Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition

3UNCERTAINTY IN A RESULT DETERMINED FROM MULTIPLE VARIABLES

Sometimes, the desired result of an experiment will be a directly measured variable X, and in that instance we can use the techniques described in Chapter 2 to determine a value for u_x and either an expanded uncertainty at some level of confidence (if we use TSM) or the values of X that represent the lower and upper bounds of a coverage interval (if we use the preferred MCM). In most cases, however, the result of our experiment or simulation will depend on several variables through a data reduction equation (DRE) or a simulation model.

An example of an experimental result is the determination of the drag coefficient for a model in a wind tunnel test where drag force F_D, fluid density ρ, velocity V, and model frontal area A are measured or evaluated and the drag coefficient C_D is calculated as

(3.1)

A simple simulation model would be the prediction of the temperature distribution T in a plane wall of thickness L by solving the equation

(3.2)

with boundary conditions

(3.3)

and

(3.4)

where k is the thermal conductivity. Both ...