About#

This project is a small, systematic database of dimensionless numbers and the physical quantities they compare. The goal is not only to make a readable reference, but also to keep every entry in a regular, easily parsable form that can be reused by scripts, calculators, visualizations, teaching material, or other tools.

Each dimensionless number is represented as a ratio of named quantities. Those quantities carry dimensions, SI-unit exponents, symbols, and short explanations, so the database can check dimensional consistency and generate pages without relying on ad hoc prose.

Number entries#

A number entry defines the formula, the physical meaning of the numerator and denominator, optional aliases and eponyms, related numbers, and any useful regimes.

{
  "id": "reynolds",
  "name": "Reynolds number",
  "symbol": "\\text{Re}",
  "aliases": [],
  "named_after": ["Osborne Reynolds (1842-1912)"],
  "description": "Measures inertial transport relative to viscous resistance.",
  "numer": {
    "quantities": ["density", "velocity", "length"],
    "exponents": [1, 1, 1],
    "label": "inertia"
  },
  "denom": {
    "quantities": ["dynamic-viscosity"],
    "exponents": [1],
    "label": "viscosity"
  },
  "regimes": {
    "pipe flow": {
      "thresholds": [0, 2300, 4000, null],
      "labels": ["laminar", "transitional", "turbulent"]
    }
  },
  "domain": "fluid-mechanics",
  "see_also": ["euler", "froude", "strouhal"]
}

quantities lists reference quantity IDs, and exponents gives the power of each quantity in the product. The numerator and denominator dimensions must cancel. A null threshold means the final regime is open-ended.

Quantity entries#

A quantity entry defines a reusable physical ingredient. Dimension and SI-unit vectors are stored as exponents in the global orders defined in quantities.json.

{
  "density": {
    "name": "mass density",
    "symbol": "\\rho",
    "dimension": [0, 0, -3, 0, 1, 0, 0],
    "si_units": [0, 0, 0, 0, 1, -3, 0, 0],
    "description": "Mass per unit volume of a substance."
  }
}

For example, the density dimension vector means mass times length to the minus third power. The SI-unit vector means kilograms per cubic metre. Because every number points to these shared quantity records, the same physical quantity is described once and reused consistently throughout the database.