Dimensional Analysis — Define the Froude Number The Froude number is defined as the ratio of which two characteristic effects in fluid motion?

Introduction / Context: Dimensionless numbers collapse complex physics into simple ratios. The Froude number Fr is essential in open-channel hydraulics, ship hydrodynamics, and free-surface flows because it compares inertia to gravity effects.

Given Data / Assumptions:

• Characteristic velocity V and length L define inertia scaling.
• Gravitational acceleration g defines gravity scaling.
• Fr used for dynamic similarity in free-surface problems.

Concept / Approach: Froude number is Fr = V / √(g L). Squaring gives Fr^2 = V^2 / (g L), which represents the ratio of inertia force per unit mass (∼ V^2 / L) to gravity acceleration g. Hence, Fr expresses the ratio of inertia force to gravity force, guiding whether waves and surface elevations dominate the behavior.

Step-by-Step Interpretation:

Verification / Alternative check: In open channels, critical depth occurs at Fr = 1, separating subcritical (gravity-dominated) from supercritical (inertia-dominated) regimes—an operational confirmation of the definition.

Why Other Options Are Wrong: “Disagree” would contradict standard dimensional analysis and textbook definitions.

Common Pitfalls: Confusing Froude with Reynolds (inertia/viscous) or Weber (inertia/surface tension). Each has distinct applicability.

Final Answer: Agree — the Froude number expresses the ratio of inertia force to gravity force.