FroudeZahl

Froudezahl, denoted often by Fr, is a dimensionless parameter used in fluid dynamics to compare inertial forces with gravitational forces in free-surface flows. It is defined by the expression Fr = v / sqrt(g L), where v is a characteristic velocity, g is the acceleration due to gravity, and L is a characteristic length scale. In open-channel flow, Fr is commonly written as Fr = v / sqrt(g D_h), where D_h is the hydraulic depth (D_h = A/P, the cross-sectional area divided by the wetted perimeter). In naval architecture and ship hydrodynamics, Fr is typically expressed as Fr = V / sqrt(g L), with L the ship length.

Interpretation and use: The Froude number characterizes the relative importance of inertial to gravitational effects. When Fr < 1 the flow is subcritical (waves can travel upstream); when Fr > 1 the flow is supercritical (waves cannot propagate upstream). This concept helps describe flow regimes, bore formation, and hydraulic transitions in rivers and channels. It is also central to similarity theories in hydraulic engineering and model testing.

Applications: Fr is widely used to achieve dynamic similarity between models and prototypes, particularly in gravity-driven hydraulic systems, open-channel design, and coastal engineering. By matching Fr between model and full scale, researchers can preserve wave propagation characteristics and flow regimes.

History and context: The Froude number is named after William Froude, a 19th-century British engineer who developed dimensional analysis and model-testing methods that rely on gravity-dominated similarity. Limitations: Fr focuses on gravity and inertia and does not account for viscous or surface-tension effects; for comprehensive modeling, Reynolds or Weber numbers may also be considered.