Introduction to Engineering CalculationsChapter 2
What’s in this chapter?Conversion factorsUnitsSignificant figuresReality CheckingStatistical calculationsDimensional analysisGraphical analysis of data
Units and DimensionsI assume none of this is new to you, especially since you all were in thermodynamics with me.Please read over pages 8 to 12Know how to use the units option on your calculatorIf you would like to check out an HP calculator see Harvey Wilson
Force and WeightAgain, this is a subject we covered in thermodynamics, just last semester.Be sure you understand the difference between lbf and lbm
Be sure you understand the difference between the physical constant g, and the conversion factor gc.
Numerical Calculations and Estimation
Scientific NotationEngineering NotationSignificant FiguresPrecision Precision vs accuracy
Validating ResultsBack substitution Plug your answer back in and see if it works
Order of magnitude estimation Round off the inputs, and check to see if
your answer is the right order of magnitudeReasonableness – does it make sense If you get a negative temp in K, you
probably have done something wrong
Statistical CalculationsMeanRangeSample VarianceSample Standard Deviation
Sample Means
NXXXXN
X ...1321
N
jjXN
X1
1
Most measured amounts are means
All means are not created equal
01020304050607080
01020304050607080
Consider these two sets of data
Range
minmax XXR
01020304050607080
01020304050607080
01020304050607080
01020304050607080
Sample Variance
22
2
2
12 ...
11 XXXXXXN Nxs
Standard Deviation
ss XX
2
Your calculator will find all of these statistical quantities for you
Spreadsheets also have built in statistical functions
Standard DeviationFor typical random variables, roughly 2/3 of all measured values fall within one standard deviation of the meanAbout 95% fall inside 2 standard deviationsAbout 99% fall within 3 standard deviations
Data RepresentationCollected data has scatterCalibration
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5
Two Point Linear Interpolation
We are experts at this from ThermoDon’t get confused by the funky equation
12
1
12
1
xxxx
yyyy
This works if you have a lot of tabulated data for your linear interpolation
Fitting a Straight LineA more general and more compact way to represent how one variable depends on another is with an equationLet’s look at straight lines firsty=ax+b
Example 2.7-1
Flow Rate Rotameter Reading(L/min) R
20.0 1052.1 3084.6 50
118.3 70151.0 90
Rotameter Datay = 1.641x + 3.15
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0 20 40 60 80 100
Rotameter Reading
Flow
Rat
e
In the example in the book they eyeballed the line – I used Excel and a linear regression approach
What if the relationship between x and y isn’t a straight line?
Plot it so that it is a straight line Why?Look at page 25
baxy 2 Plot y vs x2
bxay 2 Plot y2 vs
1/x
Let’s try Example 2.7-2Use Excel as our graphing tool
Common non-linear functions
Exponential
Power Law
xbayxbay
axy b
logloglog)ln()ln()ln(
bxaybxay
aey bx
303.2)log()log()ln()ln(
If you plot the ln(y) vs x, you get a straight line
If you plot the ln(y) vs ln(x) you get a straight line
Use Excel to make these plots
Use the trendline to find the equation of the best fit line
HomeworkChapter 2 2.6 2.10 2.18 2.22 2.23 2.32 2.34 2.45
Remember, quizes are based on homework!!!
What’s happening tomorrow?