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Research draft

dimensionless quantity

vr.tr.dimensionless-quantity · XCT.QLT

Let an agent handle dimensionless quantities with their definition and reference quantities, because the number alone says nothing about what was compared.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent handle dimensionless quantities with their definition and reference quantities, because the number alone says nothing about what was compared.

A quantity with no physical dimension, obtained as a ratio of quantities of the same dimension or as a combination in which units cancel, such as a Reynolds number, a ratio or a coefficient.

What it is for: Comparing systems independent of scale, characterising flows and processes, and expressing ratios.

It can be compute it, from its definition; compare systems by it, as in similarity analysis; express it, as a number, percentage or in units of one; use it, in engineering correlations.

Distinguishing features

Units cancel; the value is in units of one

Needs its definition to be meaningful

Supports scaling and similarity

Percentages and ratios are dimensionless

What it looks like

A plain number, sometimes with a named symbol such as Re or Ma.

How it is recognised

A number without units, often with a named symbol

Named numbers such as Reynolds, Mach, Bagnold

Coefficients such as thrust coefficient

Related models

is a kind of - of dimension one

physical quantity

has kind - dimensionless measures

ratio and efficiency

is used in - similarity

engineering

is confused with - numbers without meaning

unitless number

In practice

Families and kinds

characteristic numbers in fluid mechanics and heat transfer

ratios and fractions

coefficients

economic ratios such as return on investment

rates per hour expressed as counts

Standards and regulation

ISO 80000-1 and ISO 80000-11 characteristic numbers

SI Brochure on quantities of dimension one

Failure modes and hazards

Using the wrong reference length or velocity

Applying correlations outside their valid range

Treating hidden dimensions such as per hour as dimensionless

Also called

air changes per hourcharacteristic numberreturn on investmentBagnold numberthrust coefficientLagrange numberelasticity numberGörtler numberStokes number for vibrating particlesStokes rotameter numberStokes number for gravityStokes drag numberFroude number for heat transferheat transfer numberPomerantsev numberStark numberFourier number for mass transferPéclet number for mass transferGrashof number for mass transferNusselt number for mass transferStanton number for mass transferGraetz number for mass transfermass transfer factorBiot number for mass transferexpansion numbercapillary numberHooke numberLorentz numberBatchelor numberNusselt electric numberfirst Cowling numberStuart electrical numbermagnetic pressure numberRoberts numbermagnetic numberelectric field parameterHall numberJoule electrothermal numberGrashof magnetic numberNaze number

+313

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Definition What is compared.

The definition makes the number meaningful.

Formula

Defining ratio.

Definition

The defining formula.

  1. What is the defining formula? definition
  2. Which reference quantities are used? definition

Name

Named number.

Name

Name and symbol.

  1. Which named number is this, and what symbol does it use? definition
  2. Is the definition standard? provenance
Computation Getting the value.

Inputs must be consistent.

Inputs

Measured quantities.

Inputs

Input values and units.

  1. What input values were used, in consistent units? measurement
  2. How uncertain are they? measurement

Value

Result.

Value

The computed value.

  1. What is the value? measurement
  2. Is it within the expected range? boundary
Use What the number tells.

Dimensionless numbers classify regimes.

Regime

Flow or process regime.

Regime

The regime indicated.

  1. Which regime does this value indicate? definition
  2. Where are the transitions? boundary

Scaling

Similarity.

Similarity

Similarity conditions.

  1. Does the model match the prototype in this number? measurement
  2. Which other numbers must also match? boundary
Pitfalls Common errors.

Errors come from definitions and ranges.

Validity

Range of correlations.

Validity

Valid ranges.

  1. Is the correlation valid at this value? boundary
  2. What happens outside the range? boundary

Hidden dimensions

Per time and similar.

Dimension check

Whether it is truly dimensionless.

  1. Is this quantity truly dimensionless? boundary
  2. Which unit is implied? definition

What the second pass must settle

  • Should named characteristic numbers be separate entries?
  • How should reference quantities be recorded?
  • The registry entry includes air changes per hour, which has dimension; should it be split off?
Draft as JSON