Froude_number - Wikiparency

# Froude number The Froude number compares a flow's inertia to [[Gravity|gravity]]: Fr = U / √(gL), speed over the speed of the surface [[Wave|waves]] the flow could carry. Below one the flow is subcritical and a disturbance can travel upstream; above one it is supercritical and nothing propagates back. That single threshold decides the behaviour of every open channel — a spillway, a farm ditch, a stretch of the [[Minnesota_River]] — and it is why a [[Hydraulic_jump]] can only happen in one direction. ## Watch it in a sink Run a tap onto a flat basin. The thin fast sheet near the point of impact is supercritical; at some radius it abruptly thickens into a slower, deeper ring. That ring is the jump, and the radius is where Fr passes one. Nothing about the [[Water]] changed — only the ratio of its [[Velocity]] to the wave speed its depth allows. The same reasoning sizes a stilling basin below a dam in [[Hydraulic_engineering]] and predicts standing waves in a rapid. Unlike the [[Reynolds_number]], Froude says nothing about [[Viscosity]] or [[Turbulence]] — it is purely about gravity and speed. ## Ships, and why models scale [[Naval_architecture]] runs on it. Wave-making [[Drag_(physics)|drag]] depends on Fr, so a hull tested as a scale model must match the full-size Froude number, not its [[Reynolds_number]] — you cannot match both at once, which is the central compromise of towing-tank work and a good lesson in what a [[Dimensionless_quantity]] actually buys. Hull speed, the point where a displacement boat digs into its own wake, is a Froude limit. The same group governs sediment transport on the [[WT!Southern_Agricultural_Center_of_Excellence|southern agricultural]] bridge and density currents in [[Geophysical_fluid_dynamics]]. **Microsim brief (next pass):** Channel with draggable depth and inlet speed; Fr readout that changes colour at 1; a jump that forms, moves, and washes out as you cross the threshold. **On the spine:** [[Hydraulic_jump]] · [[Dimensionless_quantity]] · [[Reynolds_number]] · [[Fluid_dynamics]] · [[WT!Thury_Hydrodynamics_Compendium]].  *Linked from the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]], section 28, Open channels and the hydraulic jump.*   **Microsim — three.js (Wikitube framework):** *Froude number* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Froude_number.html" data-title="Froude number"></div> *Built from `MICROSIM_GUIDE/specs/variants/Froude_number.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Froude_number) : [Wikitube](https://en.wikitube.io/wiki/Froude_number) ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_WT!Thury_Hydrodynamics_Compendium]], [[PORTAL_Physics]]. --- *Fluid seed wave · 2026-09-10 · seed register · microsim layer pending.*