Dimensional Analysis and Similitude MCQ with answer and solution

Concept

Froude's Law of Similarity is applied when gravity is the predominant force influencing the fluid motion, which is the case for all free-surface flows.

Formula

Fr = V / √(gL)

Step-by-step solution

1. Identify the predominant force in open channel flow, which is gravity (due to the free surface). 2. Recall the dimensionless numbers associated with different forces: Reynolds (Viscous), Froude (Gravity), Mach (Elasticity), Euler (Pressure). 3. Select Froude number as it governs gravity-dominated flows.

Explanation

In open channel flows, the flow is primarily governed by gravity forces due to the presence of a free surface. Froude's number represents the ratio of inertia force to gravity force, making it the governing dimensionless parameter for model studies of rivers, spillways, and canals.

Why the other options are wrong

A: Reynolds number governs flows where viscous forces are predominant, such as low-velocity pipe flow. C: Mach number governs high-speed gas flows where compressibility is significant. D: Euler number is used in flows where pressure differences are the main driving force.

Shortcut

Free surface = Gravity = Froude.

Common mistake

Confusing Reynolds number with Froude number; Reynolds is used for pipe flow (pressure flow) where viscosity dominates, not open channels.