What is the main reason an engineer would use the Buckingham Pi theorem when designing something with flowing water?

The main reason an engineer would use the Buckingham Pi theorem when designing something with flowing water is to systematically reduce the number of independent physical variables required to describe a complex fluid flow phenomenon, thereby enabling efficient, accurate, and cost-effective experimental testing and reliable scaling from models to full-size prototypes. This theorem is a fundamental principle in *dimensional analysis*, which is the process of analyzing the relationships between different physical quantities by examining their fundamental dimensions (such as mass, length, and time). When working with flowing water, numerous physical properties are involved, including fluid density, fluid viscosity, flow velocity, pressure, gravitational accelerati....