Introduction to Engineering Calculations Chapter 2

What’s in this chapter? Conversion factors Units Significant figures Reality Checking Statistical calculations Dimensional analysis Graphical analysis of data

Units and Dimensions I assume none of this is new to you, especially since you all were in thermodynamics with me. Please read over pages 8 to 12 Know how to use the units option on your calculator If you would like to check out an HP calculator see Harvey Wilson

Force and Weight Again, this is a subject we covered in thermodynamics, just last semester. Be sure you understand the difference between lb f and lb m Be sure you understand the difference between the physical constant g, and the conversion factor g c.

Numerical Calculations and Estimation Scientific Notation Engineering Notation Significant Figures Precision Precision vs accuracy

Validating Results Back 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 magnitude Reasonableness – does it make sense If you get a negative temp in K, you probably have done something wrong

Statistical Calculations Mean Range Sample Variance Sample Standard Deviation

Sample Means Most measured amounts are means

All means are not created equal Consider these two sets of data

Range

Sample Variance

Standard Deviation Your calculator will find all of these statistical quantities for you Spreadsheets also have built in statistical functions

Standard Deviation For typical random variables, roughly 2/3 of all measured values fall within one standard deviation of the mean About 95% fall inside 2 standard deviations About 99% fall within 3 standard deviations

Data Representation Collected data has scatter Calibration

Two Point Linear Interpolation We are experts at this from Thermo Don’t get confused by the funky equation This works if you have a lot of tabulated data for your linear interpolation

Fitting a Straight Line A more general and more compact way to represent how one variable depends on another is with an equation Let’s look at straight lines first y=ax+b

Example 2.7-1

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

Plot y vs x 2 Plot y 2 vs 1/x Let’s try Example Use Excel as our graphing tool

Common non-linear functions Exponential Power Law 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

Homework Chapter Remember, quizes are based on homework!!!

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