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Session #: 1426

Application of Mathcad” Software in Performing Uncertainty Analysis Calculations to Facilitate Laboratory Instruction

M. H. Hosni, H. W. Coleman, W. G. Steele Kansas State UniversityA.Jniversity of Alabama in Huntsville/Mississippi State University

ABSTRACT Uncertainty analysis is a technique for determining an estimate for the intend about a reported result within which the true result is expected to lie with a certain degree of confidence. The uncertainty analysis is an extremely usefid tool for all phases of an experimental program from the initiaJ planning (general uncertainty analysis) to detailed design, debugging, testing, and data analysis (detailed uncertainty analysis).

The main objective of this article is to describe how Mathcad@ software maybe used to facilitate uncertainty analysis calculations in undergraduate laboratory instruction. This objective is accomplished by performing general uncertainty analysis calculations for several example problems using Mathcad”. These examples show how quick uncertainty analysis calculations using Mathcad@ during the planning phase of an experiment may assist students to select appropriate measurement equipment. Furthermore, an example of detailed uncertainty analysis is presented to investigate the contributions of the elemental bias and precision error sources, obtain estimates of the bias and precision limits for each measured variable, and illustrate how the measurement errors propagate into the experimental result.

INTRODUCTION Uncertainty analysisl is a technique for determining an estimate for the interval about a reported result within which the true result is expected to lie with a certain degree of confidence. The uncertainty analysis is an extremely usefil tool for all phases of an experimental program from the initial planning (general uncertainty analysis) to detailed design, debugging, testing, and data analysis (detailed uncertainty analysis).

The undergraduate laboratory experience usually includes experimentation with several previously designed experiments using various measurement equipment. For instance, a group of students is assigned to an experimental setup to obtain forced convection data for a heated horizontal cylinder placed in the test section of a wind tunnel. The students measure the amount of power supplied to the cylinder, surface temperature of the heated cylinder, air temperature, surrounding temperatures, air velocity, etc. using various transducers via either manual or automated data acquisition system. Upon completion of data collectio~ the heat transfer coefficient for the cylinder is determined and compared with the available empirical correlations. The experimental results are expected to be reported with uncertainty limits due to the measurement errors associated with each transducer or measurement equipment. The uncertainty limits for experimental results are estimated by pefiorming detailed uncertainty analysis calculations. In some laboratory experiments, the students may perform general uncertainty analysis to select appropriate measurement equipment apriori to experimentation. In either case, the students are required to quantifi the measurement uncertainties and

$iii:1996 ASEE Annual Conference Proceedings } ‘?+,~yHL: .

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Steele, W., & Hosni, M. H., & Coleman, H. W. (1996, June), Application Of Mathcad Software In Performing Uncertainty Analysis Calculations To Facilitate Laboratory Instruction Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--5887