The main use of dimensional analysis is to check the correctness of equations by ensuring the homogeneity of dimensions on both sides. It is widely used to:
- Verify that an equation or formula is dimensionally consistent and physically meaningful.
- Convert units from one system to another.
- Derive relationships between different physical quantities.
- Express one physical attribute in terms of others.
- Determine the dimensions of physical constants.
- Serve as a method to relate and compare physical quantities in scientific and engineering problems, including complex systems like fluid mechanics.
Thus, dimensional analysis is a fundamental tool for validating equations, converting units, and deriving relationships among physical quantities in physics, engineering, and mathematics.
