Dimensional Analysis and Similitude MCQ with answer and solution

Concept

Definition of Reynolds number

Formula

Re = Inertia force / Viscous force

Step-by-step solution

1. Dimensionless numbers in fluid mechanics represent ratios of different forces acting on a fluid element. 2. Reynolds number quantifies the relative importance of inertial forces to viscous forces. 3. Therefore, Reynolds number is defined as the ratio of inertia force to viscous force. Answer: D

Explanation

Reynolds number is a dimensionless quantity in fluid mechanics that compares the relative significance of fluid momentum to internal friction forces. Mathematically, it is expressed as the ratio of inertia force to viscous force within the fluid flow. This ratio helps determine whether a fluid flow regime will be laminar or turbulent.

Why the other options are wrong

A) The ratio of inertia force to gravity force is defined as Froude's number. B) The ratio of viscous force to gravity force is not a standard non-dimensional parameter in fluid dynamics. C) The ratio of inertia force to elastic force defines Mach's number.

Shortcut

Reynolds number is the ratio of Inertia force to Viscous force (Re = I/V).

Common mistake

Confusing Reynolds number (ratio of inertia to viscous force) with Froude number (ratio of inertia to gravity force).