Dimensionless Numbers

Dimensionless Numbers

Overview

Calculates the standard engineering dimensionless numbers from SI inputs:

• Flow: Re, Fr, We, Eu.
• Heat transfer: Pr, Nu (Dittus-Boelter screening), Gr, Ra, Bi, Fo, Pe.
• Mass transfer: Sc, Sh (via analogy if requested).

Validity-range warnings (e.g. Dittus-Boelter for Re >= 10000) are appended when the inputs fall outside common citations.

Prerequisites

1. uv available.

When to Use

• A correlation needs a Reynolds, Prandtl, or Grashof number.
• A regime check (laminar vs turbulent, natural vs forced convection) is

needed before picking a correlation.

• Scale-up analysis where matching a dimensionless group is the design

criterion.

Don't use for

• Picking the convective heat transfer coefficient (use

convective-heat-transfer-correlations).

• Multi-phase regime classification (use two-phase-flow).
• The Reynolds analogy for combined heat / momentum transfer — that is a

specific correlation, not a single number.

Utility Scripts

• uv run scripts/calculate_dimensionless.py reynolds --density 1000 --velocity 1.5 --length 0.05 --viscosity 0.001 --output /tmp/re.json
• uv run scripts/calculate_dimensionless.py prandtl --cp 4180 --viscosity 0.001 --thermal-conductivity 0.6 --output /tmp/pr.json
• uv run scripts/calculate_dimensionless.py nusselt-dittus-boelter --reynolds 50000 --prandtl 4 --output /tmp/nu.json

Procedure

1. Get fluid properties at the relevant film / bulk temperature.
2. Identify the geometric length scale (pipe diameter, plate length,

particle diameter) — the right one depends on the correlation.

1. Run the script. Note any validity-range warnings.
2. Pass the dimensionless number into the matching skill (correlation,

pressure drop, etc.).

Pitfalls

• Using the wrong length scale (pipe diameter vs hydraulic diameter for

non-circular ducts; characteristic length for natural convection).

• Computing Pr at room temperature and using it for a hot fluid stream.
• Computing Re with mass velocity (G = rho v) where the correlation

expects bulk velocity, or vice versa.

• Treating Dittus-Boelter Nu as the actual convective coefficient when

the validity is borderline (Re ~ 5000 or Pr > 100).

• Using the kinematic viscosity in a Re formula that expects dynamic

viscosity (or vice versa).

• Using Bi to decide a lumped-capacitance analysis without checking

whether the surface heat transfer coefficient is itself in a turbulent regime.

• Computing Sc from a guessed diffusivity; quote the source of D_AB.

Fallback Strategies

• If a needed property (k, mu, cp) is unknown, surface the missing input

with a clear error rather than guessing.

• For very high or very low Pr (e.g. liquid metals), use a different

correlation than Dittus-Boelter; this skill reports the number but the correlation choice is downstream.

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/equations.md — formula list and standard length-scale

conventions.

Anti-Patterns

• Reporting Re without stating the length scale used.
• Treating Nu = 0.023 Re^0.8 Pr^0.4 as a universal answer.
• Mixing units silently inside the script call.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.