Identify the quantity that is NOT dimensional: which of the following is not dimensional (i.e., is a dimensionless parameter)?

Introduction / Context:
Dimensionless groups are the backbone of similarity analysis, scale-up, and correlation development in fluid mechanics. Recognizing which listed quantities are dimensionless avoids unit mistakes and aids in proper use of charts and correlations.

Given Data / Assumptions:

• Euler number: pressure forces normalized by inertial forces.
• Specific gravity: density ratio relative to a reference (usually water/air).
• Fanning friction factor: wall shear normalization in internal flows.

Concept / Approach:

Each listed quantity is a ratio of like-dimensioned terms and is therefore dimensionless. Hence none of them carry base dimensions (M, L, T). The correct response is that all are dimensionless, so there is no non-dimensional among them to exclude.

Step-by-Step Solution:

Verification / Alternative check:

Handbooks list these as classic π-groups used in correlating pressure drop, scale-up, and buoyancy/pressure-driven flows.

Why Other Options Are Wrong:

Since all three are dimensionless, choosing any one as “not dimensionless” would be incorrect; therefore “None of these” is the only correct choice.

Common Pitfalls:

Confusing “unitless” with “dimensionless”; some dimensionless groups still have numerical values dependent on unit-consistent inputs but no underlying dimensions.

Final Answer:

None of these