introduction to engineering calculations chapter 2

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?