Terms and Symbols

This NCEES topic is very vague and provides little information for the aspiring professional energy. Engineers become more familiar with terms, symbols and technical drawings with experience, as they encounter new things. It is the opinion of the author that a test on your knowledge of random terms or symbols, other than those presented in the other topics is not fair nor is an adequate measure of a minimally competent professional engineer. The thermal and fluids field is a large field and it would not be prudent use of your time to memorize terms and symbols. However, you should know the terms and symbols presented in this book, since the exam will cover these topics and you should know the terms and symbols relevant to the topics covered in the exam. Luckily each term and symbol is explained when first introduced in this book.

Technical Drawings

Technical drawings are a single tool used by engineers to present ideas to others. An engineer should be able to produce technical drawings to accurately communicate ideas and the engineer should also be able to read and interpret technical drawings. Engineering drawings are not typical drawings, sketches or illustrations. These drawings show data like sizes, shapes, angles, tolerances, and dimensions. On the exam, you may be tested on your interpretation of these engineering technical drawings...

Economic Analysis

As a professional engineer, you will be tasked with determining the course of action for a design. Often times this will entail choosing one alternative instead of several other design alternatives. Engineers need to be able to present engineering economic analysis to their clients in order to justify why a certain alternative is more financially sound than other alternatives. The following sub-sections will present the engineering economic concepts that should be understood by the engineer and does not present a comprehensive look into the study of engineering economics.

Interest Rate and Time Value of Money

Before discussing interest rate, it is important that the engineer understand that money today is worth more than that same value of money in the future, due to factors such as inflation and interest. This is the time value of money concept. For example, if you were given the option to have $1,000 today or to have $1,000 ten years from now, most people will choose $1,000 today, without understand why this option is worth more. The reason $1,000 today is worth more is because of what could have done with that money; in the financial world, this means the amount of interest that could have been earned with that money. If you took $1,000 today and invested it at 4% per year, you would have $1,040 dollars at the end of the first year.

If you kept the $1,040 in the investment for another year, then you would have $1,081.60.

At the end of the 10 years the investment would have earned, $1,480.24.

An important formula to remember is the Future Value (FV) is equal to the Present Value (PV) multiplied by (1+interest rate), raised to the number of years.

As an example, what would be the present value of $1,000, 10 years from now, if the interest rate is 4%.

Thus in the previous example, receiving $1,000, 10 years from now, is only worth $675.46 today

It is important to understand present value because when analyzing alternatives, cash values will vary with time and the best way to make a uniform analysis is to first convert all values to consistent terms, like present value.

For example, if you were asked whether you would like $1,000 today or $1,500 in ten years (interest rate at 4%), then it would be a much more difficult question than the previous question. But with an understanding of present value, the "correct" answer would be to accept $1,500 ten years from now, because the $1000 today at 4% interest is only worth $1,480 ten years from now. In this example, the $1,000 today was converted to its future value 10 years from now. Once this value was converted, it was then compared to the $1,500, which was presented as future value in 10 years. Notice how all values were converted to future value for comparison.

Annual Value

The previous section described the difference between present value and future value. It also showed how a lump sum given at certain times are worth different amounts in present terms. In engineering, there are often times when annual sums are given in lieu of one time lump sums. An example would be annual energy savings due to the implementation of a more efficient HVAC system. Thus, it is important for the engineer to be able to determine the present/future value of future annual gains or losses.

For example, let's assume that a solar hot water project, provides an annual savings of $200. Using the equations from the previous section, each annual savings can be converted to either present or future value. Then these values can be summed up to determine the future and present value of annual savings of $200 for four years at an interest rate of 4%.

For longer terms, this method could become tedious. Luckily there is a formula that can be used to speed up the process in converting annuities (A) to present value and future value.

Reverse Equations, where annual value is solved:

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.

Example: A new chiller has an initial cost of $50,000 and a yearly maintenance cost of $1,000. At the end of its 15 year lifetime, the chiller will have a salvage value of $5,000. It is estimated that by installing this new chiller, there will be an energy savings of $5,000 per year. The interest rate is 4%.

Convert to Present Value

What is the Present Value (Present Worth) of this chiller? The first term, initial cost is already in present value.

The second term, maintenance cost must be converted from an annual cost to present value. However, we can add the annual energy savings to this amount to save time.

The third term, salvage value must be converted from future value to present value.

Finally, summing up all the like terms.

A negative Present Value indicates that the investment does not recoup the initial investment.

Convert to Future Value

See technical study guide for more detail.

Convert to Annual Value

See technical study guide for more detail.

Convert to Rate of Return

See technical study guide for more detail.

Factor Tables

When conducting engineering economic analyses, factor values are used in lieu of formulas. Factor values are pre-calculated values that correspond to:

• (1) A specific equation (convert present value to annual, convert present value to future, etc.)
• (2) An interest rate.
• (Number of years.

Looking up these values in a table is sometimes quicker than using the equations and lessens the possibility of calculator error. It is recommended that the engineer have the Mechanical Engineering Reference Manual (MERM), which has tables of these factor values in its Appendices. A summary of the factory values are shown below.

Units and Conversions

Many of the problems on the PE exam will require you to convert units and will have incorrect answers that use different units or wrong conversion techniques. Double check your work and make sure you use the correct units.

Use your Engineering Unit Conversions book.

The Engineering Unit Conversions book is a must have for nearly all questions in the exam. This book has all the common unit conversions used in the PE exam and this book makes it very easy to convert from one unit to the next.

Amazon Link: Engineering Unit Conversions