Uncertainties and Their Propagation
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…from CheLabWiki, an online resource for chemical-engineering laboratories located at www.chelabwiki.org; Site Revision #875; 6 January 2009.
Community Portal → Activities and Exercises → Uncertainties and Their Propagation
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The goals of this exercise are to provide a simple situation in which students can (a) collect data, (b) analyze their measurements for Type A and Type B uncertainties, (c) report their results to the correct number of significant figures, (d) track propagation of uncertainties through calculations, and (e) become sensitive to the effects of measuring instruments on results.
Student Organization
Students in groups of two.
Time Allowed for Completion
Groups are given 3 hours to perform their measurements and draft a report.
Equipment
Each student group is given (1) a short length of pipe, (2) a cheap ruler, and (3) a pair of precision calipers.
Activity
First, using the ruler, each group is to determine, for the given pipe sample, its
- outside diameter
- inside diameter
- wall thickness
- outside cross-sectional area
- inside cross-sectional area
The wall thickness is to be obtained in two ways: direct measurement and difference.
Second, the measurements are to be repeated using the precision calipers.
Cautions
Each group must decide on an appropriate number of measurements to make, balancing time available against statistical precision. Pay attention to errors that propagate through calculations. Be consistent in reporting significant figures: the number of significant figures reported for the uncertainties must be consistent with the numbers reported in averages.
Reports
The report should contain three parts:
- (1) A summary of results, in tabular form, for the five quantities requested above. Each quantity should be accompanied with its uncertainty and units.
- (2) A discussion, in paragraph form, that explains the following:
- How the choice for the number of measurements was made.
- How Type A uncertainty was determined.
- How Type B uncertainty was determined.
- How total uncertainty was estimated.
- Any differences in results and uncertainties for the wall thickness obtained by the two methods.
- Any differences in results and uncertainties in results obtained from the two measuring instruments.
- What could be done to reduce, by a factor of two, the reported uncertainty in the outside diameter.
- (3)Tables of all original data.
