# Dimensionless quantity A dimensionless quantity is a number with no units — a ratio in which the physical dimensions cancel. In [[Fluid_dynamics]] they are the whole organising apparatus: the [[Reynolds_number]], the [[Froude_number]], the [[Weber_number]], and a few dozen others each compare two competing effects, and the value of the ratio tells you which one is winning. Get the right group and a wind-tunnel model, a laboratory flume, and the full-scale machine all obey the same curve. ## Why the ratio is the physics A pipe flow does not care about [[Velocity]], diameter, [[Density]], and [[Viscosity]] separately — it cares about the single combination that is the [[Reynolds_number]]. The Buckingham π theorem makes this formal: a problem with n variables and k dimensions reduces to n − k dimensionless groups, which is often a collapse from five knobs to one. That collapse is what makes experiment possible at all, because you can sweep one number instead of exploring a five-dimensional space, and it is why a [[Mathematical_model]] built on the right group generalises while one built on raw quantities does not. ## The unavoidable compromise Matching every relevant group at model scale is usually impossible. A ship model can match [[Froude_number]] or [[Reynolds_number]] but not both, so [[Naval_architecture]] splits the [[Drag_(physics)|drag]] into a wave part scaled by one and a friction part estimated separately. Knowing which group dominates is therefore an engineering judgement, not a lookup. The same discipline runs outside fluids — [[Statistics|statistical]] effect sizes, [[Economics|economic]] ratios, and [[Reliability_engineering|reliability]] indices are all the same move. **Microsim brief (next pass):** One scene, four sliders (speed, size, density, viscosity) and a rack of live group readouts — Re, Fr, We — so the viewer sees different slider combinations produce identical numbers and identical flow. **On the spine:** [[Reynolds_number]] · [[Froude_number]] · [[Weber_number]] · [[Fluid_dynamics]] · [[Mathematical_model]] · [[WT!Thury_Hydrodynamics_Compendium]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Dimensionless_quantity) : [Wikitube](https://en.wikitube.io/wiki/Dimensionless_quantity) ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_WT!Thury_Hydrodynamics_Compendium]], [[PORTAL_Physics]], [[PORTAL_Systems_science]]. --- *Fluid seed wave · 2026-09-10 · seed register · microsim layer pending.*