# Fluids — Beggs & Brill core and friction comparisons

Source version: Fluids v1.3.1, reviewed 2026-10-19.

- Source: https://github.com/CalebBell/fluids/blob/v1.3.1/fluids/two_phase.py
- Upstream license: https://github.com/CalebBell/fluids/blob/v1.3.1/LICENSE.txt
- Local full license: [LICENSE-Fluids.txt](LICENSE-Fluids.txt)
- Upstream tests: https://github.com/CalebBell/fluids/blob/v1.3.1/tests/test_two_phase.py
- Upstream source copyright: Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
- Package copyright: Copyright (C) 2016-2025, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
- Referenced test data copyright: Copyright (C) 2016, 2017 Caleb Bell <Caleb.Andrew.Bell@gmail.com>

The JavaScript functions `beggsBrillState` and `calculateTwoPhasePressureLoss`
adapt the mathematical core of `_Beggs_Brill_holdup` and `Beggs_Brill`:
the revised L1–L4 reference-regime map, holdup coefficients, inclination
correction, transition interpolation, friction multiplier and acceleration term.
The full Python package is not bundled or executed by this website.

`compareTwoPhaseFriction` also adapts `Friedel`, `Muller_Steinhagen_Heck`,
and `Lockhart_Martinelli` from the same MIT-licensed source version. The last
method uses Chisholm's 1967 coefficients (C = 5, 10, 12, 20); it is not HTFS
and not the separate Chisholm 1973 correlation.

Comparisons use straight length, design mass flow and inlet phase properties;
they exclude fittings, elevation and acceleration. The selected friction
method replaces the straight-pipe friction term in the actual pressure profile
and pump-head calculation. Holdup, gravity and the acceleration denominator
remain Beggs & Brill, with a common no-slip fitting K term. This combination
is an application-specific hybrid, not an original full Friedel/MSH/LM model.
Missing surface tension blocks Friedel comparison alone; every full hybrid
still requires surface tension for Beggs & Brill holdup.
The Friedel/MSH friction helper uses Darcy 64/Re below 2040 and the local
Colebrook solver above that threshold, matching the upstream default branch
convention but using Colebrook rather than Clamond's numerical solver.
LM uses 64/Re below 2000 and 0.184/Re^0.2 otherwise, without roughness.
Single-phase limits and zero-flow/zero-length handling are local extensions.
Friedel is not evaluated for gas viscosity greater than liquid viscosity;
high viscosity ratio and downflow are flagged. Inclined LM results and ignored
roughness are flagged. These warnings do not establish applicability.

Additional scientific references:
- Friedel (1979), *Improved Friction Pressure Drop Correlations for Horizontal
  and Vertical Two-Phase Pipe Flow*, European Two Phase Flow Group Meeting.
- Müller-Steinhagen & Heck (1986), *A Simple Friction Pressure Drop Correlation
  for Two-Phase Flow in Pipes*, https://doi.org/10.1016/0255-2701(86)80008-3.
- Lockhart & Martinelli (1949), *Proposed correlation of data for isothermal
  two-phase, two-component flow in pipes*, Chemical Engineering Progress 45,
  39–48; Chisholm (1967), https://doi.org/10.1016/0017-9310(67)90047-6.

Local changes: application units and result fields; existing Darcy/Colebrook
friction helper (including its transition interpolation); no-slip mixture K
approximation for fittings; input validation; single-phase and zero-flow
handling; rejection of nonphysical holdup, changing quality and invalid outlet
pressure. Unlike Fluids, the local implementation does not cap the friction
exponent at 7; nonfinite pressure results are rejected. These differences mean
this is an adaptation, not a promise of identical results for every input.

The regression test includes upstream numerical fixtures for horizontal,
inclined and vertical cases. These check implementation agreement, not
engineering applicability to every fluid or pipe size.

Keep the copyright and full MIT notice in `app.js` and distribute
`LICENSE-Fluids.txt`, this notice and `licenses.html` with the site. Preserve the
license comment when minifying JavaScript. The MIT notice covers the adapted
Fluids portions; it does not relicense the whole project or grant rights to
publisher figures, paper text, or unrelated third-party assets.

Scientific reference: Beggs, H. D., and Brill, J. P. (1973), *A Study of Two-Phase
Flow in Inclined Pipes*, JPT 25(5), 607–617, https://doi.org/10.2118/4007-PA.
The revised regime boundaries are distinguished from the original published
map. Neither the authors, the publisher nor the Fluids maintainers endorse
this application.