Dimensional Analysis and Similitude MCQ with answer and solution

Concept

Definition of Reynolds number in fluid mechanics

Formula

NONE

Step-by-step solution

1. Dimensionless parameters in fluid mechanics compare relative magnitudes of fluid forces. 2. Reynolds number (Re) quantifies the relative importance of fluid inertia relative to fluid friction forces. 3. Mathematically, it is defined as the ratio of inertia force to viscous force (Re = ρ v L / μ). Answer: D

Explanation

Reynolds number is a fundamental dimensionless quantity in fluid mechanics used to predict flow patterns. It represents the ratio of inertial forces to viscous forces within a fluid moving relative to a surface. High Reynolds numbers indicate turbulent flow dominated by inertia, while low values indicate smooth laminar flow dominated by viscosity.

Why the other options are wrong

A) The ratio of inertia force to gravity force is the Froude number. B) The ratio of inertia force to pressure force is the Euler number. C) The ratio of inertia force to surface tension force is the Weber number.

Shortcut

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

Common mistake

Confusing Reynolds number (Inertia/Viscous) with Froude number (Inertia/Gravity) or Weber number (Inertia/Surface Tension).