DIMENSIONAL ANALYSIS

DIMENSIONAL ANALYSIS

Dimensional Analysis provides an in-depth exploration of a fundamental technique used to simplify the study of physical phenomena by reducing the number of variables involved. This course is essential for students and professionals in engineering, physics, and applied mathematics, offering the skills needed to perform dimensional reasoning and develop scaling laws. The course begins with an introduction to the basic concepts of dimensions and units, including the SI unit system. Students will learn the principles of dimensional homogeneity and how to apply the Buckingham π theorem to derive dimensionless groups from a set of physical variables. The course will cover the process of identifying key dimensionless parameters and using them to simplify and analyze physical problems. Key topics include the derivation and interpretation of dimensionless numbers such as Reynolds number, Mach number, and Froude number, and their significance in different fields of engineering. The course will also explore the application of dimensional analysis in experimental design, data reduction, and the development of empirical correlations. Students will engage in practical problem-solving sessions and case studies to apply dimensional analysis to real-world problems, such as fluid mechanics, heat transfer, and structural mechanics. Computational tools and software for performing dimensional analysis will also be introduced.