Author Name: BIO 218 Natural History Paper General Formatting: (10%) • 1 Margins correct? • 1 Font correct? • 2 Double-spaced? • 2 Pages numbered? • 2 All sections included? • 2 At least 3 pages of text, not more than 5 pages? Project elements (50%) • Introduction: o 8 General background on topic and species (state scientific name!)? o 2 Goes from general to specific? • Review of Journal Articles: o 4 States topic and hypothesis/hypotheses described in articles? o 3 Reports how research was conducted? o 2 Describes specialized materials used? o 2 Discusses type(s) of data collected and how to be analyzed/compared/used? o 3 Reports what happened in the experiments? o 2 If comparisons made, discusses how they were made? o 2 Figure(s) reproduced and cited? o 2 Table(s) reproduced and cited? • Summary/Conclusion: o 10 Synthesizes the results of the experiments and ties the findings of the articles together? • Literature Cited: o 4 At least 3 journal articles (primary literature) used? o 2 References used in paper properly? o 2 References all listed in this section and formatted correctly? o 2 All references listed are in the body of the paper and all references in the body are listed in this section? *0.5% for each extra citation (>3) that is correctly used* Writing Elements (40%) • /15 Grammar or spelling errors? • /15 Writing is clear and flows logically throughout paper? • /10 Appropriate content in each section? Final Paper Total ( %) = /40 Comments:

Author Name: BIO 218 Natural History Paper General Formatting: (10%) • 1 Margins correct? • 1 Font correct? • 2 Double-spaced? • 2 Pages numbered? • 2 All sections included? • 2 At least 3 pages of text, not more than 5 pages? Project elements (50%) • Introduction: o 8 General background on topic and species (state scientific name!)? o 2 Goes from general to specific? • Review of Journal Articles: o 4 States topic and hypothesis/hypotheses described in articles? o 3 Reports how research was conducted? o 2 Describes specialized materials used? o 2 Discusses type(s) of data collected and how to be analyzed/compared/used? o 3 Reports what happened in the experiments? o 2 If comparisons made, discusses how they were made? o 2 Figure(s) reproduced and cited? o 2 Table(s) reproduced and cited? • Summary/Conclusion: o 10 Synthesizes the results of the experiments and ties the findings of the articles together? • Literature Cited: o 4 At least 3 journal articles (primary literature) used? o 2 References used in paper properly? o 2 References all listed in this section and formatted correctly? o 2 All references listed are in the body of the paper and all references in the body are listed in this section? *0.5% for each extra citation (>3) that is correctly used* Writing Elements (40%) • /15 Grammar or spelling errors? • /15 Writing is clear and flows logically throughout paper? • /10 Appropriate content in each section? Final Paper Total ( %) = /40 Comments:

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Tornado Eddy Investigation Abstract The objective of this lab was to write a bunch of jibberish to provide students with a formatting template. Chemical engineering, bioengineering, and environmental engineering are “process engineering” disciplines. Good abstracts contains real content, such as 560 mL/min, 35 deg, and 67 percent yield. Ideal degreed graduates are technically strong, bring broad system perspectives to problem solving, and have the professional “soft skills” to make immediate contributions in the workplace. The senior lab sequence is the “capstone” opportunity to realize this ideal by integrating technical skills and developing professional soft skills to ensure workforce preparedness. The best conclusions are objective and numerical, such as operating conditions of 45 L/min at 32 deg C with expected costs of $4.55/lb. Background Insect exchange processes are often used in bug filtration, as they are effective at removing either positive or negative insects from water. An insect exchange column is a packed or fluidized bed filled with resin beads. Water flows through the column and most of the insects from the water enter the beads, but some of them pass in between the beads, which makes the exchange of insects non-ideal. Insectac 249 resin is a cation exchange resin, as it is being used to attract cationic Ca2+ from the toxic waste stream. This means the resin is negatively charged, and needs to be regenerated with a solution that produces positively charged insects, in this case, salt water which contains Na+ insects. The resin contains acidic styrene backbones which capture the cationic insects in a reversible process. A curve of Ca2+ concentration concentration vs. time was obtained after a standard curve was made to determine how many drops from the low cost barium test kit from Aquarium Pharmaceuticals (API)1 bottle #2 would correspond to a certain concentration in solution. A standard curve works by preparing solutions with known concentrations and testing these concentrations using the kit to create a curve of number of drops from bottle #2 (obtained result) vs. concentration of Ca2+ in solution (desired response). The standard curve can then be used for every test on the prototype and in the field, to quickly and accurately obtain a concentration from the test kit. The barium concentration vs. time curve can be used to calculate the exchange capacity of the resin and, in later tests, the regeneration efficiency. The curves must be used to get the total amount of barium removed from the water, m. Seen in Equation 2, the volumetric flow rate of water, , is multiplied by the integral from tinitial to tfinal of the total concentration of Ca2+ absorbed by the resin as a function of time, C. (2) 1 http://aquariumpharm.com/Products/Product.aspx?ProductID=72 , date accessed: 11/26/10 CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 9 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A graphical trapezoid method was used to evaluate the integral and get the final solution in equivalents of Ca2+ per L, it must be noted that there are 2 equivalents per mole of barium, as the charge of the barium insect is +2. An initial exchange capacity was calculated for the virgin resin, and an adjusted exchange capacity was calculated once the resin was regenerated. The regenerated resin capacity was found by multiplying the virgin resin capacity by the regeneration efficiency, expressed in Equation 3. (3) See Appendix A for the calculation of the exchange capacities and the regeneration efficiency. Materials and Methods Rosalie and Peter Johnson of Corvallis established the Linus Pauling Chair in Chemical Engineering to honor Oregon State University’s most famous graduate. Peter Johnson, former President and owner of Tekmax, Inc., a company which revolutionized battery manufacturing equipment, is a 1955 graduate of the College of Engineering.2 The Chair, also known as the Linus Pauling Distinguished Engineer or Linus Pauling Engineer (LPE), was originally designed to focus on the traditional “capstone” senior lab sequence in the former Department of Chemical Engineering. The focus is now extended to all the process engineering disciplines. The LPE is charged with establishing strong ties with industry, ensuring current and relevant laboratory experiences, and helping upperclass students develop skills in communication, teamwork, project management, and leadership. Include details about lab procedures not sufficiently detailed in the SOP, problems you had, etc. The bulk solution prepared to create the standard curve was used in the second day of testing to obtain the exchange capacity of the insectac 249 resin. The solution was pumped through a bathroom scale into the prototype insect exchange column. 45 mL of resin was rinsed and added to the column. The bed was fluidized as the solution was pumped through the resin, but for the creation of the Ca2+ concentration vs. time curve, the solution was pumped down through the column, as illustrated in the process flow diagram seen in Figure 1. Figure 1. Process sketch of the insect exchange column used for the project. Ref: http://www.generon.co.uk/acatalog/Chromatography.html 2 Harding, P. Viscosity Measurement SOP, Spring, 2010. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 10 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A bathroom scale calibration curve was created to ensure that the 150 mL/min, used to calculate the breakthrough time, would be delivered to the resin. The bathroom scale used was a Dwyer brand with flowrates between 0 and 300 cc/min of water. Originally, values between 120 and 180 mL/min were chosen for the calibration, with three runs for each flowrate, however the bathroom scale values were so far away from the measure values the range was extended to 100 to 200 mL/min. The regeneration experiment was performed using a method similar to that used in the water softening experiment, however instead of using a 640 ppm Ca2+ solution to fill the resin, a 6000 ppm Na+ solution was used to eject the Ca2+ from the resin. Twelve samples times were chosen and adjusted as the experiment progressed, with more than half of the samples taken at times less than 10 minutes, and the last sample taken at 45 minutes. The bulk exit solution was also tested to determine the regeneration efficiency. Results and Discussion The senior lab sequence has its roots in the former Department of Chemical Engineering. CHE 414 and 415 were taught in Winter and Spring and included 6 hours of lab time per week. The School has endeavored to incorporate the courses into the BIOE and ENVE curriculum, and this will be complete in 2008-2009. Recent development of the senior lab course sequence is shown chronologically in Fig. 1. In 2006-2007, CHE 414 and 415 were moved to Fall and Winter to enable CHE 416, an elective independent senior project course. Also that year, BIOE students took BIOE 414 in the Fall and BIOE 415 was developed and taught. No BIOE students enrolled in the optional CHE. In 2007-2008, the program transitioned in a new Linus Pauling Engineer and ENVE 414 was offered. Also, approximately 30 percent of BIOE students enrolled in the optional CHE 416. Accommodating the academic calendars of the three disciplines required a reduction in weekly student lab time from 6 to 3 hours. The expected relationship between coughing rate, y, and length of canine, x, is Bx z y Fe− (1) where F is a pre-exponential constant, B is vitamin B concentration and z is the height of an average trapeze artist. 3 The 2008-2009 brings the challenge of the dramatic enrollment increase shown in Fig. 1 and the first offering of ENVE 415. The result, shown on the right in Fig. 1, is the delivery of the senior lab sequence uniformly across the process engineering disciplines. CBEE 416 is expected to drawn approximately of the students that take the 415 courses. In 2007-2008, 414 and 415 were required for CHEs, 414 and 415 for BIOEs, and only 414 for ENVEs. CHE 416 is ostensibly an elective for all disciplines. In 2008-2009, 414 and 415 is required for all disciplines and CHE 416 will be an elective. The content of 414 is essentially 3 Fundamentals of Momentum, Heat, and Mass Transfer, Welty, J.R. et al., 4th edition, John Wiley & Sons, Inc. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 11 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE identical for all three disciplines, 415 has discipline-specific labs, and 416 consists of senior projects with potentially cross-discipline teams of 2 to 4 students. Tremendous labor and struggling with the lab equipment resulted in the data shown in y = –‐0.29x + 1.71 y = –‐0.25x + 2.03 y = –‐0.135x + 2.20 –‐1.5 –‐1.0 –‐0.5 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 10 ln y (units) x (units) ln y_1 ln y_2 ln y_3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Case 1 Case 2 Case 3 Slope (units) (a) (b) Figure 1. (a) Data for y and x plotted for various values of z and (b) a comparison of slopes for the 3 cases investigate. The log plot slope yields the vitamin B concentration. The slopes were shown to be significantly at the 90% confidence level, but the instructor ran out of time and did not include error bars. The slope changed as predicted by the Snirtenhoffer equation. Improvements to the lab might include advice on how to legally change my name to something less embarrassing. My whole life I have been forced to repeat and spell it. I really feel that this has affected my psychologically. This was perhaps the worst lab I have ever done in my academic career, primarily due to the fact that there was no lab time. I simply typed in this entire report and filled it with jibberish. Some might think nobody will notice, but I know that …… Harding reads every word. Acknowledgments The author acknowledges his elementary teacher for providing truly foundational instruction in addition and subtraction. Jenny Burninbalm was instrumental with guidance on use of the RT-345 dog scratching device. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 12

Tornado Eddy Investigation Abstract The objective of this lab was to write a bunch of jibberish to provide students with a formatting template. Chemical engineering, bioengineering, and environmental engineering are “process engineering” disciplines. Good abstracts contains real content, such as 560 mL/min, 35 deg, and 67 percent yield. Ideal degreed graduates are technically strong, bring broad system perspectives to problem solving, and have the professional “soft skills” to make immediate contributions in the workplace. The senior lab sequence is the “capstone” opportunity to realize this ideal by integrating technical skills and developing professional soft skills to ensure workforce preparedness. The best conclusions are objective and numerical, such as operating conditions of 45 L/min at 32 deg C with expected costs of $4.55/lb. Background Insect exchange processes are often used in bug filtration, as they are effective at removing either positive or negative insects from water. An insect exchange column is a packed or fluidized bed filled with resin beads. Water flows through the column and most of the insects from the water enter the beads, but some of them pass in between the beads, which makes the exchange of insects non-ideal. Insectac 249 resin is a cation exchange resin, as it is being used to attract cationic Ca2+ from the toxic waste stream. This means the resin is negatively charged, and needs to be regenerated with a solution that produces positively charged insects, in this case, salt water which contains Na+ insects. The resin contains acidic styrene backbones which capture the cationic insects in a reversible process. A curve of Ca2+ concentration concentration vs. time was obtained after a standard curve was made to determine how many drops from the low cost barium test kit from Aquarium Pharmaceuticals (API)1 bottle #2 would correspond to a certain concentration in solution. A standard curve works by preparing solutions with known concentrations and testing these concentrations using the kit to create a curve of number of drops from bottle #2 (obtained result) vs. concentration of Ca2+ in solution (desired response). The standard curve can then be used for every test on the prototype and in the field, to quickly and accurately obtain a concentration from the test kit. The barium concentration vs. time curve can be used to calculate the exchange capacity of the resin and, in later tests, the regeneration efficiency. The curves must be used to get the total amount of barium removed from the water, m. Seen in Equation 2, the volumetric flow rate of water, , is multiplied by the integral from tinitial to tfinal of the total concentration of Ca2+ absorbed by the resin as a function of time, C. (2) 1 http://aquariumpharm.com/Products/Product.aspx?ProductID=72 , date accessed: 11/26/10 CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 9 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A graphical trapezoid method was used to evaluate the integral and get the final solution in equivalents of Ca2+ per L, it must be noted that there are 2 equivalents per mole of barium, as the charge of the barium insect is +2. An initial exchange capacity was calculated for the virgin resin, and an adjusted exchange capacity was calculated once the resin was regenerated. The regenerated resin capacity was found by multiplying the virgin resin capacity by the regeneration efficiency, expressed in Equation 3. (3) See Appendix A for the calculation of the exchange capacities and the regeneration efficiency. Materials and Methods Rosalie and Peter Johnson of Corvallis established the Linus Pauling Chair in Chemical Engineering to honor Oregon State University’s most famous graduate. Peter Johnson, former President and owner of Tekmax, Inc., a company which revolutionized battery manufacturing equipment, is a 1955 graduate of the College of Engineering.2 The Chair, also known as the Linus Pauling Distinguished Engineer or Linus Pauling Engineer (LPE), was originally designed to focus on the traditional “capstone” senior lab sequence in the former Department of Chemical Engineering. The focus is now extended to all the process engineering disciplines. The LPE is charged with establishing strong ties with industry, ensuring current and relevant laboratory experiences, and helping upperclass students develop skills in communication, teamwork, project management, and leadership. Include details about lab procedures not sufficiently detailed in the SOP, problems you had, etc. The bulk solution prepared to create the standard curve was used in the second day of testing to obtain the exchange capacity of the insectac 249 resin. The solution was pumped through a bathroom scale into the prototype insect exchange column. 45 mL of resin was rinsed and added to the column. The bed was fluidized as the solution was pumped through the resin, but for the creation of the Ca2+ concentration vs. time curve, the solution was pumped down through the column, as illustrated in the process flow diagram seen in Figure 1. Figure 1. Process sketch of the insect exchange column used for the project. Ref: http://www.generon.co.uk/acatalog/Chromatography.html 2 Harding, P. Viscosity Measurement SOP, Spring, 2010. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 10 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE A bathroom scale calibration curve was created to ensure that the 150 mL/min, used to calculate the breakthrough time, would be delivered to the resin. The bathroom scale used was a Dwyer brand with flowrates between 0 and 300 cc/min of water. Originally, values between 120 and 180 mL/min were chosen for the calibration, with three runs for each flowrate, however the bathroom scale values were so far away from the measure values the range was extended to 100 to 200 mL/min. The regeneration experiment was performed using a method similar to that used in the water softening experiment, however instead of using a 640 ppm Ca2+ solution to fill the resin, a 6000 ppm Na+ solution was used to eject the Ca2+ from the resin. Twelve samples times were chosen and adjusted as the experiment progressed, with more than half of the samples taken at times less than 10 minutes, and the last sample taken at 45 minutes. The bulk exit solution was also tested to determine the regeneration efficiency. Results and Discussion The senior lab sequence has its roots in the former Department of Chemical Engineering. CHE 414 and 415 were taught in Winter and Spring and included 6 hours of lab time per week. The School has endeavored to incorporate the courses into the BIOE and ENVE curriculum, and this will be complete in 2008-2009. Recent development of the senior lab course sequence is shown chronologically in Fig. 1. In 2006-2007, CHE 414 and 415 were moved to Fall and Winter to enable CHE 416, an elective independent senior project course. Also that year, BIOE students took BIOE 414 in the Fall and BIOE 415 was developed and taught. No BIOE students enrolled in the optional CHE. In 2007-2008, the program transitioned in a new Linus Pauling Engineer and ENVE 414 was offered. Also, approximately 30 percent of BIOE students enrolled in the optional CHE 416. Accommodating the academic calendars of the three disciplines required a reduction in weekly student lab time from 6 to 3 hours. The expected relationship between coughing rate, y, and length of canine, x, is Bx z y Fe− (1) where F is a pre-exponential constant, B is vitamin B concentration and z is the height of an average trapeze artist. 3 The 2008-2009 brings the challenge of the dramatic enrollment increase shown in Fig. 1 and the first offering of ENVE 415. The result, shown on the right in Fig. 1, is the delivery of the senior lab sequence uniformly across the process engineering disciplines. CBEE 416 is expected to drawn approximately of the students that take the 415 courses. In 2007-2008, 414 and 415 were required for CHEs, 414 and 415 for BIOEs, and only 414 for ENVEs. CHE 416 is ostensibly an elective for all disciplines. In 2008-2009, 414 and 415 is required for all disciplines and CHE 416 will be an elective. The content of 414 is essentially 3 Fundamentals of Momentum, Heat, and Mass Transfer, Welty, J.R. et al., 4th edition, John Wiley & Sons, Inc. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 11 Josephine Hornsnogger CBEE 414, Lab Section M 1300–‐1550 April 19, 2010 Oregon State University School of CBEE identical for all three disciplines, 415 has discipline-specific labs, and 416 consists of senior projects with potentially cross-discipline teams of 2 to 4 students. Tremendous labor and struggling with the lab equipment resulted in the data shown in y = –‐0.29x + 1.71 y = –‐0.25x + 2.03 y = –‐0.135x + 2.20 –‐1.5 –‐1.0 –‐0.5 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 10 ln y (units) x (units) ln y_1 ln y_2 ln y_3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Case 1 Case 2 Case 3 Slope (units) (a) (b) Figure 1. (a) Data for y and x plotted for various values of z and (b) a comparison of slopes for the 3 cases investigate. The log plot slope yields the vitamin B concentration. The slopes were shown to be significantly at the 90% confidence level, but the instructor ran out of time and did not include error bars. The slope changed as predicted by the Snirtenhoffer equation. Improvements to the lab might include advice on how to legally change my name to something less embarrassing. My whole life I have been forced to repeat and spell it. I really feel that this has affected my psychologically. This was perhaps the worst lab I have ever done in my academic career, primarily due to the fact that there was no lab time. I simply typed in this entire report and filled it with jibberish. Some might think nobody will notice, but I know that …… Harding reads every word. Acknowledgments The author acknowledges his elementary teacher for providing truly foundational instruction in addition and subtraction. Jenny Burninbalm was instrumental with guidance on use of the RT-345 dog scratching device. CBEE 102: ENGINEERING PROBLEM SOLVING AND COMPUTATIONS PROJECT DESCRIPTION 12

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Biologists, researching the effects of adding limestone sand as buffer for acid rain effects in streams, monitored the pH levels of two streams each month for 36 months. The first stream had a mean pH level of 6.8 with a standard deviation of 2.3. The control stream had a mean pH level of 9.2 with a standard deviation of 1.5. Assume a .05 significance level for testing the claim that the mean pH of the first stream was less (more acidic) than the mean pH of the control stream. Also, assume the two samples are independent simple random samples selected from normally distributed populations, but do not assume that the population standard deviations are equal.

Biologists, researching the effects of adding limestone sand as buffer for acid rain effects in streams, monitored the pH levels of two streams each month for 36 months. The first stream had a mean pH level of 6.8 with a standard deviation of 2.3. The control stream had a mean pH level of 9.2 with a standard deviation of 1.5. Assume a .05 significance level for testing the claim that the mean pH of the first stream was less (more acidic) than the mean pH of the control stream. Also, assume the two samples are independent simple random samples selected from normally distributed populations, but do not assume that the population standard deviations are equal.

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Phy 2201 page – 1 – Physics 2201 Homework III part 2. Fall 2015. Due: Tuesday November 17, 2015 Show all work with clear setup and/or explain all answers. All solutions must be based on work and/or energy methods. 10 points each. Partial credit is available. 1) A 1.4 kg falling object (subject to the effects of aerodynamic drag) is 1800 m high, traveling at 34 m/s and has not yet reached terminal speed. It first reaches terminal speed at a height of 1340 m and the terminal speed is 37.3 m/s. a) Determine if the mechanical energy ( ? E = K +Ug ) of the system consisting of the falling object and Earth’s gravity field has been conserved during the fall from 1800 m to 500 m. b) How much work (if any) including the correct sign (+ or -­‐) has been done on the system over this interval (presumably by the external drag force)? c) Will the energy of the system consisting of the object, the gravity field and the surrounding air be conserved over this interval? Explain your answer. Is there an additional energy that must be accounted for in this analysis? What is it and how much of it has been generated? Note: terminal speed is a constant speed. 2) The 0.2 kg box below slides down a curved ramp, jumps a small gap and lands on a flat platform. At the point on the ramp shown it is 1.5 m above the floor and its speed is 2.0 m/s. At the point shown on the platform the box is 0.4 m above the floor and sliding at 4.2 m/s. a) If we consider a system consisting of the box and Earth’s gravity field so that ? E = K +Ug , has the energy of this system been conserved during the described process? Explain how you know. b) If we consider the exact same process but broaden our system definition so that ? E = K +Ug + Eother and ? Eother includes any “other” form of energy that might have been produced through the process (most of it is thermal), what objects are included in this system? Discuss, don’t just state a list. c) Determine ? ΔEother for the process as described. d) How much kinetic energy would the box have on the platform if ? ΔEother = 0 ? Phy 2201 page – 2 – 3) The system below consists of two masses attached through a string of negligible mass over a pulley that turns with negligible friction. ? m1 > m2 and the sphere ? m2 is immersed in a viscous fluid that exerts a considerable drag force. Starting from rest the system is set into motion by releasing ? m1 which causes this mass to descend while the other rises (assume the string instantly becomes taut). In what follows analyze the motion by defining the “system” as both masses and Earth’s gravity field. a) Once released each mass travels a distance ? h1 and somewhere during this interval both masses reach terminal speed ? VT . Write out (derive/formulate) a mathematical expression for the change of the potential energy of the system over this interval (Using the givens! Don’t make up numbers or define your own variable names.) Has the system gained or lost potential energy? Explain how you know. b) Write out (derive/formulate) a mathematical expression for the change in the kinetic energy of the system over the ? h1 interval (using the givens). Write out an expression for the work done by the drag force over this interval using the givens. c) Following the ? h1 interval the system moves a distance ? h2 while the sphere is still immersed in the fluid. Write out an expression for the work done by the drag force over this interval. Can you tell from this expression if the work done by drag is positive or negative? (You should.) Which is it and how do you know? d) If ? h1 = h2 over which interval does the drag force do more work in an absolute value sense? How do you know? Phy 2201 page – 3 – 4) A 48 kg diver jumps off a cliff (with a running start) into the ocean. The cliff is 50 m above the ocean below. Her coach, using a video of the dive, determines that at a point in flight when she has risen 0.7 m above the cliff, her speed1 (center of mass) is 0.5 m/s. Frictional effects such as drag are negligible. Formulate your solution using the diver and Earth’s gravity field as a system. Gravity does not do work on this system. It’s effects are captured in changes in potential energy. a) How much kinetic energy did she have at takeoff? What was her speed? b) How much kinetic energy will she have as she splashes into the ocean? c) What minimum amount of chemical energy needed to be consumed within the diver’s body in order for her to walk to the cliff, from ocean level, and then take off (jump)? Explain how you know. 1 Includes both x and y velocity components. This is not the highest point in the jump.

Phy 2201 page – 1 – Physics 2201 Homework III part 2. Fall 2015. Due: Tuesday November 17, 2015 Show all work with clear setup and/or explain all answers. All solutions must be based on work and/or energy methods. 10 points each. Partial credit is available. 1) A 1.4 kg falling object (subject to the effects of aerodynamic drag) is 1800 m high, traveling at 34 m/s and has not yet reached terminal speed. It first reaches terminal speed at a height of 1340 m and the terminal speed is 37.3 m/s. a) Determine if the mechanical energy ( ? E = K +Ug ) of the system consisting of the falling object and Earth’s gravity field has been conserved during the fall from 1800 m to 500 m. b) How much work (if any) including the correct sign (+ or -­‐) has been done on the system over this interval (presumably by the external drag force)? c) Will the energy of the system consisting of the object, the gravity field and the surrounding air be conserved over this interval? Explain your answer. Is there an additional energy that must be accounted for in this analysis? What is it and how much of it has been generated? Note: terminal speed is a constant speed. 2) The 0.2 kg box below slides down a curved ramp, jumps a small gap and lands on a flat platform. At the point on the ramp shown it is 1.5 m above the floor and its speed is 2.0 m/s. At the point shown on the platform the box is 0.4 m above the floor and sliding at 4.2 m/s. a) If we consider a system consisting of the box and Earth’s gravity field so that ? E = K +Ug , has the energy of this system been conserved during the described process? Explain how you know. b) If we consider the exact same process but broaden our system definition so that ? E = K +Ug + Eother and ? Eother includes any “other” form of energy that might have been produced through the process (most of it is thermal), what objects are included in this system? Discuss, don’t just state a list. c) Determine ? ΔEother for the process as described. d) How much kinetic energy would the box have on the platform if ? ΔEother = 0 ? Phy 2201 page – 2 – 3) The system below consists of two masses attached through a string of negligible mass over a pulley that turns with negligible friction. ? m1 > m2 and the sphere ? m2 is immersed in a viscous fluid that exerts a considerable drag force. Starting from rest the system is set into motion by releasing ? m1 which causes this mass to descend while the other rises (assume the string instantly becomes taut). In what follows analyze the motion by defining the “system” as both masses and Earth’s gravity field. a) Once released each mass travels a distance ? h1 and somewhere during this interval both masses reach terminal speed ? VT . Write out (derive/formulate) a mathematical expression for the change of the potential energy of the system over this interval (Using the givens! Don’t make up numbers or define your own variable names.) Has the system gained or lost potential energy? Explain how you know. b) Write out (derive/formulate) a mathematical expression for the change in the kinetic energy of the system over the ? h1 interval (using the givens). Write out an expression for the work done by the drag force over this interval using the givens. c) Following the ? h1 interval the system moves a distance ? h2 while the sphere is still immersed in the fluid. Write out an expression for the work done by the drag force over this interval. Can you tell from this expression if the work done by drag is positive or negative? (You should.) Which is it and how do you know? d) If ? h1 = h2 over which interval does the drag force do more work in an absolute value sense? How do you know? Phy 2201 page – 3 – 4) A 48 kg diver jumps off a cliff (with a running start) into the ocean. The cliff is 50 m above the ocean below. Her coach, using a video of the dive, determines that at a point in flight when she has risen 0.7 m above the cliff, her speed1 (center of mass) is 0.5 m/s. Frictional effects such as drag are negligible. Formulate your solution using the diver and Earth’s gravity field as a system. Gravity does not do work on this system. It’s effects are captured in changes in potential energy. a) How much kinetic energy did she have at takeoff? What was her speed? b) How much kinetic energy will she have as she splashes into the ocean? c) What minimum amount of chemical energy needed to be consumed within the diver’s body in order for her to walk to the cliff, from ocean level, and then take off (jump)? Explain how you know. 1 Includes both x and y velocity components. This is not the highest point in the jump.

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4. The report “Biological Effects of Ionizing Radiation” (1972) assesses about 10,000 person-rem per death (statistically). The death rate by automobile is about 1/10 million passenger miles. At TMI-2, Governor Thornburg recommended that everyone susceptible to radiation within a 5 mile radius evacuate. Assuming that 25,000 people evacuated and each traveled a distance of 20 miles, compare the risk of evacuation with the risk of not evacuating, assuming their exposure is 0.5 mrem/hr and they evacuate for 2 days.

4. The report “Biological Effects of Ionizing Radiation” (1972) assesses about 10,000 person-rem per death (statistically). The death rate by automobile is about 1/10 million passenger miles. At TMI-2, Governor Thornburg recommended that everyone susceptible to radiation within a 5 mile radius evacuate. Assuming that 25,000 people evacuated and each traveled a distance of 20 miles, compare the risk of evacuation with the risk of not evacuating, assuming their exposure is 0.5 mrem/hr and they evacuate for 2 days.

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ENGR 1120 – PROGRAMMING FOR ENGINEERS (MATLAB) Homework Program #2 Objectives: Demonstrate knowledge of data files, vector variables, intrinsic functions, subscript manipulation, for loops, and plotting in MATLAB. You have been given a set of ASCII data files that contain directions for laying out patterns in a field. The data files contain in the first column a distance to travel and in the second column a direction heading. Unfortunately, the person who created the data did not have a good understanding of orienteering and the direction headings are given as referenced to a clock face. The pattern begins at the origin of a Cartesian coordinate system with the person facing 12 o’clock, see the figure below. The figure shows an example of the first step in the pattern being a distance of 1.5 feet in the direction of 7 o’clock. All direction headings are given in terms of this clock orientation. The distance values given are in feet. There are 5 data files provided online for testing of the program. Write a script file that will allow the user to input from the keyboard the filename of the file that they wish to analyze. Load only that ONE data file and plot the resulting pattern. Once each point forming the pattern has been located, find and designate on the plot which of the resulting nodes was the farthest away from the origin. Also find and designate the center of the pattern as defined to occur at the coordinate location corresponding to (average x, average y). When plotting the resulting pattern on the Cartesian coordinate system, set the axes limits to appropriate values. HINT: Correlate the direction headings provided in the data files to a Cartesian coordinate system by using the following vector in your script file. This requires subscript manipulation. angle = [60; 30; 0; 330; 300; 270; 240; 210; 180; 150; 120; 90] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 7 8 9 10 11 12 you are here

ENGR 1120 – PROGRAMMING FOR ENGINEERS (MATLAB) Homework Program #2 Objectives: Demonstrate knowledge of data files, vector variables, intrinsic functions, subscript manipulation, for loops, and plotting in MATLAB. You have been given a set of ASCII data files that contain directions for laying out patterns in a field. The data files contain in the first column a distance to travel and in the second column a direction heading. Unfortunately, the person who created the data did not have a good understanding of orienteering and the direction headings are given as referenced to a clock face. The pattern begins at the origin of a Cartesian coordinate system with the person facing 12 o’clock, see the figure below. The figure shows an example of the first step in the pattern being a distance of 1.5 feet in the direction of 7 o’clock. All direction headings are given in terms of this clock orientation. The distance values given are in feet. There are 5 data files provided online for testing of the program. Write a script file that will allow the user to input from the keyboard the filename of the file that they wish to analyze. Load only that ONE data file and plot the resulting pattern. Once each point forming the pattern has been located, find and designate on the plot which of the resulting nodes was the farthest away from the origin. Also find and designate the center of the pattern as defined to occur at the coordinate location corresponding to (average x, average y). When plotting the resulting pattern on the Cartesian coordinate system, set the axes limits to appropriate values. HINT: Correlate the direction headings provided in the data files to a Cartesian coordinate system by using the following vector in your script file. This requires subscript manipulation. angle = [60; 30; 0; 330; 300; 270; 240; 210; 180; 150; 120; 90] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 7 8 9 10 11 12 you are here

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Project 1: Particle Trajectory in Pleated Filters Due: 12:30 pm, Dec. 1, 2015, submission through blackboard Course: Numerical Methods Instructor: Dr. Hooman V. Tafreshi Most aerosol filters are made of pleated fibrous media. This is to accommodate as much filtration media as possible in a limited space available to an air filtration unit (e.g., the engine of a car). A variety of parameters contribute to the performance of a pleated filter. These parameters include, but are not limited to, geometry of the pleat (e.g., pleat height, width, and count), microscale properties of the fibrous media (e.g., fiber diameters, fiber orientation, and solid volume fraction), aerodynamic and thermal conditions of the flow (e.g., flow velocity, temperature, and operating pressure), and particle properties (e.g., diameter, density, and shape). Figure 1: Examples of pleated air filters [1‐2]. In this project you are asked to calculate the trajectory of aerosol particles as they travel inside a rectangular pleat channel. Due to the symmetry of the pleat geometry, you only need to simulate one half of the channel (see Figure 2). Figure 2: The simulation domain and boundary conditions (the figure’s aspect ratio is altered for illustration purposes). Trajectory of the aerosol particles can be calculated in a 2‐D domain by solving the Newton’s 2nd law written for the particles in the x‐ and y‐directions, v(h) inlet velocity fibrous media v(y) y tm l h x Ui u(l) u(x) 2 2 p 1 p 1 ( , ) d x dx u x y dt  dt    2 2 p 1 p 1 ( , ) d y dy v x y dt  dt    where 2 1/18 p p   d    is the particle relaxation time, 10 μm p d  is the particle diameter, 1000 kg/m3 p   is the particle density, and   1.85105 Pa.s is the air viscosity. Also, u(x, y) and v(x, y) represent the components of the air velocity in the x and y directions inside the pleat channel, respectively. The x and y positions of the particles are denoted by xp and yp, respectively. You may use the following expressions for u(x, y) and v(x, y) .     2 3 1 2 u x, y u x y h                  sin 2 v x,y v h π y h        where   i 1 u x U x l h          is the average air velocity inside the pleat channel in the x‐direction and Ui is the velocity at the pleat entrance (assume 1 m/s for this project). l = 0.0275 m and h =0.0011 m are the pleat length and height, respectively. Writing the conservation of mass for the air flowing into the channel, you can also obtain that   i v h U h l h         . These 2nd order ODEs can easily be solved using a 4th order Rung‐Kutta method. In order to obtain realistic particle trajectories, you also need to consider proper initial conditions for the velocity of the particles: x(t  0)  0 , ( 0) i p p y t   y , p ( 0) cos i i dx t U dt    , p ( 0) sin i i dy t U dt     . where i  is the angle with respect to the axial direction by which a particle enters the pleat channel (see Figure 3). The inlet angle can be obtained from the following equation: 2 75 0.78 +0.16 1.61St i i p p i y y e h h                    where   2 St 18 2 ρPdPUi μ h  is the particles Stokes number. Figure 3: An illustration of the required particle trajectory calculation inside a rectangular pleated filter. You are asked to calculate and plot the trajectories of particles released from the vertical positions of ?? ? ? 0.05?, ?? ? ? 0.25?, ?? ? ? 0.5?, ?? ? ? 0.75? , and ?? ? ? 0.95? in one single figure. To do so, you need to track the trajectories until they reach one of the channel walls (i.e., stop when xp  l or p y  h ). Use a time step of 0.00001 sec. For more information see Ref. [3]. For additional background information see Ref. [4] and references there. In submitting your project please stick to following guidelines: 1‐ In blackboard, submit all the Matlab files and report in one single zip file. For naming your zip file, adhere to the format as: Lastname_firstname_project1.zip For instance: Einstein_albert_project1.zip 2‐ The report should be in pdf format only with the name as Project1.pdf (NO word documents .docx or .doc will be graded). 3‐ Your zip file can contain as many Matlab files as you want to submit. Also please submit the main code which TA’s should run with the name as: Project1.m (You can name the function files as you desire). Summary of what you should submit: 1‐ Runge–Kutta 4th order implementation in MATLAB. 2‐ Plot 5 particle trajectories in one graph. 3‐ Report your output (the x‐y positions of the five particles at each time step) in the form of a table with 11 columns (one for time and two for the x and y of each particle). Make sure the units are second for time and meter for the x and y. 4‐ Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit. Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not have unnecessary frames around them or are not plotted on a grey background (default setting of some software programs!). inlet angle Particle trajectory i p y i 0 p x  Important Note: It is possible to solve the above ODEs using built‐in solvers such as ode45 in MATLAB, and you are encouraged to consider that for validating your MATLAB program. However, the results that you submit for this project MUST be obtained from your own implementation of the 4th order Runge‐Kutta method. You will not receive full credit if your MATALB program does not work, even if your results are absolutely correct! References: 1. http://www.airexco.net/custom‐manufacturedbr12‐inch‐pleated‐filter‐c‐108_113_114/custommadebr12‐ inch‐pleated‐filter‐p‐786.html 2. http://www.ebay.com/itm/Air‐Compressor‐Air‐Filter‐Element‐CFE‐275‐Round‐Pleated‐Filter‐ /251081172328 3. A.M. Saleh and H.V. Tafreshi, A Simple Semi‐Analytical Model for Designing Pleated Air Filters under Loading, Separation and Purification Technology 137, 94 (2014) 4. A.M. Saleh, S. Fotovati, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Service Life of Pleated Filters Exposed to Poly‐Dispersed Aerosols, Powder Technology 266, 79 (2014)

Project 1: Particle Trajectory in Pleated Filters Due: 12:30 pm, Dec. 1, 2015, submission through blackboard Course: Numerical Methods Instructor: Dr. Hooman V. Tafreshi Most aerosol filters are made of pleated fibrous media. This is to accommodate as much filtration media as possible in a limited space available to an air filtration unit (e.g., the engine of a car). A variety of parameters contribute to the performance of a pleated filter. These parameters include, but are not limited to, geometry of the pleat (e.g., pleat height, width, and count), microscale properties of the fibrous media (e.g., fiber diameters, fiber orientation, and solid volume fraction), aerodynamic and thermal conditions of the flow (e.g., flow velocity, temperature, and operating pressure), and particle properties (e.g., diameter, density, and shape). Figure 1: Examples of pleated air filters [1‐2]. In this project you are asked to calculate the trajectory of aerosol particles as they travel inside a rectangular pleat channel. Due to the symmetry of the pleat geometry, you only need to simulate one half of the channel (see Figure 2). Figure 2: The simulation domain and boundary conditions (the figure’s aspect ratio is altered for illustration purposes). Trajectory of the aerosol particles can be calculated in a 2‐D domain by solving the Newton’s 2nd law written for the particles in the x‐ and y‐directions, v(h) inlet velocity fibrous media v(y) y tm l h x Ui u(l) u(x) 2 2 p 1 p 1 ( , ) d x dx u x y dt  dt    2 2 p 1 p 1 ( , ) d y dy v x y dt  dt    where 2 1/18 p p   d    is the particle relaxation time, 10 μm p d  is the particle diameter, 1000 kg/m3 p   is the particle density, and   1.85105 Pa.s is the air viscosity. Also, u(x, y) and v(x, y) represent the components of the air velocity in the x and y directions inside the pleat channel, respectively. The x and y positions of the particles are denoted by xp and yp, respectively. You may use the following expressions for u(x, y) and v(x, y) .     2 3 1 2 u x, y u x y h                  sin 2 v x,y v h π y h        where   i 1 u x U x l h          is the average air velocity inside the pleat channel in the x‐direction and Ui is the velocity at the pleat entrance (assume 1 m/s for this project). l = 0.0275 m and h =0.0011 m are the pleat length and height, respectively. Writing the conservation of mass for the air flowing into the channel, you can also obtain that   i v h U h l h         . These 2nd order ODEs can easily be solved using a 4th order Rung‐Kutta method. In order to obtain realistic particle trajectories, you also need to consider proper initial conditions for the velocity of the particles: x(t  0)  0 , ( 0) i p p y t   y , p ( 0) cos i i dx t U dt    , p ( 0) sin i i dy t U dt     . where i  is the angle with respect to the axial direction by which a particle enters the pleat channel (see Figure 3). The inlet angle can be obtained from the following equation: 2 75 0.78 +0.16 1.61St i i p p i y y e h h                    where   2 St 18 2 ρPdPUi μ h  is the particles Stokes number. Figure 3: An illustration of the required particle trajectory calculation inside a rectangular pleated filter. You are asked to calculate and plot the trajectories of particles released from the vertical positions of ?? ? ? 0.05?, ?? ? ? 0.25?, ?? ? ? 0.5?, ?? ? ? 0.75? , and ?? ? ? 0.95? in one single figure. To do so, you need to track the trajectories until they reach one of the channel walls (i.e., stop when xp  l or p y  h ). Use a time step of 0.00001 sec. For more information see Ref. [3]. For additional background information see Ref. [4] and references there. In submitting your project please stick to following guidelines: 1‐ In blackboard, submit all the Matlab files and report in one single zip file. For naming your zip file, adhere to the format as: Lastname_firstname_project1.zip For instance: Einstein_albert_project1.zip 2‐ The report should be in pdf format only with the name as Project1.pdf (NO word documents .docx or .doc will be graded). 3‐ Your zip file can contain as many Matlab files as you want to submit. Also please submit the main code which TA’s should run with the name as: Project1.m (You can name the function files as you desire). Summary of what you should submit: 1‐ Runge–Kutta 4th order implementation in MATLAB. 2‐ Plot 5 particle trajectories in one graph. 3‐ Report your output (the x‐y positions of the five particles at each time step) in the form of a table with 11 columns (one for time and two for the x and y of each particle). Make sure the units are second for time and meter for the x and y. 4‐ Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit. Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not have unnecessary frames around them or are not plotted on a grey background (default setting of some software programs!). inlet angle Particle trajectory i p y i 0 p x  Important Note: It is possible to solve the above ODEs using built‐in solvers such as ode45 in MATLAB, and you are encouraged to consider that for validating your MATLAB program. However, the results that you submit for this project MUST be obtained from your own implementation of the 4th order Runge‐Kutta method. You will not receive full credit if your MATALB program does not work, even if your results are absolutely correct! References: 1. http://www.airexco.net/custom‐manufacturedbr12‐inch‐pleated‐filter‐c‐108_113_114/custommadebr12‐ inch‐pleated‐filter‐p‐786.html 2. http://www.ebay.com/itm/Air‐Compressor‐Air‐Filter‐Element‐CFE‐275‐Round‐Pleated‐Filter‐ /251081172328 3. A.M. Saleh and H.V. Tafreshi, A Simple Semi‐Analytical Model for Designing Pleated Air Filters under Loading, Separation and Purification Technology 137, 94 (2014) 4. A.M. Saleh, S. Fotovati, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Service Life of Pleated Filters Exposed to Poly‐Dispersed Aerosols, Powder Technology 266, 79 (2014)

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