Dynamic similarity for channels dominated by inertia and gravity When inertia and gravity are the primary forces and friction has a minor role, channel design and model–prototype comparison should be based on which dimensionless number?

Introduction / Context:
Choice of the correct similarity parameter is crucial in hydraulic modeling. Free-surface flows such as rivers, spillways, and ship hydrodynamics are governed mainly by inertia and gravity, so the corresponding dimensionless group must capture that balance.

Given Data / Assumptions:

• Free-surface flow conditions; wave and surface effects matter.
• Inertia and gravity dominate; viscous effects are relatively small.
• Geometric similarity between model and prototype is assumed.

Concept / Approach:

The Froude number Fr = V / sqrt(g * L) compares inertial forces to gravitational forces. Dynamic similarity requires Fr_model = Fr_prototype, ensuring homologous behavior of waves, hydraulic jumps, and critical transitions.

Step-by-Step Solution:

Verification / Alternative check:

Reynolds number governs inertia–viscosity; Weber number inertia–surface tension; Mach number compressibility; Euler number pressure–inertia. None of these match inertia–gravity dominance like Froude.

Why Other Options Are Wrong:

They address different force balances and cannot alone preserve wave-related phenomena in open channels.

Common Pitfalls:

Attempting to match both Reynolds and Froude simultaneously is often impossible; prioritize Froude for free-surface flows.

Final Answer:

Froude number