18 psi.


SECTION 9

ENERGY/POWER SYSTEM APPLICATIONS

Energy/Power Applications-1 http://www.engproguides.com

TABLE OF CONTENTS 1.0 Introduction ........................................................................................................................ 4

1.1 Energy/Power Cycles ..................................................................................................... 4


3.0 Turbines ........................................................................................................................... 10

3.1 Steam Turbine .............................................................................................................. 10

3.2 Gas Turbine .................................................................................................................. 10

4.0 Boilers and Steam Generators ......................................................................................... 11

4.1 Steam generation system ............................................................................................. 11

4.2 Types of boilers ............................................................................................................ 12

4.3 Electric boilers .............................................................................................................. 13

4.4 Boiler energy balance ................................................................................................... 13

4.6 Steam Piping ................................................................................................................ 15

5.0 Internal Combustion Engines ........................................................................................... 16

5.1 Reciprocating engines .................................................................................................. 16

5.2 Two-stroke engine ........................................................................................................ 16

5.3 Four-stroke engine ....................................................................................................... 16

5.4 Compression ratio ........................................................................................................ 16

5.5 BMEP ........................................................................................................................... 17

5.6 Otto cycle ...................................................................................................................... 18

6.0 Heat Exchangers .............................................................................................................. 21

6.1 Types of Heat Exchangers ........................................................................................... 21

6.2 Log Mean Temperature Difference (LMTD) ................................................................. 22

6.3 Heat Balance ................................................................................................................ 23

6.4 Feedwater Heaters ....................................................................................................... 23

7.0 Cooling Towers ................................................................................................................ 26

7.1 Characterizing Cooling Towers .................................................................................... 27

7.2 Cooling Tower Performance ......................................................................................... 30

7.3 Cooling Tower Water Loss and Make-up ..................................................................... 32

8.0 Condensers ...................................................................................................................... 33

9.0 Cooling/Heating ................................................................................................................ 35

9.1 Cooling/Heating coils – air -water ................................................................................. 35

9.2 Cooling & Heating Coil Fluids ....................................................................................... 35

9.3 Cooling & Heating Coil Terms ...................................................................................... 36


10.0 Energy Recovery .............................................................................................................. 39

11.0 Combined Cycles ............................................................................................................. 44

11.1 Brayton cycle with regeneration ................................................................................... 45

Step 1 to 2: Compressor ..................................................................................................... 46

Step 2 to 3: Combustion chamber and heat exchanger ..................................................... 46

Step 3 to 4: Turbine ............................................................................................................ 46

Step 4 to 1: Exhaust ........................................................................................................... 46

11.2 Brayton cycle with intercooling ..................................................................................... 49

11.3 Rankine cycle with reheat ............................................................................................. 51

11.4 Rankine cycle with regeneration ................................................................................... 55

12.0 Practice Problems ............................................................................................................... 57

12.1 Problem 1 – Net positive suction head ......................................................................... 57

12.2 Solution 1 – Net positive suction head ......................................................................... 58

12.3 Problem 2 – Cooling towers ......................................................................................... 59

12.4 Solution 2 – Cooling towers .......................................................................................... 60

12.5 Problem 3 - Boilers ....................................................................................................... 61

12.6 Solution 3 – Boilers ....................................................................................................... 62

12.7 Problem 4 - Turbine ...................................................................................................... 63

12.8 Solution 4 – Turbine ..................................................................................................... 64

12.9 Problem 5 – Internal combustion engine ...................................................................... 65

12.10 Solution 5 – Internal combustion engine ................................................................... 66

12.11 Problem 6 - Internal combustion engine ................................................................... 67

12.12 Solution 6 - Internal combustion engine .................................................................... 68

12.13 Problem 7 – Heat exchanger .................................................................................... 70

12.14 Solution 7 - Heat exchanger ..................................................................................... 71

12.15 Problem 8 - Condenser ............................................................................................. 72

12.16 Solution 8 - Condenser ............................................................................................. 73

12.17 Problem 9 – Cooling load .......................................................................................... 74

12.18 Solution 9 - Cooling load ........................................................................................... 75

12.19 Problem 10 - Turbine ................................................................................................ 76

12.20 Solution 10 - Turbine ................................................................................................. 77

12.21 Problem 11 – Brayton cycle ...................................................................................... 79

12.22 Solution 11 – Brayton cycle ...................................................................................... 80

12.23 Problem 12 – Brayton cycle ...................................................................................... 81

12.24 Solution 12 – Brayton cycle ...................................................................................... 82


12.25 Problem 13 – Rankine cycle ..................................................................................... 83

12.26 Solution 13 – Rankine cycle ...................................................................................... 84

12.27 Problem 14 – Rankine cycle ..................................................................................... 85

12.28 Solution 14 – Rankine cycle ...................................................................................... 86


1.0 INTRODUCTION “Energy/Power System Applications” accounts for approximately 24 questions on the Thermal & Fluids Mechanical PE exam.

Energy/Power System Applications is broken up between four different parts:

1. Energy/Power Equipment (turbines, boilers/steam generators, internal combustion engines, heat exchangers, cooling towers and condensers) 8 questions

2. Cooling/Heating (capacity, loads, cycles) 6 questions 3. Energy/Recovery (waste heat, storage) 5 questions 4. Combined Cycles (components, efficiency) 5 questions

1.1 ENERGY/POWER CYCLES The following diagram shows that all four of these parts are actually part of bigger Energy/Power cycles that are used in power plants throughout the country. For this reason, Thermal & Fluids engineers should know the overall power cycle and how all the individual parts work together. These cycles are depicted on the following diagram. If you are able to grasp this diagram and understand how each part works within the diagram, then you will put yourself in a very good position to pass the exam by having a high probability of answering 24 out of 80 questions. At first glance, this diagram may appear daunting, but this guide will take you through each individual piece and build up the diagram, to help you understand this diagram. From top to bottom, gas turbines burn fuel. The turbine compresses air and mixes it with fuel that is heated to a very high temperature. The hot air-fuel mixture turns the gas turbine and generates electricity through a generator.

Waste heat from the above sequence is used to heat water to a high pressure steam. The high pressure steam turns turbines and generates electricity. Steam leaves the turbine at a lower pressure.

A portion of the low pressure steam is condensed back to low pressure water and then heated through a heat exchanger or feedwater heater. At this heat exchanger, steam is used to heat water. The hot water is then pressurized and fed to a boiler, where it is turned into steam and then used to drive a turbine.

The condenser is used to condense the low pressure steam to water, through the use of condenser water fluid. Cool water travels to the condenser, removes the heat from the low pressure steam, which condenses the steam. The initially cool water then leaves as warm water, since it has picked up heat from the steam. Then the warm condenser water is cooled back down through the use of a cooling tower.


Energy/Power System Applications

24 questions total includes all items below

Heat exchangers (Shell and tube, feedwater

heaters)

Turbines (Gas)

Energy Recovery (Heat rate, efficiency)

5 questions

Cooling towers (Approach, drift, blowdown)

Condensers (Surface area, materials)

Turbines (Steam)

Internal combustion engines (Compression ratio, BMEP)

Compressor

Generator Boilers (Heat rate, efficiency)

Turbines (Steam)

Electricity

Fuel

Waste Heat

HP Hot Water

HP Steam

Warm CDW

Cool CDW

LP Steam

HP Steam

Warm water

LP Steam

Warm Water

Exhaust

Exhaust

Pumps

LP Hot Water

HP Hot Water

Cooling/Heating (Capacity, loads, cycles)

6 questions

Fuel

Exhaust

Combined Cycles 5 questions

(Brayton & Rankine)

Blue box Indicates equipment/item on exam)

Green box Indicates Fluid/Medium

Generator Electricity

Generator Electricity

HP = high pressure LP = low pressure CDW = condenser water

Energy/Power Equipment 8 questions

(Turbines, boilers/steam generators, internal

combustion engines, heat exchangers, cooling towers,

condensers)

1

1

2

3

4

5

5

5 5

5 5

5


SECTION 10

CONCLUSION

Conclusion -1 http://www.engproguides.com

10.0 CONCLUSION If you have any questions on this book or any other Engineering Pro Guides product, then please contact:

Justin Kauwale at [email protected]

Hi. My name is Justin Kauwale, the creator of Engineering Pro Guides. I will be happy to answer any questions you may have about the PE exam. Good luck on your studying! I hope you pass the exam and I wish you the best in your career. Thank you for your purchase!

mailto:[email protected]

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