Asi Bunyajitradulya Department of Mechanical Engineering Faculty of Engineering Chulalongkorn University A Systematic Approach to Overview, Conduct, and

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)

What is this lecture about?

A systematic approach to

overview, conduct, and design of an experiment

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:

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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?

);;( cpxfy

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

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This much is expected of you at the end of the hour.

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.

Goal of an Experiment

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

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.

Background and motivation for the systematic approach based on

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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?

Is there really a (truly-constant) constant?

Is gravitational acceleration g a constant,

g = 9.81 m/s2 ?

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

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 collapsesFigure 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

E depends on the condition: E = f (Material, T, …)

relation or function

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

vs cold and dry day

vs cold and humid day?

“Per” depends on the condition

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 (x1, x2, …)

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:

q1, q2, … 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?

,...),( 21 qqfq

Typical Engineering Questions (not yet complete)

Whether and, if so, how does y vary with x ……?

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y = dependent variable

x = independent variables

ILL-defined problem

VS Well-defined problem

The roles of different variables in a problem:

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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

....);(

)....;(

Tfv

xfy

freely moving lid compressiony = v

x = T

Helium



Whether and how does specific volume v vary with temperature T

under the condition of constant pressure P = P1 for a gas Helium (R)?

The problem is now well-defined.

),;;(

);;(

RPTfv

cxfy

y = v

x = T

c = [R=Ro( Helium), P=P1]

P=P1

);;( cxfy

freely moving lid

P = P1



…

c = constant parameters

Well-defined Problem and The Roles of Different Variables in a Problem:

Well-defined Problem and The Roles of Different Variables in a Problem:

Whether and how does specific volume v vary with temperature T

under the condition of various constant pressures P = P1 , P2, P3, for a gas

Helium (R)?

);;(

);;(

RPTfv

cpxfy

y = v

x = T

c = R (=Ro, Helium)

);;( cpxfy

P=P1

freely moving lid

P = P1

freely moving lid

P = P2

P=P2

freely moving lid

P = P3

P=P3

p = P



p = variable parameters


Typical Engineering Questions

Whether and how does y vary with x under the condition

of various p and constant c?

);;( cpxfy





Convention for the functional form: );;( cpxfy





x

y c = co

p = p1

p = p2

p = p3

p

Graphical representation

c = co

p = p1 p = p2 p = p3

x y y y

. . . .

. . . .

. . . .

Tabular representation

);;( cpxfy

),...,;,...,;,...,( ccppxxfy

semicolons

More Examples

Problem 1:

Problem 2:

);;( RPTfv

);;( RTPfv

T

v R

P = P1

P = P2

P = P3 What process is this?

Isobaric

P

v R

T = T1

T = T2

T = T3 What process is this?

Isothermal

More Examples

Problem 3:

Problem 4:

);;( PRTfv

T

v P=Patm

R = R1 (air)

R = R2 (Helium)

R = R3 (Hydrogen) What process is this?

Isobaric

)substanceoftype;;,( waterTvfP

Figure from http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/pvtexp.html

Water

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

);;( cpxfy

Example 1: Identify );;( cpxfy

Figure from Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York.

);;( atmPPfluidsoftypeTf

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



Developing state of flow

)flowdevelopedfully

flowofstatedeveloping;flowtheofstate/,/;Re(

TLDeff

Laminar/Turbulent state of flow


Table from http://depts.washington.edu/matseed/mse_resources/Webpage/Bicycle/Bicycle%20Materials%20Case%20Study.htm

);;( cpxfy

),,;;( STPrefSTPref TTPPSteelCarbonMediumMaterialfE

),;;( STPrefSTPref TTPPMaterialfE

NOTE 2:

x, p, c slots can be empty

[but usually not all empty at the same time.]

);;(

);;(

cfy

cxfy

How does

affect the design of an experiment,

especially the test rig?

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

Problem 1:

Problem 2:

);;( kmxfa

x

|a| k=ko

m = m1

m = m2

m = m3

m x

Equilibriumk

Design of experiment and test rig:

change mass, fix spring

);;( mkxfa

Design of experiment and test rig:

change spring, fix mass

x

|a| m=mo

k = k1

k = k2

k = k3

);;( cpxfy

Defining an experiment:

Three-Column Objective

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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.

);;( cpxfy y = dependent variable




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.

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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 ….

);;( cpxfy y

x

c=co

p

p =p1

p=p2

p=p3

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

…. ….);;( cpxfy

);;( cpxfy

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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.

);;( cpxfy

);;( cpxfy

Convention: - Semicolonned slots);;( cpxfy





x

y c = co

p = p1

p = p2

p = p3

p

Graphical representation

c = co

p = p1 p = p2 p = p3

x y y y

. . . .

. . . .

. . . .

Tabular representation

);;( cpxfy

),...,;,...,;,...,( ccppxxfy

semicolons

Definition of an experiment/objective

Experimental condition

Scope of an experiment

Defining an Experiment/ObjectiveDefinition, 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

);;( cpxfy

);( cp

);with;with( 2121 occppppxxxx

Various types of questions/objectives in an experiment

Many variables in any

one slot

No variable parameter

Many questions

Fixed condition

Etc.

),...,;,...,;,...,( oo ccccppxxfy

);;( occxfy

);;(

);;(

);;(

cpxfy

cpxfy

cpxfy

);;( cfy

…….

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

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Practice Problem: Experiment 1


.

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 (= Patm)].

Experimental Condition: for various fluids (…, …, …)

and at a fixed pressure (at atmospheric)

Scope: over temperature range of -20 <= T <= 120 oC, T = … oC

fluids tested are hydrogen, air,…..

at a fixed pressure at atmospheric

);;( PfluidsofTypeTf



.

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 [p2 = 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 (p2 = L/T state of the flow)

under the condition of fully-developed flows

Scope: over Reynolds number range of 500 <= Re <= 8x108, Re = …

over relative roughness range of 0 (smooth pipe) <= e/D <= 0.05, (e/D) = …

laminar and turbulent flows

fully-developed flow only

)flowdevelopedfully


TLDeff


Properties of water

Figure From Fox, R. W., Pritchard, P. J., and McDonald, A. T., 2008, Fluid Mechanics, Seventh Edition, Wiley, New York.

Practice Problem: Experiment 4 (red) & 5 (blue)

Table from http://depts.washington.edu/matseed/mse_resources/Webpage/Bicycle/Bicycle%20Materials%20Case%20Study.htm

Data Reduction Diagram (DRD)

The mechanic for the design and conduct of an experiment


);;( cpxfy

x

y c = co

pcp

yx,

),(

How exactly do you get the numerical values

for the coordinates in your

experiment?

cpyx

,),(

cp

xy

DRD,DRD

,DRD,DRD

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).

);;( cpxfy

cDRDpDRDxDRDyDRD

Example: DRD’s of an experiment/objective

)flowdevelopedfully


);,;( 21

TLDeff

cppxfyObjective:

DRD - f

][)/(

2

1),,,,(

2essDimensionl

DLV

pDLVpf

Bottommost level boxes

DRD - Re

][),,(Re essDimensionlDV

DV

Bottommost level boxes

DRD.. DRD.. DRD..

DRD of the experiment/objective

refers to DRD’s of all variables in y, x, p, and c-slots in

the objective.

);;( cpxfy

);;( cpxfy

cDRDpDRDxDRDyDRD

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.

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 .

),...,( 21 xxfy

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.


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).

Examples of Derived Quantity Boxes

Examples of Measured Quantity Boxes

Down to instrument identity

Example of Referenced Quantity Boxes

Down to the page number.

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}

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

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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.

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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

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Summary

Summary

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 ….

….

cDRDpDRDxDRDyDRD

);;( cpxfy

);( cp

);with;with( 2121 occppppxxxx

y

x

c=co

p

p =p1

p=p2

p=p3

Summary

cDRDpDRDxDRDyDRD

);;( cpxfy

Upper Levels

All derived quantity boxes

Bottommost Level

All measured quantity boxes

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 ?

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);;( cpxfy

Documents

Asi Bunyajitradulya Department of Mechanical Engineering Faculty of Engineering Chulalongkorn University A Systematic Approach to Overview, Conduct, and