Fundamentals hp33s exam-review


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Fundamentals hp33s exam-review

  1. 1. Ag engineering PE review: Exam prep, III.B. Characterization of biological products, and engineering economic analysis Marybeth Lima, Ph.D., P.E. Professor, Biological & Agricultural Engineering NOTE: copyright permission was obtained from ASABE. Interest tables are reprinted with permission from Professional Publications, Inc., Civil Engineering Reference Manual for the PE Exam, 8 th ed, © 2001
  2. 2. Part 1: Exam preparation <ul><li>Tips for taking this class </li></ul><ul><li>References (must have) </li></ul><ul><li>Time (in preparing for exam and during exam) </li></ul><ul><li>Strategies (preparation and test taking) </li></ul><ul><li>What you must know about the PE exam </li></ul><ul><ul><li>What to bring, calculator policy, pencils, etc. </li></ul></ul><ul><li>Caveat: the exam changes substantially every year (25% of questions are re-used) </li></ul>
  3. 3. Tips for taking this class <ul><li>Confidence </li></ul><ul><ul><li>Miss with gusto, you’ll remember your mistakes better and won’t make them on the actual test!  </li></ul></ul><ul><li>Attend every session if possible; even the ones that you don’t find as useful still give a good review and overview (listen later if you can’t attend “live”) </li></ul><ul><li>Repetition among speakers is probably a good indicator of importance </li></ul><ul><li>If someone says, “I’d REALLY study for this for the test,” DO IT! </li></ul><ul><li>Whatever you do, don’t miss Sue Nokes, Crowell Bowers, and Ann Christy </li></ul>
  4. 4. References <ul><li>Are an absolutely critical part of your preparation; you will not pass the exam without the proper references </li></ul><ul><li>There is a comprehensive list of references in the booklet entitled “A Guide to Professional Licensure for Agricultural, Food, and Biological Systems Engineers.” </li></ul><ul><li>Some references are more useful than others </li></ul>
  5. 5. References I used for 80% of the exam problems (must haves) <ul><li>A Guide to Professional Licensure for Agricultural, Food, and Biological Systems Engineers </li></ul><ul><li>The notes from this on-line review course (bound) </li></ul><ul><li>ASAE Standards (I used the 2000 edition and was fine) </li></ul><ul><li>The Civil Engineering Reference Manual for the PE exam (soil and water, wastewater, pumps, econ tables, INDEX) </li></ul><ul><li>The Mechanical Engineering Reference Manual for the PE exam (HVAC, machine systems, econ tables, fans, INDEX) </li></ul><ul><ul><li>You don’t have to bring both PE manuals but have one; I’d recommend civil over mechanical because of the Crowell Bowers factor. If you pick the civil manual, bring ASHRAE Fundamentals or another strong HVAC book. </li></ul></ul>
  6. 6. Other references I used <ul><li>Wastewater Engineering, Metcalf and Eddy (used 3 rd edition) </li></ul><ul><li>Henderson, Perry and Young, Principles of Process Engineering </li></ul><ul><li>Wood Engineering, Gurfinkel (any wood engineering book will do; you need the tables at the back; you may find in civil vs. ag parts of library) </li></ul><ul><li>A soil physics book </li></ul><ul><li>MWPS-1: Structures and Environment Handbook (op) </li></ul><ul><li>Schwab et al. Soil and water conservation engineering (4 th edition) </li></ul>
  7. 7. References I brought and did not use <ul><li>Irrigation Systems (don’t remember author, couldn’t get my hands on the James irrigation book) </li></ul><ul><li>NRCS handbook parts 650 and 651 </li></ul><ul><li>Goering and Hansen, Engine and tractor power </li></ul><ul><li>Shuler and Kargi, Bioprocess Engineering Basic Concepts </li></ul><ul><li>Salvendy, Handbook of Human Factors </li></ul><ul><li>MWPS-8, Swine Housing and Equipment Handbook </li></ul>
  8. 8. Time <ul><li>You need to spend time to prepare for the exam and you need to budget your time within the exam </li></ul><ul><li>Preparation: Lindeburg: You need 300 hours of study time to fully prepare for the exam (who has that?) </li></ul><ul><li>Suggest that you set aside blocks of time that are routine and “sacred” (absolutely no interruptions) </li></ul>
  9. 9. Time: preparing for the exam <ul><li>Get your references and get used to using them (tab Standards) </li></ul><ul><li>Make an index of where specific information is located so that you don’t have to search during the exam </li></ul><ul><li>Do and re-do all the problems you are given in the on-line course </li></ul><ul><li>Do problems in your reference books (especially A Guide to Professional Licensure for ag, food and bio engineers) </li></ul><ul><li>Focus your time: general ag engineering knowledge, your expertise area, your secondary knowledge areas </li></ul><ul><li>Don’t spend time on what you KNOW you won’t touch (there is something you won’t) </li></ul><ul><li>The week before the test, do a sample test using the 8 hr exam format (road test caffeine issues, etc.) </li></ul>
  10. 10. Time during the exam <ul><li>The exam is designed such that each question takes an average of six minutes </li></ul><ul><ul><li>There are 30 second problems and 15-20 minute problems </li></ul></ul><ul><li>Go through the test and answer questions in the following order: </li></ul><ul><ul><li>The quick, easy ones that you know you can do </li></ul></ul><ul><ul><li>The ones you know that you can do that take a little more time </li></ul></ul><ul><ul><li>Guess (with gusto!) at the ones that are beyond your scope </li></ul></ul><ul><ul><ul><li>Guess the same letter every time </li></ul></ul></ul><ul><ul><li>Go back and do the ones that you think you can do that are time consuming </li></ul></ul><ul><ul><li>If there’s time, go back and check your answers; also go to the ones that are bugging you (if there are any) </li></ul></ul>
  11. 11. My time during the PE exam <ul><li>Morning session: I finished in 2 hrs and 45 minutes </li></ul><ul><ul><li>I went back through and focused on three questions I knew I could get right if I had time </li></ul></ul><ul><ul><li>I checked all my answers and made sure that the question number and correct answer letter matched </li></ul></ul><ul><ul><li>I stayed the entire four hours </li></ul></ul><ul><li>LUNCH: my conversation with the five time test taker </li></ul><ul><li>Afternoon session: I finished in 3 hrs and 30 minutes </li></ul><ul><ul><li>I checked all my answers and made sure that the question number and correct answer letter matched </li></ul></ul><ul><ul><li>I went back to two questions that were bugging me </li></ul></ul><ul><ul><li>I stayed the entire four hours </li></ul></ul>
  12. 12. Strategies <ul><li>You need to develop problem recognition </li></ul><ul><li>You need to develop flexible thinking (the orifice and Mary Lou Retton!) </li></ul><ul><li>Pick what you will not answer and guess with pleasure (I guessed at 10% of the questions on the exam) </li></ul><ul><li>Many times you can eliminate two of the four choices easily (even with areas you know nothing about) </li></ul><ul><li>The sample exam in the licensure book was very much like the actual exam in terms of format and somewhat alike in terms of types of problems </li></ul><ul><ul><li>The exam doesn’t specify which section is which, but you’ll have four or five consecutive questions that are from the same area and then on to the next area) </li></ul></ul><ul><li>Knowing fundamental knowledge is critical (the PE reference manuals in civil and mechanical were invaluable) </li></ul>
  13. 13. Strategies <ul><li>You need to answer 60% of the problems correctly to pass </li></ul><ul><ul><li>Having a strong base in general agricultural engineering knowledge will “take you over the top” </li></ul></ul><ul><ul><li>My experience: for the various expertise areas, about 60% of the problems were solvable without expert knowledge in the area (as long as you had good references and knew where to look for info) </li></ul></ul><ul><ul><li>The other 40% of the expertise questions were expert knowledge level, involved problems (I skipped P&M, irrigation, and structures/environment expert problems) </li></ul></ul>
  14. 14. Strategies: examples of flexible thinking <ul><li>The orifice: </li></ul><ul><ul><li>Problem 111, Guide to Professional Licensure </li></ul></ul><ul><ul><ul><li>At 40 psi, spray nozzles have an 84° spray angle. A 30% overlap is required to achieve a uniform spray pattern. If nozzles are spaces 30 inches apart, the optimum boom height (inches) above the field surface should be most nearly: </li></ul></ul></ul><ul><ul><ul><ul><li>(a) 16.7 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>(b) 17.6 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>(c) 21.7 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>(d) 26.6 </li></ul></ul></ul></ul>
  15. 15. The orifice <ul><li>I searched high and low for an equation to solve this problem (didn’t have access to reference listed in Licensure book) </li></ul><ul><ul><li>Found the orifice flow equation (CE manual, p. 17-17) </li></ul></ul><ul><ul><ul><li>Q = C d A o (2gh) 0.5 where </li></ul></ul></ul><ul><ul><ul><ul><li>Q = flow rate </li></ul></ul></ul></ul><ul><ul><ul><ul><li>C d = coefficient of discharge (tabulated for various geometries) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>A o = cross sectional area of orifice </li></ul></ul></ul></ul><ul><ul><ul><ul><li>g = acceleration due to gravity </li></ul></ul></ul></ul><ul><ul><ul><ul><li>h = height </li></ul></ul></ul></ul><ul><ul><li>This equation is useful in other problems (see question 508 in Licensure), but not in this one! </li></ul></ul>
  16. 16. The orifice <ul><li>Flexible thinking: do you really need an equation or can you use trig? </li></ul>
  17. 17. The orifice
  18. 18. The orifice
  19. 19. The orifice
  20. 20. Flexible thinking: Mary Lou Reton <ul><li>Problem #523, Licensure: A 200 pound man walks on a 2 inch x 8 inch Southern Pine #2 board suspended between supports located 10 feet apart. He is carrying 100 pounds of shingles. Neglecting the dead weight of the board, the deflection (inches) of the board when he reaches the center is most nearly: </li></ul><ul><li>(a) 0.4, (b) .7, (c) 2.1, (d) 3.3 </li></ul>
  21. 21. Flexible thinking: Mary Lou Reton <ul><li>Background </li></ul><ul><ul><li>The deflection of a wood beam with a load at the center of its span will be maximal </li></ul></ul><ul><ul><li>The equation for maximum deflection is (p. 412.4, MWPS-1) </li></ul></ul><ul><ul><ul><li>Where P = load (weight of man + shingles) </li></ul></ul></ul><ul><ul><ul><li>L = length of beam </li></ul></ul></ul><ul><ul><ul><li>E = modulus of elasticity (property of wood, #2 Southern pine, averaged “dense select” and “dense standard factory” in Table A.2.5, Properties of Structural Lumber, p. 430, Wood Engineering), 1,600,000 lb f /in 2 </li></ul></ul></ul><ul><ul><ul><li>I = moment of inertia (property of wood geometry), can calculate, or can look up in tables, in this case, Table A.2.4, Properties of structural lumber. </li></ul></ul></ul>
  22. 22. Flexible thinking: Mary Lou Reton <ul><li>Moment of inertia: in problem, given a 2 inch x 8 inch board </li></ul><ul><ul><li>Table A.2.4, p. 401: I = 47.635 </li></ul></ul><ul><li>This was wrong! STUMPED…. </li></ul>
  23. 23. Flexible thinking <ul><li>When board sizes are tabulated, the convention is to report sizes as base x height (b x h); </li></ul><ul><ul><li>I = bh 3 </li></ul></ul><ul><li>My incorrect assumption: 2” x 8” is base of the board x height of the board </li></ul>
  24. 24. Flexible thinking <ul><li>Who except Mary Lou Retton is going to walk on a board 2” wide (actually 1.5” wide)? </li></ul><ul><li>Table A.2.4 p. 402, 8 inch by 2 inch board, I = 2.039 in 4 </li></ul><ul><li>Using this value, I got the correct answer: </li></ul>
  25. 25. Flexible thinking <ul><li>Note on #523 </li></ul><ul><li>This question is “tricky.” PE exam problems are not tricky; they may contain information that you don’t need, but they tend to be very straightforward </li></ul>
  26. 26. What you must know about the PE exam <ul><li>Information can be found at </li></ul><ul><li>The only calculators allowed into the exam are: </li></ul><ul><ul><li>Hewlett Packard – HP 33S Casio – FX 115MS or FX 115MSPlus (may have SR designation) Texas Instruments – TI 30X IIS Texas Instruments – TI 36X SOLAR </li></ul></ul><ul><li>You will use a 0.7 mm lead NCEES pencil (provided) </li></ul>
  27. 27. What you must know about the PE exam <ul><li>It is better to have it and not need it than need it and not have it </li></ul><ul><li>I got “Katrina-ed”: something similar could happen to you, so be prepared! </li></ul><ul><li>Bring </li></ul><ul><ul><li>Photo ID and your admission paper for the exam </li></ul></ul><ul><ul><li>2 calculators </li></ul></ul><ul><ul><li>Your lunch </li></ul></ul><ul><ul><li>A bottle of water </li></ul></ul><ul><ul><li>Your pain reliever of choice </li></ul></ul>
  28. 28. Any questions on exam prep?
  29. 29. Exercise <ul><li>On the PE exam, you want the “30 second questions” that appear on the test to take 30 seconds to answer </li></ul><ul><li>Practice: find the answers to the questions on the following slides </li></ul><ul><ul><li>Approach </li></ul></ul><ul><ul><ul><li>First, classify the problem: in which area of the Ag PE do you think the problem is contained? In which references might you find the information? </li></ul></ul></ul><ul><ul><ul><li>When you find the answer, record the value, the reference in which you found the answer, AND descriptive information within the reference (page number, table number, figure number, equation number, etc.) </li></ul></ul></ul>
  30. 30. Question 1 <ul><li>What is the heat of combustion of propane? </li></ul><ul><li>NOTE: heat of combustion is also referred to as heating value </li></ul>
  31. 31. Heat of combustion
  32. 32. Question 2 <ul><li>The Atterburg limit test measures what? </li></ul>
  33. 33. Question 3 <ul><li>What is the Young’s modulus of elasticity of stainless steel? </li></ul>
  34. 34. Question 4 <ul><li>What is the density of air at 10° C? </li></ul>
  35. 35. Question 5 <ul><li>What is the curve number for contoured row crops in good hydrologic condition for hydrologic soil group B? </li></ul>
  36. 36. Question 6 <ul><li>What is the allowable unit stress in horizontal shear (F v ) for Douglas Fir-Larch Number 2 for a nominal size piece that is 3” x 4”? </li></ul>
  37. 37. Question 7 <ul><li>What is the typical concentration of suspended solids (SS) in septage? </li></ul>
  38. 38. Question 8 <ul><li>What is the equilibrium moisture content of rough rice at 30° C and 80% RH? </li></ul>
  39. 39. Question 8
  40. 40. Part 2: III.B. Characterization of biological products <ul><li>Description </li></ul><ul><ul><li>Fundamental physical chemistry </li></ul></ul><ul><ul><ul><li>Physical and chemical properties of gases and particles, phase change, thermodynamics, liquid dynamics, molecular materials, protein conformation, etc. </li></ul></ul></ul><ul><ul><li>Particle characterization and dynamics </li></ul></ul><ul><ul><ul><li>Particle size, particle distribution, particle density, aerosol distribution </li></ul></ul></ul><ul><ul><li>Bulk solids characterization </li></ul></ul><ul><ul><ul><li>Angle of repose, bulk density </li></ul></ul></ul><ul><ul><li>Compatibility of biological materials </li></ul></ul><ul><ul><ul><li>Properties of plastics, food and biological processing materials, nanotechnology and implants </li></ul></ul></ul>
  41. 41. Standards you might need for III.B <ul><li>D241.4: Density, specific gravity, and mass-moisture relationships of grain for storage (FPE) </li></ul><ul><li>D243.3: Thermal properties of grain and grain products (FPE) </li></ul><ul><li>D245.5: Moisture relationships of plant-based agricultural products (FPE) </li></ul><ul><li>EP545: Loads exerted by free-flowing grain on shallow storage structures (S&E) </li></ul><ul><li>Hellevang, AE-84, Temporary grain storage, </li></ul>
  42. 42. Background <ul><li>Bulk density a property of particulate materials. It is the mass of many particles of the material divided by the volume they occupy. The volume includes the space between particles as well as the space inside the pores of individual particles. (Wikipedia) </li></ul>
  43. 43. D241.4: grain properties
  44. 44. D241.4: grain properties
  45. 45. D243.3: thermal properties grain
  46. 46. D245.5: moisture relationships <ul><li>Moisture content wet basis </li></ul><ul><ul><li>Where m = wet basis moisture content (decimal) </li></ul></ul><ul><ul><li>W m = mass of moisture </li></ul></ul><ul><ul><li>W d = mass of dry matter </li></ul></ul><ul><li>Moisture content dry basis </li></ul><ul><ul><li>Where M = dry basis moisture content (decimal) </li></ul></ul><ul><ul><li>Dry basis moisture content can exceed 1 (or 100%) </li></ul></ul>
  47. 47. D245.5 <ul><li>To convert from dry basis to wet basis: </li></ul><ul><li>To convert from wet basis to dry basis: </li></ul>
  48. 48. D245.5 <ul><li>Isotherm data (used in drying calculations) </li></ul><ul><ul><li>In table format or graphical format </li></ul></ul>
  49. 49. EP545: Loads exerted by free-flowing grain on shallow storage structures
  50. 50. EP545 <ul><li>Total equivalent grain height: taken as the “average” grain height if the top grain surface is not horizontal (may not be, angle of repose) </li></ul><ul><li>Design approach, shallow grain holding structures: </li></ul><ul><ul><li>Determine material properties (bulk density, angle of repose, coefficient of friction) </li></ul></ul><ul><ul><li>Use properties to calculate total equivalent grain height </li></ul></ul><ul><ul><li>Calculate static pressures (static vertical pressure at any point, static lateral pressure, and vertical pressure on floor) </li></ul></ul><ul><ul><li>Calculate resultant wall forces (resultant lateral force, resultant shear force) </li></ul></ul><ul><ul><ul><li>Ex., Lateral force per unit length P H = LH 2 /2 where </li></ul></ul></ul><ul><ul><ul><ul><li>L is the lateral pressure (function of depth z) and H is the equivalent grain height </li></ul></ul></ul></ul><ul><ul><ul><li>Lateral pressure L(z) = kV(z) </li></ul></ul></ul><ul><ul><ul><ul><li>Where L(z) = lateral pressure at grain depth z, psf (pounds per square fot) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>k = ratio of lateral to vertical pressure, dimensionless and assumed to be 0.5 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>V(z) = vertical pressure at equivalent grain depth z, psf </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V(z) = Wgz where W is the bulk density (lb/ft 3 ), g is acceleration to due gravity </li></ul></ul></ul></ul></ul>
  51. 51. Hellevang <ul><li>Overview of temporary grain storage (free reference!) </li></ul><ul><ul><li>The pressure grain exerts per foot of depth is called the equivalent fluid density </li></ul></ul><ul><ul><li>Table 1. Approximate equivalent fluid density of some peaked grains. </li></ul></ul><ul><ul><li>Crop Equivalent Fluid Density   lb/cu. ft </li></ul></ul><ul><ul><li>Barley 20 </li></ul></ul><ul><ul><li>Corn (shelled) 23 Oats 14 </li></ul></ul><ul><ul><li>Grain Sorghum 22 </li></ul></ul><ul><ul><li>Soybeans 21 </li></ul></ul><ul><ul><li>Sunflower (non-oil) 9 </li></ul></ul><ul><ul><li>Sunflower (oil) 12 </li></ul></ul><ul><ul><li>Durum wheat 26 HRS wheat 24 </li></ul></ul>
  52. 52. Particle size distribution <ul><li>Different for different materials! </li></ul><ul><ul><li>Good reference: Chapter 35, CE manual, soil properties and testing </li></ul></ul><ul><ul><ul><li>Sieve sizes and corresponding opening sizes (ASTM) </li></ul></ul></ul><ul><ul><ul><li>Typical particle size distribution (for soil): </li></ul></ul></ul><ul><li>Remember statistics! A friend of mine does research on particle size distributions of nanoparticles. They usually get a normal distribution and are interested in the mean (“average”) particle size and the dispersion (standard deviation, for example) </li></ul>
  53. 53. Particle size distribution
  54. 54. Sample questions <ul><li>#119, Licensure: A building with an 8-foot high wall is storing grain. Grain was placed into the storage building and leveled until it is within 6 inches of the top of the wall. The grain density is 56 pounds per bushel. The lateral force per unit length at the base of the wall is most nearly </li></ul><ul><li>(a) 638, (b) 672, (c) 717, (d) 1260 </li></ul>
  55. 55. Solution
  56. 56. Solution
  57. 57. Sample questions <ul><li>#519, Licensure: In an operation where minimizing mechanical damage to grain is important, the conveyor type least satisfactory for use in grain is </li></ul><ul><li>(a) auger or screw conveyor </li></ul><ul><li>(b) en masse conveyor </li></ul><ul><li>(c) belt conveyor </li></ul><ul><li>(d) bucket conveyor </li></ul>
  58. 58. Solution <ul><li>No calculation, consult a reference on auger design </li></ul><ul><ul><li>Chapter 11, Srivista et al., Ag Machines </li></ul></ul>
  59. 59. Sample questions <ul><li>#520, Licensure: if corn is treated as a non-cohesive granular material (shelled), the equivalent fluid density (pounds per cubic foot) is most nearly: </li></ul><ul><li>(a) 22 </li></ul><ul><li>(b) 28 </li></ul><ul><li>(c) 35 </li></ul><ul><li>(d) 56 </li></ul>
  60. 60. Solution <ul><li>Look up in Hellevang table! </li></ul><ul><ul><li>Hellevang’s table for shelled corn: 23 #/sqft </li></ul></ul><ul><ul><li>Answer is A </li></ul></ul><ul><li>Do not be deterred by the fact that the values are not exactly the same! PE questions are constructed to accommodate minor differences in tabulated values! </li></ul>
  61. 61. Any questions on III.B? <ul><li>Tips: </li></ul><ul><ul><li>Have a table or set of tables with material properties handy </li></ul></ul><ul><ul><li>Additional material property references: </li></ul></ul><ul><ul><ul><li>Johnson, Biological Process Engineering, has many material property charts (density, specific heat, thermal conductivity, thermal diffusivity, etc.) </li></ul></ul></ul><ul><ul><ul><li>Brodkey and Hershey, Transport Phenomena: A unified approach, Appendix C </li></ul></ul></ul><ul><ul><li>This area overlaps with many others </li></ul></ul><ul><ul><li>Know how to convert between wet and dry basis moisture contents! </li></ul></ul><ul><ul><li>Remember common sense and statistics </li></ul></ul>
  62. 62. Part 3: Engineering economic analysis <ul><li>An easy question or two on the exam if you know how to use factor tables (slang, interest tables) </li></ul><ul><ul><li>Tabulated in the ME reference manual, A-132-150 or CE manual A-112-130 </li></ul></ul><ul><li>Types of problems in engineering economic analysis </li></ul><ul><ul><li>Decision making: you have a material you’re trying to choose, or a part, or a machine. Compare which is most economical given present cost, maintenance costs, etc. </li></ul></ul><ul><ul><li>Replacement/retirement analysis (when should you replace or retire a product?) </li></ul></ul><ul><ul><li>Rate of return problem (to find percentage return on an investment) </li></ul></ul><ul><ul><li>Break even point on an investment </li></ul></ul><ul><ul><li>Loan repayment (how long will it take) </li></ul></ul><ul><ul><li>Economic life analysis (life cycle costs) </li></ul></ul><ul><ul><li>Benefit/cost analysis (do the benefits outweigh the costs) </li></ul></ul>
  63. 63. Engineering econ <ul><li>Almost all engineering econ problems will involve cash flows ; it is like a material balance using money instead of mass. </li></ul><ul><li>Types of cash flows: </li></ul><ul><ul><li>Single payment cash flows (P or F) </li></ul></ul><ul><ul><ul><li>P = present value of money </li></ul></ul></ul><ul><ul><ul><li>F = future value of money </li></ul></ul></ul><ul><ul><li>Uniform series cash flow (A) </li></ul></ul><ul><ul><ul><li>An amount that is the same every month, like a house or car payment </li></ul></ul></ul><ul><ul><li>Gradient series cash flow (not used much) (G) </li></ul></ul><ul><ul><ul><li>A value that goes up or down the same amount every time period </li></ul></ul></ul><ul><li>You use types of cash flows to compare alternatives and solve econ problems </li></ul>
  64. 64. Engineering econ <ul><li>Cash flow problems can be calculated using equations or are tabulated for fast problem solving </li></ul><ul><li>Example </li></ul><ul><ul><li>If you put $1,000 into a savings account and the annual interest rate on the account was 6%, how much money would be in the account after 5 years? </li></ul></ul><ul><li>The equation to convert a present value to a future value is </li></ul>
  65. 65. Engineering econ <ul><li>(1 + i) n is called the single payment compound amount factor, and is tabulated for various combinations of i (interest rate) and n (time period) </li></ul><ul><li>The notation (symbol) for the single payment compound factor is (F/P, i%, n) </li></ul><ul><li>This notation indicates that F (future $ amount) is unknown, that you have P (the present value), and given the interest rate (i) in percent and the time period (n), you can find F. </li></ul>
  66. 66. Engineering econ <ul><li>Back to our example: If you put $1000 into a savings account and the annual interest rate on the account was 6%, how much money would be in the account after 5 years? </li></ul><ul><li>Solve by equation: F = 1000(1 + 0.06) 5 = $1338.23 </li></ul><ul><li>Solve by interest table </li></ul>
  67. 67. Engineering econ
  68. 68. Engineering econ <ul><li>Example solve by interest table: </li></ul><ul><ul><li>Go to F/P column with n = 5, for table with i = 6%: Factor = 1.3382 </li></ul></ul><ul><li>F = ($1000) 1.3382 = $1338.2 </li></ul>
  69. 69. Engineering econ <ul><li>Biggest thing to keep in mind: make sure that your UNITS match; interest rate, n, and dollar amounts may be given on a different basis </li></ul><ul><li>You try: How much should you put into a 10% effective annual rate savings account in order to have $10,000 in four years? (10% interest table included on next page) </li></ul>
  70. 70. Engineering econ
  71. 71. Engineering econ <ul><li>You are given a future amount of money (F) and ask to solve for a present amount of money </li></ul><ul><li>Solve using the i = 10% interest table, with n = 4 years; (P/F, 10%, 4) = 0.6830 </li></ul><ul><li>P = F (P/F, 10%, 4) = $10,000*0.6830 = $6,830 </li></ul><ul><li>Notice that n is given in years and i is given as an annual interest rate (per year); units match </li></ul>
  72. 72. Last problem of the night! <ul><li>Maintenance costs for a machine are $250/year. What is the present worth of these maintenance costs over a 12 year period if the annual interest rate is 10%? </li></ul><ul><ul><li>Given: </li></ul></ul><ul><ul><li>Find: </li></ul></ul>
  73. 73. Engineering econ <ul><li>You have A, you need P: Go to i = 10% interest chart and go to the P/A column (remember in this notation your unknown comes first): (P/A, 10%, 12) = 6.8137 </li></ul><ul><li>P = A (P/A) = -250*6.8137 = -$1703 (negative sign indicates a cash sink or loss of $) </li></ul><ul><li>Any questions on engineering econ? </li></ul>
  74. 74. Take home points <ul><li>If your brain feels like it’s leaking out of your ears right now, don’t worry, it’s normal  </li></ul><ul><li>Best things I did for the PE: </li></ul><ul><ul><li>Had a reference book with a great index </li></ul></ul><ul><ul><li>Had a list of where to find critical equations and important information </li></ul></ul><ul><li>Time management tips </li></ul><ul><li>GOOD LUCK!! </li></ul>