29. ISO 80000-11 — Characteristic numbers
The sixth part specified is ISO 80000-11, Characteristic numbers — and it is where the dimension does not classify the kind thesis (R1) becomes total. Every item is catalogued: all 115 of items 11-4.1 … 11-9.2, across the six clauses — momentum transfer (the Reynolds, Euler, Froude, Mach, Knudsen, … numbers), transfer of heat (Fourier, Péclet, Rayleigh, Nusselt, Biot, …), transfer of matter in a binary mixture (the mass-transfer analogues), constants of matter (Prandtl, Schmidt, Lewis, …), magnetohydrodynamics (the magnetic and electric numbers), and miscellaneous — each carrying its exact source as data: the part, the printed item designation, the principal quantity symbol, and the coherent SI unit symbol. Only citation locators are recorded; no normative content from the licensed standard is reproduced.
A characteristic number is a dimensionless ratio. So every one of the 115 is dimension
one: the dimension functor sends the Reynolds number (inertial / viscous forces), the
Mach number (flow speed / sound speed), and the Prandtl number (momentum / thermal
diffusivity) all to the single point 1. A dimension-only model sees one type — "a real
number" — for the entire part and cannot tell any two of its 115 members apart. What keeps
them apart is their measurement principle: the physical ratio each one expresses, carried
as an examination principle (requirement R2). This is the pattern Part 3 set on the length family, Part 4 on the
force family, Part 7 on the radiation trios — here at its widest, over a part with no
dimensional variation at all.