Dimensional Analysis and Similitude MCQ with answer and solution

Concept

Froude number (Fr) dominates fluid phenomena involving free surfaces where gravity is the driving or restoring force.

Formula

Fr = V / √(g × L)

Step-by-step solution

1. Identify the definition of Froude number: Fr = √(Inertia force / Gravity force) = V / √(g × L). 2. Recognize that gravity effects are predominant in systems with free surfaces, such as rivers, canals, spillways, and open channels. 3. Match with the given options, confirming that Open channel flows (Option B) are governed by the Froude number.

Explanation

The Froude number represents the ratio of inertia force to gravity force. It is the governing dimensionless parameter in flows characterized by a free surface where gravity plays a predominant role, such as open channel flows, wave motions, and spillway flows. Therefore, it is most important in open channel flows.

Why the other options are wrong

A: Governed primarily by the Mach number where fluid compressibility and elasticity are significant. C: Governed primarily by the Reynolds number where viscous shear forces predominate. D: Governed primarily by the Weber number where surface tension forces dominate.

Shortcut

Free surface / gravity-driven flow = Froude number; Viscous / pipe flow = Reynolds number; Compressible flow = Mach number; Surface tension = Weber number.

Common mistake

Confusing Froude number with Reynolds number, which governs enclosed pipe flows dominated by viscous forces.