Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Dimensional analysis – concepts of geometric dimensionless numbers
Question Statement:
In Buckingham's Pi theorem of dimensional analysis, if a physical phenomenon involves $n$ physical variables expressed in $m$ fundamental dimensions ($M, L, T$), the number of independent dimensionless $\Pi$-groups is:
Options:
(A) $n - m$
(B) $n + m$
(C) $n \times m$
(D) $m / n$
Answer Key:
A
Step-by-Step Solution & Explanation
Buckingham Pi theorem states the number of dimensionless groups equals $k = n - m$, where $m$ is the rank of the dimensional matrix.