1. Asi Bunyajitradulya Department of Mechanical Engineering Faculty of Engineering Chulalongkorn University A Systematic Approach to Overview, Conduct, and Design of an Experiment: Part I: Defining an Experiment / Objective / Experimental Condition / Scope Part II: DRD (partial)

2. What is this lecture about? A systematic approach to overview, conduct, and design of an experiment

3. Contents  Goal of an experiment  Background and motivation to the systematic approach based on  ILL-defined problem VS Well-defined problem, and the roles of different variables in a problem: Typical engineering problems are related to the question of whether and, if so, how does y vary with x under the condition of various p and constant c ?

4. Contents  Practice: Identifying from familiar engineering relations, graphs, tables Recognizing the underlying condition/assumption [especially c in y = f ( x ; p ; c ) ] of these relations, graphs, tables  Defining an experiment: Three-Column Objective  Definition of an experiment/objective Experimental condition Scope of an experiment This much is expected of you at the end of the hour.

5. Contents  Practice:Setting up the objective of an experiment (defining an experiment), stating the experimental condition and the scope of an experiment  Data Reduction Diagram (DRD): The mechanic for the design and conduct of an experiment  Summary This much is expected of you at the end of the hour.This much is expected of you to know at the end of the hour. But to do, may be some time later.

6. Goal of an Experiment

7. Goal of An Experiment for physical sciences / physical systems  Extract knowledge and useful information  regarding certain aspects of the physical system of interest  with reasonable justification and high level of confidence (that it is reasonably true and accurate) justification = approach/method + supporting evidences

8. Uses of the results of an experiment That knowledge can be used for,  design and product development (data for the)  determine Young’s modulus of structural steel at standard condition  determine power-rpm relation for the newly designed engine  product testing and qualification according to some standard  test an air conditioner whether it qualifies for energy efficiency  qualification of an instrument  calibrate an instrument and quantify its performance parameters, e.g., accuracy, etc.  development of a mathematical model for a physical system (data for the)  empirical coefficients in many mathematical models  determine the scope and the level of accuracy of a theory (“verification/ falsification”)  “verify” beam deflection theory  etc.

9. Background and motivation for the systematic approach based on Typical engineering problems are related to the question of whether and, if so, how does y vary with x under the condition of various p and constant c ?

10. Is there really a (truly-constant) constant?  Is gravitational acceleration g a constant, g = 9.81 m/s 2 ? It may be a constant in this work of yours, but how about your next work? g depends on the condition: g = f ( h,…) In this case, elevation h, and ….? relation or function

11. Is there really a (truly-constant) constant?  Is Young’s modulus of structural steel a constant, E = 200 GPa? It may be a constant in this work of yours, but how about your next work? NIST Report on the properties of structural steel from World Trade Center collapses Figure from Luecke, et al., 2005, Federal Building and Fire Safety Investigation of The World Trade Center Disaster: Mechanical Properties of Structural Steels, NIST NCSTAR1-3D, http://fire.nist.gov/bfrlpubs/fire05/PDF/f05158.pdf http://fire.nist.gov/bfrlpubs/fire05/PDF/f05158.pdf E depends on the condition: E = f (Material, T, …) relation or function

12. Similar problem with “constant” Is the “performance” of a car (the same car) the same as I drive in  Bangkok vs Chiang Mai ?  Bangkok vs New York ? To put it more physically, i.e., in terms of physical quantities: hot and dry day vs hot and humid day vscold and dry day vscold and humid day? “Per” depends on the condition

13. Similar problem with “constant” To put this in even more workable engineering terms:  Whether and, if so, how does intake air temperature ( T ) affect the “performance = power P ” of an engine of a car …? P = f (T,…)  Whether and, if so, how does intake air humidity ratio (  ) affect the “performance = power” of an engine of a car …? P = f ( ,T,…) “Per” depends on the condition Relation / Function of many variables: y = f (x 1, x 2, …)

14. Problem with “constant”  Problem with “constant”  It is rare that you will encounter a true/universal constant in engineering work.  The physical quantity of interest q depends on other physical quantities: q 1, q 2, … through a physical relation:  Physical Quantities (PQ) and Physical Relations (PR)  Because of PR, this specific number is valid only under certain condition.  It may be constant in this work of yours, but how about next work of yours?

15. Typical Engineering Questions (not yet complete)  Whether and, if so, how does y vary with x ……? y = dependent variable x = independent variables

16. ILL-defined problem VS Well-defined problem The roles of different variables in a problem:

17. ILL-Defined Problem The problem of the definition of the problem  Whether and how does the (specific) volume v of a gas (Helium) vary with its temperature T ?  The problem is not well-defined.  Depending on the condition, e.g.,  constant pressure, T v  if compressed fast enough, T v freely moving lid compression y = v x = T Helium y = dependent variable x = independent variables

18.  Whether and how does specific volume v vary with temperature T under the condition of constant pressure P = P 1 for a gas Helium (R) ?  The problem is now well-defined. y = v x = T c = [ R=R o ( Helium), P=P 1 ] P=P1P=P1 freely moving lid P = P 1 y = dependent variable x = independent variables … c = constant parameters Well-defined Problem and The Roles of Different Variables in a Problem:

19.  Whether and how does specific volume v vary with temperature T under the condition of various constant pressures P = P 1, P 2, P 3, for a gas Helium (R) ? y = v x = T c = R (=R o, Helium) P=P1P=P1 freely moving lid P = P 1 freely moving lid P = P 2 freely moving lid P = P 3 p = P y = dependent variable x = independent variables p = variable parameters c = constant parameters

20. Typical Engineering Questions  Whether and how does y vary with x under the condition of various p and constant c ? y = dependent variable x = independent variables p = variable parameters c = constant parameters

21. Convention for the functional form: y = dependent variable x = independent variables p = variable parameters c = constant parameters x y c = c o p = p 1 p = p 2 p = p 3 p Graphical representation c = c o p = p 1 p = p 2 p = p 3 xyyy............ Tabular representation semicolons

22. More Examples  Problem 1:  Problem 2: T v R P = P 1 P = P 2 P = P 3 What process is this? Isobaric P v R T = T 1 T = T 2 T = T 3 What process is this? Isothermal

23. More Examples  Problem 3:  Problem 4: T v P=P atm R = R 1 (air) R = R 2 (Helium) R = R 3 (Hydrogen) What process is this? Isobaric Figure from http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/pvtexp.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/thermo/pvtexp.html Water

24. Practice  Identifying from familiar engineering relations, graphs, tables  Recognizing the underlying condition/assumption [especially c in y = f ( x ; p ; c ) ] of these relations, graphs, tables

25. Example 1: Identify Figure from Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York. NOTE 1: y, x, p, c can be type, state, condition, e.g., Type of fluids Type of beam supports simply support, cantilever, etc. State of flows laminar, turbulent

26. Example 2: Identify Figure from Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York. Developing state of flow Laminar/Turbulent state of flow

27. Example 3: Identify Table from http://depts.washington.edu/matseed/mse_resources/Webpage/Bicycle/Bicycle%20Materials%20Case%20Study.htm NOTE 2: x, p, c slots can be empty [but usually not all empty at the same time.]

28. How does affect the design of an experiment, especially the test rig?

29. How does affect the design of an experiment, especially the test rig?  Problem 1:  Problem 2: x |a| k=k o m = m 1 m = m 2 m = m 3 m x Equilibrium k Design of experiment and test rig:  change mass, fix spring Design of experiment and test rig:  change spring, fix mass x |a| m=m o k = k 1 k = k 2 k = k 3

30. Defining an experiment: Three-Column Objective

31. Question and Definition of An Experiment Question: Whether and how does y vary with x under the condition of various p and constant c ? Definition of an Experiment: y, x, p, and c play different roles in our problem. y = dependent variable x = independent variables p = variable parameters c = constant parameters

32. Whether and how does y vary with x under the condition of various p and constant c ? NOTE: The question of Whether (and correlation study) If we do not know that x affects y (or x and y are related) or not, especially in complex systems where there are many and random factors involved, for example:  Whether there is a relation between GPAX of first-year students ( x ) and GPAX of the students when they graduate ( y )?  Whether the pill x for curing disease z has the side effect y on patients of disease z ? This kind of study is usually referred to as ‘correlation study.’  In correlation study, typically we need to find the correlation coefficient between y and x in order to answer the question whether y and x are related.

33. Defining an experiment with the three-column objective Objective Statement (Question) Objective Functional Form Objective Graphical Representation The effect of x on y under the condition of various p and constant c …. y x c=c o p p =p 1 p=p 2 p=p 3

34. Defining an experiment with the three-column objective  Formulate clearly a well-defined problem. [List all relevant variables and/or conditions: y, x, p, and c. Use functional form: ]  We know what to plot right from the beginning once we formulate our problem. NOT collect data first, then think what to plot later.  We know and can outline how to extract results (or answer to your question posted in the objective) right from the beginning. [From the graphical presentation of.] Formulate hypotheses:  What does it mean when y increase/decrease with x ?  What does it mean if it has or has no local minimum/maximum? Objective Statement (Question) Objective Functional Form Objective Graphical Representation ….

35. Well-defined = Well-defined system  Well-defined = Well-defined system and well-defined problem/question regarding the system  All relevant variables: y, x, p, and c, must be accounted for.

36. Convention: - Semicolonned slots y = dependent variable x = independent variables p = variable parameters c = constant parameters x y c = c o p = p 1 p = p 2 p = p 3 p Graphical representation c = c o p = p 1 p = p 2 p = p 3 xyyy............ Tabular representation semicolons

37.  Definition of an experiment/objective  Experimental condition  Scope of an experiment

38. Defining an Experiment/Objective Definition, Experimental Condition, Scope, and Resolution Definition of an experiment/objective: Experimental Condition: Scope of an experiment: Range and resolution of each x and p, the value of each c

39. Various types of questions/objectives in an experiment  Many variables in any one slot  No variable parameter  Many questions  Fixed condition  Etc. …….

40. Practice Setting up the objective of an experiment (defining an experiment), stating the experimental condition and the scope of an experiment 1. Identify 2. State the objective 3. State the experimental condition 4. Specify the scope of the following experiments

41. Practice Problem: Experiment 1 Figure from Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York.

42. ..  Objective: To investigate the effect of temperature [ x = T] on absolute viscosity [ y =  ] of various fluids [ p = type of fluids] under the condition of a fixed pressure at atmospheric [ c = P (= P atm )].  Experimental Condition: for various fluids (…, …, …) and at a fixed pressure (at atmospheric)  Scope:over temperature range of -20 <= T <= 120 o C,  T = … o C fluids tested are hydrogen, air,….. at a fixed pressure at atmospheric

43. Practice Problem: Experiment 2 Figure from Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York.

44. ..  Objective: To investigate the effect of Reynolds number [ x = Re] on the friction factor [ y = f ] in pipe flows for various relative roughness [ p  = e/D] and two states of the flow [ p 2 = L/T state of the flow]: laminar and turbulent, under the condition of fully-developed flows [ c = developing state of flow].  Experimental Condition: various relative roughness ( p  = e/D ) for both laminar and turbulent flows ( p 2 = L/T state of the flow) under the condition of fully-developed flows  Scope:over Reynolds number range of 500 <= Re <= 8x10 8,  Re = … over relative roughness range of 0 (smooth pipe) <= e/D <= 0.05,  ( e/D ) = … laminar and turbulent flows fully-developed flow only

45. Practice Problem: Experiment 3 Properties of water Figure From Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York.

46. Practice Problem: Experiment 4 (red) & 5 (blue) Table from http://depts.washington.edu/matseed/mse_resources/Webpage/Bicycle/Bicycle%20Materials%20Case%20Study.htm

47. Data Reduction Diagram (DRD) The mechanic for the design and conduct of an experiment

48. Data Reduction Diagram (DRD) x y c = c o p How exactly do you get the numerical values for the coordinates in your experiment?

49. DRD of the experiment  Construct DRD for each and every quantity in your objective functional form.  The underlying idea of DRD is  We must be able to trace each and every numerical transformation in our experiment, exactly as we do in our experiment,  from the sources (the bottomost level boxes) to the final quantity at the top (the top box).

50. Example: DRD’s of an experiment/objective Objective: DRD - f Bottommost level boxes DRD - Re Bottommost level boxes DRD..

51.  DRD of the experiment/objective refers to DRD’s of all variables in y, x, p, and c- slots in the objective.

52. Measured Quantities VS Derived Quantities  In physical science, there are two and only two types of quantities  Measured Quantities  Derived Quantities The reason is that we don’t want anybody to just make up any number for a physical quantity at their will.

53. Measured Quantity VS Derived Quantity Measured Quantity:A quantity whose numerical value in the current experiment is obtained/read from an instrument in the unit of that instrument directly (no unit conversion). Derived Quantity:A quantity whose numerical value in the current experiment is derived from  a (valid) physical relation: [be it in the form of an equation, graph, table, etc., or unit conversion relation], and  the values of other quantities in the relation.

54. Referenced Quantities  In our experiment, we may not be able to measure q.  We then refer its numerical value from a reliable source/reference.  Recognize that, even then, someone somewhere must either measure it or derive it.

55. Data Reduction Diagram (DRD) Bottommost Level All measured (or referenced) quantity boxes Upper Level All derived quantity boxes The idea of DRD is We must be able to trace each and every numerical transformation in our experiment, exactly as we do in our experiment, from the sources (the bottomost level boxes) to the final quantity at the top (the top box).

56. Examples of Derived Quantity Boxes

57. Examples of Measured Quantity Boxes Down to instrument identity

58. Example of Referenced Quantity Boxes Down to the page number.

59.  The key idea is “how do you know (in your experiment)?” DRD – L/T State of Flow L/T State of Flow {Visual observation at the jet exit}

60. Use(fulness) of DRD:  In the Design Stage  Roadmap:Roadmap for our experiment  All Measured Quantities:Know all measured quantities from all bottomost boxes of all DRD’s of the experiment  All Derived Quantities:Know all derived quantities from all derived boxes of all DRD’s of the experiment All Underlying Assumptions: Know all underlying assumptions of our experiment  Instruments:Know all necessary instruments to be used in our experiment  Choose/Select instruments  DCW:Construct Data Collection Worksheet (DCW) – All bottomost boxes  DAW: Construct Data Analysis Worksheet (DAW) – All derived boxes

61. Use(fulness) of DRD:  In the Design Stage  Design-Stage Uncertainty Analysis:Roadmap for design-stage uncertainty analysis  Selecting/Choosing Instruments :Selecting/Choosing all instruments such that our final results have uncertainties within the desired/specified levels.

62. Use(fulness) of DRD:  In the Qualification Stage  Diagnostic Roadmap  In the Conduct / Final Stage  Analysis Roadmap:Roadmap for analyzing data  Diagnostic Roadmap:If something does not look right, we can trace things 1) right from the beginning/sources (of numerical values), 2) through all the analyses and assumptions, and 3) to the ends.  Final Uncertainty Analysis

63. Summary

64. Experimental Condition: Scope of an experiment: Range and resolution of each x and p, the value of each c Objective Statement (Question) Objective Functional Form (Definition of an experiment) Objective Graphical Representation The effect of x on y under the condition of various p and constant c …. …. y x c=c o p p =p 1 p=p 2 p=p 3

65. Summary Upper Levels All derived quantity boxes Bottommost Level All measured quantity boxes

66. Summary  All things in an experiment go back to  Goal of an experiment (knowledge with high level of confidence), and  Objective of an experiment:  For example:  Experimental condition and scope:  What is the scope of validity of your answer to ?  DRD’s:  How exactly do you get numerical values for each y, x, p, and c in ?  Approach: experimental setup (test rig + instrument):  How do you get the answer to ?  Uncertainties  How accurate is your answer to ?