Question

Which of the following principle is related to dimensional analysis ?

• A. Casson's Theorem
• B. Davis's Theorem
• C. Buckingham's Theorem
• D. Maxwell's Theorem

Hint:

Buckingham's Pi Theorem is used to reduce a large number of physical variables into a smaller set of dimensionless numbers (like the Nusselt, Prandtl, or Reynolds numbers), simplifying experimental design.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Dimensional analysis is a mathematical technique used in fluid mechanics and heat transfer to simplify complex physical problems by grouping variables into dimensionless parameters.
Detailed Explanation:
Buckingham's Pi Theorem is the fundamental theorem of dimensional analysis.
It states that if a physical process involves \( n \) dimensional variables containing \( m \) fundamental dimensions (such as mass, length, and time), the variables can be grouped into \( n - m \) independent dimensionless parameters, denoted as \(\Pi\) (Pi) terms.
For example, in fluid flow through a pipe, variables like density, viscosity, velocity, pipe diameter, and pressure drop are grouped using this theorem to derive the dimensionless Reynolds Number and friction factor.
Let us review the other theorems listed:
- Casson's Equation: A rheological model used to describe the flow behavior of non-Newtonian fluids (like chocolate).
- Maxwell's Equations: Fundamental equations of electromagnetism.
- Davis's Theorem: Not associated with dimensional analysis in engineering.
Therefore, Buckingham's Theorem is the only principle directly related to dimensional analysis.

Step 2: Final Answer:
The principle related to dimensional analysis is Buckingham's Theorem.