SME 1912 Week6 Part1

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FACULTY OF MECHANICALENGINEERING

UNIVERSITI TEKNOLOGI MALAYSIA

SME 1912 EXPERIMENTAL METHODS

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INTERPRETATION OFEXPERIMENTAL DATA

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INTRO

When a scientist or an engineer discovers something new,he or she may wish to share it with other people.Other people also want to know as much as possible about

the new discoveryThe new discovery may involve such thing as thequantity, property, behavior of a new material.But, the new discovery may not be well explained if it isnot presented in a standard measuring system that isunderstood by all.

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DIMENSIONS AND UNITS

Dimensions : Physical parameters are distinguished by theirdimensions . For instance, parameters representing distanceare expressed in dimensions of length, symbolically

denoted by L. Mass is expressed by M , time by T, andtemperature by .For example, if D is a length term suchas the diameter of a pipe or cylinder, [ D] indicates thedimensions of D. Symbolically then, [ D] = L, reads: Dhas dimension of length.

Units : The magnitudes assigned to the dimensions arecalled units

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DIMENSIONS AND UNITS- primary and secondary

Primary or Fundamental Dimensions : Some basicdimensions such as mass M , length L, time T , andtemperature are selected as Primary or

Fundamental Dimensions .

Secondary or Derived Dimensions : Othersdimension such as area A ( L2), velocity V ( L/T ),and Force F ( ML/T 2) are expressed in term of the

primary dimensions and are called Secondary or Derived Dimensions .

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DIMENSIONS AND UNITS

MLT : Mass, Length, Time - widely used

FLT : Force, Length, Time

FMLT : Force, Mass, Length, Time

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BASIC SI QUANTITY AND UNIT

Basic SI UnitsThere are seven fundamental quantity and unitsQuantity Unit SymbolLength meter mMass kilogram kgTime second s

Electric Curent ampere ATemperature kelvin KLuminous Intensity candela cdAmount of Matter mole mole

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BASIC SI QUANTITY AND UNIT- engineering units

Engineering Units

Unit Symbol

Radian radHertz Hz

Newton NPascal PaCoulomb CHenry HHectare ha

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BASIC SI QUANTITY AND UNIT- engineering units

Tonne tLiter lVolt VAmpere AFarad FJoule J

Watt WWeber WbDegree Minute

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BASIC SI QUANTITY AND UNIT- MLT system

Symbol Quantity Basic Dimension SI Units

A area L2 m2

a acceleration L/T 2 m/s 2

A speed of sound L/T m/s F force ML/T 2 N g gravitational L/T 2 m/s 2

acceleration

H head L m L length L m M mass M kgm mass flow rate M/T kg/s

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N rotational speed 1/T 1/s P power ML2 /T 3 W p pressure M/(LT 2 ) PaQ discharge L3 /T m3/st time T sV volume L3 m3

v velocity L/T m/s

W work ML2 /T 2 N.m compressibility coefficient LT 2 /M m2/N viscosity M/(LT) N.s/m2

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kinematic viscosity L2/T m 2/s angular velocity 1/T 1/s density M/L3 kg/m 3

shear stress M/LT 2 Pa

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NUMERICAL, MULTIPLE ANDSMALL DIVISION UNITS

Small integer numbers without unit alwayswritten in word:

rotodynamic pump can be classified tothree categories.

Number always written as a numerical:at velocity1400 rpm, mass flow rate.

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In engineering, the small or very bignumber will be written according to the

scientific notation format.For example:

3.089 x 10 6

1.548 x 10 -3

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Multiple Scientific notation Prefix Symbol1,000,000,000,000 10 12 tera T1,000,000,000 10 9 giga G1,000,000 10 6 mega M

1,000 103

kilo k10.001 10 -3 milli m0.000 001 10 -6 micro 0.000 000 001 10 -9 nano n

0.000 000 000 001 10 -12 pico p

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TABLE OF DATA

Table should be easily understandDraw a line :

below the title of table below the title of columnBelow the table

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Performance at the Maximum Efficiency forArrangement A05

Test Introduction 960308a 960313a 960313bmax (%) 70 63 66mC (kg/s) 0.224 0.118 0.152

C 0.068 0.036 0.046 P R 1.80 1.70 1.651s (degree) -7 67 55i (degree) -23 -14 -16

M 1s,rel

0.6 0.3 0.4 2 (degree) 83 100 93

M 2 0.70 0.80 0.70W 2 /W 1s 0.60 0.65 0.77Diffusion factor 0.73 0.94 0.61

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Number in every column should bearranged in a straight line

Table 4.6 Performance of the compressor impeller A at amaximum efficiency

N mC M 1s,rel M 2(rpm) (kg/s)60000 0.20 0.56 0.5670000 0.25 0.66 0.5875000 0.24 0.69 0.62

60000 0.09 0.29 0.5970000 0.10 0.33 0.6780000 0.12 0.39 0.7685000 0.13 0.41 0.81

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Numbering the Table

If a number of table more than one, eachtable should be numbered and referred

using that number.Locate the table after the passageFor example:

.see Table 6.1 or ..Table 6.1 Avoid: .at table above or at table below

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SIGNIFICANT VALUEIf a value obtained from the experiment as 9.36, that meantthe real value between 9.35 and 9.37.

A significant digit is defined as any digit used in writing a

number, except those zeros that are used only for locationof the decimal point or those zeros that do not have anynonzero digit on their left.

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SIGNIFICANT VALUE

9.36 : three significant digit0.005 010 8 : five significant digit0.00150 : three significant digit

1980 : three significant digit4.00 x 10 3 : three significant digit4.0 x 10 3 : two significant digit

Round value4.252 761 2 : round off to the two significant value is 4.3.

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SIGNIFICANT VALUE

(2.43)(17.675) = 42.95025 43.0(2.479 h)(60 min/h) = 148.74 min 148.7 min.589.62 / 1.246 = 473.210 27 473.2

1725.463

+ 189.2 + 016.731931.393 1931.4

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ORDER OF MAGNITUDE

We have to know the range of value that wewant to measure.

These will avoid from making a mistake.

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STATISTICAL ANALYSIS- median

Median : is a mid value of a data group

For example:(61, 62, 72, 74, 76, 77, 78, 80, 81, 82, 84)

The median value is 77

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STATISTICAL ANALYSIS- mod

Mod is a value that occurs the most in a group ofdata.

For example:(11, 12, 13, 14, 15, 16, 17): no mod value

(4, 6, 6, 8, 10, 9): mod value is 6

(8, 4, 12, 12, 13, 12, 16, 14, 14, 14): have amultiple mod : 12 and 14.

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STATISTICAL ANALYSIS- mean

Mean is probably one of the most widelyused values in statistical studies since it may

be thought of as representing the typicalvalue of a population .

X = ( x1+ x2+ x3++ xn)/n

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STATISTICAL ANALYSIS- deviation

The difference of value between individualdata and mean

d i = xi - x

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Measured value, deviation from mean and (deviation from mean) 2

xi d i = xi x d i2 = (xi x)2(s) (s) (s 2)2.2 0.0 0.002.0 -0.2 0.042.6 0.4 0.161.9 -0.3 0.092.1 -0.1 0.012.4 0.2 0.042.2 0.0 0.002.3 0.1 0.012.3 0.1 0.01

2.0 -0.2 0.04


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The mean square of the difference betweenthe random variable and its mean is the

variance or second central moment of thedistribution.

The equation of variance is 2=(1/n) ( xi x)2

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STATISTICAL ANALYSIS- standard deviation

The standard deviation is numerically equalto the square root of the variance:

= 2

The equation show that the standarddeviation will increase if the varianceincreases

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GRAPHIC ANALYSIS

Practically everything measurable may be presentedgraphically.Plotted on coordinate paper as points that represent values

of variables.Line graph can show the relation between variables byusing straight line, curve line or both.The most commonly used graph is the 2-D graph drawn oncartesan coordinate (x,y).Usually to investigate the relationship between two

parameters on two different axis horizontal axis(abscissa) and vertical axis (ordinate)

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GRAPHIC ANALYSIS

To make a graph effective, certain considerations must beobserved.1. Choosing the coordinate scales

The scale of the independent variables is usually plotted along the x-axis(horizontal).

2. Labeling the coordinate scales3. Plotting the data

4. Fitting the curve to the plotted points5. Labeling the curves6. Preparing the title properly

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GRAPHIC ANALYSIS

when plotting on x-y graph,If y is a function of x, then y is plotted on vertical axis,and x is plotted on horizontal axisIf parameter Q is influenced by changes in parameter P,then Q is plotted on vertical axis, and P is plotted onhorizontal axis

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GRAPHIC ANALYSIS

The most common x-y graph is the one where the x axis andy axis are divided equallyAs shown in the following figure

x 1 2 4 6 8 10 12 14 16 18 20

y 1 8 64 216 512 1000 1728 2744 4096 5832 8000

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GRAPHIC ANALYSIS - Graph x - y

Graph x-y (linear-linear scales)

0

2000

400060008000

10000

x-axis(linear scale)

x-axis (linear scale)

Y - a x

i s ( l i n e a r s

c a

l e )

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GRAPH semi log

Sometimes, graph is plotted as log y versus xThis is called semi log graphExponential function will NOT plot as a straight line on

rectangular x-y coordinate paperBut, if plotted on semilog paper, will look linearSemi log graph is used whenever;

Range of y value is too big, several magnitude (multiple

power of 10)Exponential equation, y = ae bx , looks like a straight linewhen plotted on semi log graph

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GRAPH semi log

Insert Figure 4.2 pg 92

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GRAPH semi log

Semi log graph is used whenever;Range of y value is too big, several magnitude (multiple

power of 10)Exponential equation, y = ae bx

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GRAPH semi log

The basic equation is y = ae bx It can be written in log form

log y = log a + bx log e = log a + 0.434294bx It can also be written in ln form

ln y = ln a + bx ln e = ln a + bx (because ln e = 1)

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GRAPH semi log

We can define a general equation for a straight line on agraph as ;ordinate = ( slope x abscissa ) + constant

We can define the exponential equation mentioned beforeas

log y = ordinate0.434294 b = slope

x = abscissalog a = constant

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GRAPH semi log

Or, we can also define the exponential equation mentioned before as

ln y = ordinate

b = slope x = abscissaln a = constant

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GRAPH log-log

Log-log graph has log coordinates along both axes.It is a plot of log y versus log x .

plotted as a straight line on a log-log paperLog-log graph does not have log 0 because log 0 is notdefined

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GRAPH log-log

Insert fig 4.3 pg 94

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GRAPH log-log

This type of graph is suitable for data that can berepresented by power equation y = ax b

It can be written in log formlog y = log a + b log x

It can also be written in ln form

ln y = ln a + b lnx

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GRAPH log-log

We can define power equation mentioned before aslog y = ordinateb = slopelog x = abscissalog a = constant

We can define power equation mentioned before asln y = ordinateb = slopeln x = abscissa

ln a = constant

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FACULTY OF MECHANICAL ENGINEERING

THE END

SME 1912 Week6 Part1

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