AUCS 340: Ethics in the Professions Individual Written Assignment #1 Medical Ethics: Historical names, dates and ethical theories assignment As you read chapters 1 and 2 in the “Ethics and Basic Law for Medical Imaging Professionals” textbook you will be responsible for identifying and explaining each of the following items from the list below. You will respond in paragraph format with correct spelling and grammar expected for each paragraph. Feel free to have more than one paragraph for each item, although in most instances a single paragraph response is sufficient. If you reference material in addition to what is available in the textbook it must be appropriately cited in your work using either APA or MLA including a references cited page. The use of Wikipedia.com is not a recognized peer reviewed source so please do not use that as a reference. When responding about individuals it is necessary to indicate a year or time period that the person discussed/developed their particular ethical theory so that you can look at and appreciate the historical background to the development of ethical theories and decision making. Respond to the following sixteen items. (They are in random order from your reading) 1. Francis Bacon 2. Isaac Newton 3. Prima Facie Duties – Why do they exist? LIST AND DEFINE ALL TERMS 4. Hippocrates 5. W.D. Ross – what do the initials stand for in his name and what was his contribution to the study of ethics? 6. Microallocation – define the term and provide an example separate from the book example (You should develop your own example rather than looking for an online example; this will use your critical thinking skills. Consider an application to your own profession as microallocation is NOT limited to the medical field.) 7. Deontology – Discuss at length the basic types/concepts of this theory 8. Thomas Aquinas – 1) Discuss the ethical theory developed by Aquinas, 2) his religious affiliation, 3) why that was so important to his ethical premise and 4) discuss the type of ethical issues resolved to this day using this theory. 9. Macroallocation – define and provide an example separate from the book example (You should develop your own example rather than looking for an online example; this will use your critical thinking skills. Consider an application to your own profession as macroallocation is NOT limited to the medical field.) 10. David Hume 11. Rodericus Castro 12. Plato and “The Republic” 13. Pythagoras 14. Teleology – Discuss at length the basic types/concepts of this theory 15. Core Values – Why do they exist? LIST AND DEFINE ALL TERMS 16. Develop a timeline that reflects the ethical theories as developed by the INDIVIDUALS presented in this assignment. This assignment is due Saturday March 14th at NOON and is graded as a homework assignment. Grading: Paragraph Formation = 20% of grade (bulleted lists are acceptable for some answers) Answers inclusive of major material for answer = 40% of grade Creation of Timeline = 10% of grade Sentence structure, application of correct spelling and grammar = 20% of grade References (if utilized) = 10% of grade; references should be submitted on a separate references cited page. Otherwise this 10% of the assignment grade will be considered under the sentence structure component for 30% of the grade. It is expected that the finished assignment will be two – three pages of text, double spaced, using 12 font and standard page margins.

AUCS 340: Ethics in the Professions Individual Written Assignment #1 Medical Ethics: Historical names, dates and ethical theories assignment As you read chapters 1 and 2 in the “Ethics and Basic Law for Medical Imaging Professionals” textbook you will be responsible for identifying and explaining each of the following items from the list below. You will respond in paragraph format with correct spelling and grammar expected for each paragraph. Feel free to have more than one paragraph for each item, although in most instances a single paragraph response is sufficient. If you reference material in addition to what is available in the textbook it must be appropriately cited in your work using either APA or MLA including a references cited page. The use of Wikipedia.com is not a recognized peer reviewed source so please do not use that as a reference. When responding about individuals it is necessary to indicate a year or time period that the person discussed/developed their particular ethical theory so that you can look at and appreciate the historical background to the development of ethical theories and decision making. Respond to the following sixteen items. (They are in random order from your reading) 1. Francis Bacon 2. Isaac Newton 3. Prima Facie Duties – Why do they exist? LIST AND DEFINE ALL TERMS 4. Hippocrates 5. W.D. Ross – what do the initials stand for in his name and what was his contribution to the study of ethics? 6. Microallocation – define the term and provide an example separate from the book example (You should develop your own example rather than looking for an online example; this will use your critical thinking skills. Consider an application to your own profession as microallocation is NOT limited to the medical field.) 7. Deontology – Discuss at length the basic types/concepts of this theory 8. Thomas Aquinas – 1) Discuss the ethical theory developed by Aquinas, 2) his religious affiliation, 3) why that was so important to his ethical premise and 4) discuss the type of ethical issues resolved to this day using this theory. 9. Macroallocation – define and provide an example separate from the book example (You should develop your own example rather than looking for an online example; this will use your critical thinking skills. Consider an application to your own profession as macroallocation is NOT limited to the medical field.) 10. David Hume 11. Rodericus Castro 12. Plato and “The Republic” 13. Pythagoras 14. Teleology – Discuss at length the basic types/concepts of this theory 15. Core Values – Why do they exist? LIST AND DEFINE ALL TERMS 16. Develop a timeline that reflects the ethical theories as developed by the INDIVIDUALS presented in this assignment. This assignment is due Saturday March 14th at NOON and is graded as a homework assignment. Grading: Paragraph Formation = 20% of grade (bulleted lists are acceptable for some answers) Answers inclusive of major material for answer = 40% of grade Creation of Timeline = 10% of grade Sentence structure, application of correct spelling and grammar = 20% of grade References (if utilized) = 10% of grade; references should be submitted on a separate references cited page. Otherwise this 10% of the assignment grade will be considered under the sentence structure component for 30% of the grade. It is expected that the finished assignment will be two – three pages of text, double spaced, using 12 font and standard page margins.

Francis Bacon was a 16th century ethical theorist who was … Read More...
Problem 3 (25 Points) A bracket is subjected to a 610 N force as shown in the figure. (a) Express the force in Cartesian vector form. (8 points) (b) Determine the moment of the force about point C. (10 points) (c) Determine the moment of the force about line CD. (7 points)

Problem 3 (25 Points) A bracket is subjected to a 610 N force as shown in the figure. (a) Express the force in Cartesian vector form. (8 points) (b) Determine the moment of the force about point C. (10 points) (c) Determine the moment of the force about line CD. (7 points)

  Problem 3 (25 Points) A bracket is subjected to … Read More...
Problem 1: (30 points) A 20 lb bucket is supported by three cables DA, DB, and DC as shown in the figure. 1) Draw a complete free body diagram at point D. (10 pt) 2) Express all forces in Cartesian form. (5 pt) 3) Determine the tensions in cable DC and springs DA and DB. (15pt)

Problem 1: (30 points) A 20 lb bucket is supported by three cables DA, DB, and DC as shown in the figure. 1) Draw a complete free body diagram at point D. (10 pt) 2) Express all forces in Cartesian form. (5 pt) 3) Determine the tensions in cable DC and springs DA and DB. (15pt)

 
Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1  4 −2 1 3  is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0   2346  (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : →  which rotates a point about the origin through an angle of   radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices  and  are row equivalent, they have the same reduced echelon form. In general,  +  ≠  +  (assume  and  are  x  matrices). If a matrix  is symmetric, then so is  + “#. A matrix  must be a square matrix to be invertible. If $%&’( ≠ 0, then columns of  are linearly independent. If an  x  matrix  is equivalent to “#, then )* is also equivalent to “#. If an + x  matrix  has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If  = “, then  is invertible.

Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1  4 −2 1 3  is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0   2346  (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : →  which rotates a point about the origin through an angle of   radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices  and  are row equivalent, they have the same reduced echelon form. In general,  +  ≠  +  (assume  and  are  x  matrices). If a matrix  is symmetric, then so is  + “#. A matrix  must be a square matrix to be invertible. If $%&’( ≠ 0, then columns of  are linearly independent. If an  x  matrix  is equivalent to “#, then )* is also equivalent to “#. If an + x  matrix  has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If  = “, then  is invertible.

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PAPER 1- Pick from ONE of the questions below and answer in essay form. 1. Write out and answer the question. Check all spelling and grammar in MLA format. 2. Cite all sources, direct quotes or indirect ideas using elliptic giving author AND page numbers, i.e. (Soccio 26). Failure here could result in a 0%! 3. Include a Works Cited page at the end. 4. Make sure you submit the work in Turn It In in a single Word document in doc. or docx. or richtext format. 7. Your essay is to be between 1000-1600 words. Extensive quotes (more than 20%) do not count toward this. If you cannot answer a question in these parameters, use another question. Minimum word count DOES NOT insure an excellent grade. Questions and Works Cited do not count towards the word count. You may not use Wikipedia as a source, nor recycle a previous paper from another class. 4 pages answering one question out of many questions

PAPER 1- Pick from ONE of the questions below and answer in essay form. 1. Write out and answer the question. Check all spelling and grammar in MLA format. 2. Cite all sources, direct quotes or indirect ideas using elliptic giving author AND page numbers, i.e. (Soccio 26). Failure here could result in a 0%! 3. Include a Works Cited page at the end. 4. Make sure you submit the work in Turn It In in a single Word document in doc. or docx. or richtext format. 7. Your essay is to be between 1000-1600 words. Extensive quotes (more than 20%) do not count toward this. If you cannot answer a question in these parameters, use another question. Minimum word count DOES NOT insure an excellent grade. Questions and Works Cited do not count towards the word count. You may not use Wikipedia as a source, nor recycle a previous paper from another class. 4 pages answering one question out of many questions

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a) Find the inverse of the matrix A, where A is A= | 1 0 3, 2 0 1, 0 2 4, 4 0 0| b) given the following system of equations x+z=15, y+z=12, x+y=7, b1) Write the above system of equation in the form AX=B identifying each of the matrices A, X and respectively B. b2) Find A-1, the inverse of matrix A. b3) solve the system of equations by matrix inversion method

a) Find the inverse of the matrix A, where A is A= | 1 0 3, 2 0 1, 0 2 4, 4 0 0| b) given the following system of equations x+z=15, y+z=12, x+y=7, b1) Write the above system of equation in the form AX=B identifying each of the matrices A, X and respectively B. b2) Find A-1, the inverse of matrix A. b3) solve the system of equations by matrix inversion method

 
three cables connected a point A are used to tether a balloon , and the system is in static equilibrium. The balloon exert the upward force P at point A, and the tension in cable AB is 240N. a) Draw a free-body diagram (FBD) around point A. , b) Express the force P the tension in each of the three cables in cartesian vector form . , c) Determine the magnitude of the tension in cable Ac.

three cables connected a point A are used to tether a balloon , and the system is in static equilibrium. The balloon exert the upward force P at point A, and the tension in cable AB is 240N. a) Draw a free-body diagram (FBD) around point A. , b) Express the force P the tension in each of the three cables in cartesian vector form . , c) Determine the magnitude of the tension in cable Ac.

 
Who are the actors in the dialogue and who is more powerful? A. The Lacedaemons and the Melians. The Melians are more powerful. B. The Athenians and the Melians. The Athenians are more powerful. C. The Lacedaemons, the Melians, and the Athenians. The Melians are most powerful. D. The Athenians and the Melians. The Melians are more powerful. E. The Lacedaemons and the Melians. They are equally powerful. The Athenian envoy was dispatched to address the Melians. Who did they end up talking to? A. The people of Lacedaemon. B. A group of Melian magistrates. C. The Melian magistrates and the population. D. Just the general Melian population. The magistrates did not show out of protest. E. The Lacedaemon population and the Melian population. What is the main point in question upon which both parties seem to agree? A. Whether to go to war against Athenian enemies. B. Whether to form an equal alliance with the Athenians. C. Whether there will be war between the Melians and the Athenians or whether the Melians will submit to Athenian power. D. How many ships and soldiers the Melians will give to the Athenian campaign. E. How many ships and soldiers the Athenians will give to the Melian movement for independence. What do the Athenians suggest about right and justice in terms of power? A. Questions about what is “right” only happen among equals in power. B. Justice and right come about when the powerful are wise. C. Power has no relation to right and justice. D. Questions about what is “right” only happen among equals in power AND justice and right come about when the powerful are wise. E. Justice and right come about when the powerful are wise AND power has no relation to right and justice. What is the necessary “law of their nature” that the Athenians are referring to? A. That states, both weak and strong, will seek peace. B. The law of chance and luck operates universally among men. C. The belief that, given the opportunity, men will seek to rule whenever they can. D. Whenever a treaty is created, states will settle those treaties with due consideration to the weaker side. E. That the nature of men is towards justice rather than power.

Who are the actors in the dialogue and who is more powerful? A. The Lacedaemons and the Melians. The Melians are more powerful. B. The Athenians and the Melians. The Athenians are more powerful. C. The Lacedaemons, the Melians, and the Athenians. The Melians are most powerful. D. The Athenians and the Melians. The Melians are more powerful. E. The Lacedaemons and the Melians. They are equally powerful. The Athenian envoy was dispatched to address the Melians. Who did they end up talking to? A. The people of Lacedaemon. B. A group of Melian magistrates. C. The Melian magistrates and the population. D. Just the general Melian population. The magistrates did not show out of protest. E. The Lacedaemon population and the Melian population. What is the main point in question upon which both parties seem to agree? A. Whether to go to war against Athenian enemies. B. Whether to form an equal alliance with the Athenians. C. Whether there will be war between the Melians and the Athenians or whether the Melians will submit to Athenian power. D. How many ships and soldiers the Melians will give to the Athenian campaign. E. How many ships and soldiers the Athenians will give to the Melian movement for independence. What do the Athenians suggest about right and justice in terms of power? A. Questions about what is “right” only happen among equals in power. B. Justice and right come about when the powerful are wise. C. Power has no relation to right and justice. D. Questions about what is “right” only happen among equals in power AND justice and right come about when the powerful are wise. E. Justice and right come about when the powerful are wise AND power has no relation to right and justice. What is the necessary “law of their nature” that the Athenians are referring to? A. That states, both weak and strong, will seek peace. B. The law of chance and luck operates universally among men. C. The belief that, given the opportunity, men will seek to rule whenever they can. D. Whenever a treaty is created, states will settle those treaties with due consideration to the weaker side. E. That the nature of men is towards justice rather than power.

Who are the actors in the dialogue and who is … Read More...
Name: _____________________ Wire Resistance and Ohm’s Law PhET MiniLab Introduction: When an electrical potential exists in a circuit, a current may flow. Current is the flow of electrons in a circuit. Resistance in the circuit slows the flow of the electrons, reducing the current in the circuit. We will use the mathematical form of Ohm’s Law frequently when we investigate electric current and circuits later in this unit. Additional Material Needed: Clean Drinking Straw Procedure Part I Wire Resistance: • Blow through the drinking straw. • Cut the drinking straw in half and blow through a half-straw. • Describe the effect of length on ease to blow air through the straw. _________________________________________ • Cut the halves again in half. • With the four pieces, blow through one, then blow through all four made into a larger, square-shaped straw. • Describe the effect of straw size (diameter) on ease to blow air through the straw. ______________________________ • Now, open the PhET Simulation Electricity, Magnets, and Circuits  Resistance in a Wire As wire length (cm) increases, the resistance (Ω) _________________ As wire area (cm2) increases, the resistance (Ω) __________________ As wire density (Ωcm) increases, the resistance (Ω) _______________ Procedure Part II: Ohm’s Law: Electricity, Magnets, and Circuits  Ohm’s Law mA is milliamps, and _________ milliamps equals one Ampere. • Move the potential (volts) and resistance (ohms) sliders and observe the current (amps) As voltage increases, current __________________. As resistance increases, current ________________. Fill out the tables below and check your work in the simulation. ( ½ pt each ) • Remember, the simulation shows milliamps. • You should show Amperes V = I * R 8.0 V A 800 Ω 2.0 V .044 A Ω V .0058 A 430 Ω V .069 A 100 Ω 6.4 V A 300 Ω Conclusion Questions: ( ½ pt each) 1. Incandescent light bulbs have a very thin filament that glows when hot. Thin filaments have very high / low resistance. 2. The 12V battery in your car operates a 25 amp car stereo. What is the resistance of this stereo system? ___________ 3. A “2D” Maglite flashlight runs on 3.0V. What is the current through the bulb if resistance is 15 Ω ? ____________ 4. How many volts must an iPod charger provide to charge an iPOD using .85 Amps at 35 Ω? _____________ 5. You need to buy a long extension cord to power a stereo at your spring break BBQ. You need 200feet. You have a 50 ft cord that will work. You rationalize that four such 50 ft cords will do the job. Is this a good idea? Why or Why not? ___________________________________________________________________________________________

Name: _____________________ Wire Resistance and Ohm’s Law PhET MiniLab Introduction: When an electrical potential exists in a circuit, a current may flow. Current is the flow of electrons in a circuit. Resistance in the circuit slows the flow of the electrons, reducing the current in the circuit. We will use the mathematical form of Ohm’s Law frequently when we investigate electric current and circuits later in this unit. Additional Material Needed: Clean Drinking Straw Procedure Part I Wire Resistance: • Blow through the drinking straw. • Cut the drinking straw in half and blow through a half-straw. • Describe the effect of length on ease to blow air through the straw. _________________________________________ • Cut the halves again in half. • With the four pieces, blow through one, then blow through all four made into a larger, square-shaped straw. • Describe the effect of straw size (diameter) on ease to blow air through the straw. ______________________________ • Now, open the PhET Simulation Electricity, Magnets, and Circuits  Resistance in a Wire As wire length (cm) increases, the resistance (Ω) _________________ As wire area (cm2) increases, the resistance (Ω) __________________ As wire density (Ωcm) increases, the resistance (Ω) _______________ Procedure Part II: Ohm’s Law: Electricity, Magnets, and Circuits  Ohm’s Law mA is milliamps, and _________ milliamps equals one Ampere. • Move the potential (volts) and resistance (ohms) sliders and observe the current (amps) As voltage increases, current __________________. As resistance increases, current ________________. Fill out the tables below and check your work in the simulation. ( ½ pt each ) • Remember, the simulation shows milliamps. • You should show Amperes V = I * R 8.0 V A 800 Ω 2.0 V .044 A Ω V .0058 A 430 Ω V .069 A 100 Ω 6.4 V A 300 Ω Conclusion Questions: ( ½ pt each) 1. Incandescent light bulbs have a very thin filament that glows when hot. Thin filaments have very high / low resistance. 2. The 12V battery in your car operates a 25 amp car stereo. What is the resistance of this stereo system? ___________ 3. A “2D” Maglite flashlight runs on 3.0V. What is the current through the bulb if resistance is 15 Ω ? ____________ 4. How many volts must an iPod charger provide to charge an iPOD using .85 Amps at 35 Ω? _____________ 5. You need to buy a long extension cord to power a stereo at your spring break BBQ. You need 200feet. You have a 50 ft cord that will work. You rationalize that four such 50 ft cords will do the job. Is this a good idea? Why or Why not? ___________________________________________________________________________________________

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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