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CM4110 Unit Operations Lab Measurement Basics

CM4110 Unit Operations Lab Measurement Basics. Fundamentals of Measurement and Data Analysis D. Caspary September, 2007. CM4110 Unit Operations Lab Measurement Basics. Outline: Principles of measurement Error Analysis “Propagation of error”.

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CM4110 Unit Operations Lab Measurement Basics

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  1. CM4110Unit Operations LabMeasurement Basics Fundamentals of Measurement and Data Analysis D. Caspary September, 2007

  2. CM4110Unit Operations LabMeasurement Basics Outline: • Principles of measurement • Error Analysis • “Propagation of error”

  3. CM4110Unit Operations LabMeasurement Basics Principles of Measurement • Nothing can be measured exactly • Measurements are merely approximations of a characteristic or property • Associated with every measurement is an “uncertainty” or “error”

  4. CM4110Unit Operations LabMeasurement Basics Reporting Measured Values • Engineering and scientific reporting must be ethical and honest – report appropriate estimate of uncertainty with the results • Learn/ Use appropriate statistical tools • Use common sense

  5. CM4110Unit Operations LabMeasurement Basics Typical UO Lab assignment: “Calculate the overall heat transfer coefficient for a shell and tube heat exchanger.”

  6. CM4110Unit Operations LabMeasurement Basics Think about your experimental strategy: • What is known? • What do I need to measure? • What measuring instruments are available? • What is the precision of each instrument? • How will the precision effect the calculated results? • And, what about accuracyin measurements?

  7. CM4110Unit Operations LabMeasurement Basics Two types of InstrumentError • Systematic error – determinate (or fixed) error – defines accuracy • Random error – indeterminate error associated with the instrument – defines precision

  8. CM4110Unit Operations LabMeasurement Basics Accuracy vs. Precision in Measurement Accurate measurement – small systematic error Precise measurement – small random variation (random error)

  9. CM4110Unit Operations LabMeasurement Basics Poor Accuracy Poor Precision Poor Accuracy Good Precision Good Accuracy Good Precision Good Accuracy Poor Precision

  10. CM4110Unit Operations LabMeasurement Basics What instruments are available? What is the effect of the instrument error on the calculated result?

  11. Reading Rotameters • Always read at the largest diameter flow

  12. Reading Pressure Gauges • know if gauge is calibrated to psig or psia • don’t get caught: compound pressure gauge scale changes units 0 30 60

  13. Reading Manometers • scale may not zero – read both sides of u-tube • well-type – disregard the small change in well level O Δh Δh O

  14. CM4110Unit Operations LabMeasurement Basics Reporting Instrument Error For analog scales Typically plus or minus ½ the smallest increment For digital readouts Report the value as displayed, then look up the accuracy spec’s in manufacturer’s data

  15. CM4110Unit Operations LabMeasurement Basics Validity of Experimental Measurement Bad Data • caused by obvious blunders • can be discarded • has an “assignable cause” “Unexplained” Data • cannot be discarded because it doesn’t meet our expectations • no assignable cause Any data filtering must be consistent and unbiased.

  16. CM4110Unit Operations LabError Analysis Back to the assignment : “Calculate the overall heat transfer coefficient for a shell and tube heat exchanger.” How will Experimental Error affect my results?

  17. CM4110Unit Operations LabError Analysis Develop an Experimental Strategy Usually you will perform a set of experiments: • What do you need to measure? • What instrument will you use for each measurement? • Are the instruments you propose to use acceptable? • How many repeats of each experiment will you perform? • How will the uncertainty of each measured value affect the result?

  18. CM4110Unit Operations LabError Analysis Three Types of Experimental Error • Gross error – mistakes • Systematic error – determinate (or fixed) error • Random error – indeterminate error How will these errors affect my results?

  19. CM4110Unit Operations LabError Analysis Evaluating Experimental Error • Estimating the magnitude of error in each measured value • Commonly called “Error Analysis”

  20. CM4110Unit Operations LabError Analysis … liars, damned liars, and statisticians… “I haven’t got time to read the whole story. Just give me the unabridged, condensed version.” Your goal is to present the Location and Dispersion of your results. Wheeler and Chambers, Understanding Statistical Process Control, SPC Press, 1992

  21. CM4110Unit Operations LabError Analysis Location of Data • With three or more replicates typically report the Average • With a single value (or 2 values), report the value(s).

  22. CM4110Unit Operations LabError Analysis Dispersion of Data Range • Lowest value and highest value • Often used for small data sets • Easy to report • Generally not used for our purposes as it hides data – says nothing about the dispersion of the “middle values”

  23. CM4110Unit Operations LabError Analysis Dispersion of Data RMS Deviation (aka Standard Deviation) • calculate the average for the sample set • calculate the deviation from the average for each value • square the individual deviations • sum all the squares of the deviations • find the average squared deviation • take the square root of the average squared deviation

  24. CM4110Unit Operations LabError Analysis Dispersion of Data Standard Deviation (aka Average Std. Dev.) • Calculate like RMS deviation except use (n-1) in the denominator when calculating the average squared deviation • As data set gets large, Std. Dev. approaches the value for RMS Dev.

  25. CM4110Unit Operations LabError Analysis Rules of Thumb • Compare reading error with the random error. Use the larger of these two as the uncertainty. • Be realistic (honest) in reporting the measurement error or uncertainty. • Normally report Average, Error, and sample size for UO Lab measurements

  26. CM4110Unit Operations LabError Analysis Rules of Thumb • Combine dependant measurements and calculate a single value and an uncertainty for the combined quantity. • Do not hide data. • Do not allow yourself to adjust the results to match some “expected value”.

  27. CM4110Unit Operations LabPropagation of Error Estimating the error in your calculated results: • The Error in measured quantities that are arithmetically combined must also be combined. • Use standard practice for “propagating” error through calculations. • Error can be reported in EU’s or %.

  28. CM4110Unit Operations LabPropagation of Error Several Choices: • Take the “worst-case” error of each measurement and add them up to find a “maximum error.” • Take the worst case of the largest source of error and use this as the uncertainty in the result. • Use some commonly accepted method. • Need a fundamental understanding of statistics • Use this approach for UO Lab data

  29. CM4110Unit Operations LabPropagation of Error When adding/subtracting terms: The error in the result is the square root of the sum of the squares of the individual errors. When multiplying/dividing terms: The error in the result is the magnitude of the result multiplied by the square root of the sum of the squares of the relative errors. See references for additional cases and detailed examples

  30. CM4110Unit Operations LabPropagation of Error Reporting the Results– Significant Figures • Maintain the appropriate number of significant figures in the calculated result and round off after you complete your calculations. • The number of significant figures assigned to the propagated error should never be more than the number of significant figures in the calculated result, usually one, maybe two significant figures.

  31. CM4110Unit Operations LabPropagation of Error Text References Understanding Statistical Process Control, 2nd edition, D.J. Wheeler, D.S. Chambers, SPC Press, 1992. Experimental Methods for Engineers, 3rd edition, J.P. Holman, McGraw-Hill, 1978. Data Reduction and Error Analysis for the Physical Sciences, P.R. Bevington, Mcgraw-Hill, 1969.

  32. CM4110Unit Operations LabPropagation of Error Web References http://science.widener.edu/svb/stats/error.html – shows how to arithmetically combine individual errors to get error in calculated result. http://www.upscale.utoronto.ca/PVB/Harrison/ErrorAnalysis/Propagation.html – propagation of error and error analysis for all situations Dr. Pintar’s Error Analysis Handout – link on course web page for definitions and a worked out example from actual UO Lab data

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