Check Your Work: The Value of Analyzing Units of Measure and Dimensional Homogeneity, as Demonstrated in a Fluid Mechanics Exam
AbstractFluid mechanics is a field rife with diverse units of measure and, consequently, potential for errors. Unlike their experience in mathematics, undergraduate students must learn to manipulate both numbers and units in order to satisfy dimensional homogeneity and succeed in engineering. Using written exam responses from students in an undergraduate fluid mechanics class, this paper 1) compares scores according to whether students carefully handled units or not and 2) provides examples of mistakes that may have been avoided by analyzing units. In the exams, students who consistently tracked units scored higher and with less variance than those who did not; both results are statistically significant. The selected examples highlight errors in algebra, fluid properties, and geometry that may have been detected had students properly handled units. The findings suggest that the habit of analyzing units is desirable for students to develop, helping them both understand concepts and check their work as they become engineers.