The Froude number is defined as the ratio of inertial forces to gravitational forces.

The Froude number is defined as the ratio of inertial forces to gravitational forces.

• A. The ratio of viscous forces to inertial forces
• B. The ratio of inertial forces to gravitational forces
• C. The ratio of buoyancy to viscous forces
• D. The ratio of thermal to inertial forces

Answer: (B)

The Froude number compares inertial effects to gravitational effects in a flow. It is defined so that the ratio of the inertial term, scaling like ρV²/L, to the gravitational term, scaling like ρg, gives a dimensionless group: Fr ≈ V²/(gL). Equivalently, Fr is often written as V/√(gL). This means it tells you how important inertia is relative to gravity for a flow with characteristic velocity V and length L. Why this is the best choice: it directly quantifies the balance between inertia and gravity, which governs behavior in free-surface and open-channel flows, wave formation, and buoyancy-driven motions influenced by gravity. When Fr is small, gravity dominates and surface effects are strong; when Fr is large, inertia dominates and gravity has less influence on the flow’s motion. For context, other common nondimensional numbers describe different force balances: the ratio of viscous to inertial forces is the Reynolds number; buoyancy to viscous forces is the Grashof number; the ratio involving thermal effects to inertial effects relates to other groups like the Rayleigh or Prandtl numbers, depending on the exact context.

The Froude number compares inertial effects to gravitational effects in a flow. It is defined so that the ratio of the inertial term, scaling like ρV²/L, to the gravitational term, scaling like ρg, gives a dimensionless group: Fr ≈ V²/(gL). Equivalently, Fr is often written as V/√(gL). This means it tells you how important inertia is relative to gravity for a flow with characteristic velocity V and length L.

Why this is the best choice: it directly quantifies the balance between inertia and gravity, which governs behavior in free-surface and open-channel flows, wave formation, and buoyancy-driven motions influenced by gravity. When Fr is small, gravity dominates and surface effects are strong; when Fr is large, inertia dominates and gravity has less influence on the flow’s motion.

For context, other common nondimensional numbers describe different force balances: the ratio of viscous to inertial forces is the Reynolds number; buoyancy to viscous forces is the Grashof number; the ratio involving thermal effects to inertial effects relates to other groups like the Rayleigh or Prandtl numbers, depending on the exact context.