environmental-engineering-ai999x — offline, verified environmental engineering solver with step-by-step answers

Desktop app & command line · Compute in your browser · Install (Python) · Guides · Evaluation · AI999X on Hugging Face · Website · Support: Buy Me a Coffee

License: Apache-2.0 · Author: Ibnul Jaif Farabi (creator and engineer) · Organization: AI999X · Version 1.0.0

Field: Engineering · Tasks: Question Answering, Sentence Similarity, Feature Extraction

environmental-engineering-ai999x is an offline, deterministic Python solver that answers environmental engineering questions with verified results from 99 certified capabilities, gives 613 documented answers identically on Windows and Linux, and refuses rather than guesses when an answer cannot be verified.

environmental-engineering-ai999x is a compact, deterministic environmental engineering engine for Python. It reads a question in plain English (or a typed call), picks a certified environmental engineering capability, computes the answer exactly, checks it, and returns the result with its steps, units, LaTeX and assumptions — or an honest refusal that says what is missing. It runs fully offline on any CPU, needs no GPU, no API key and no internet, and is built to give zero wrong answers: when it is not sure, it refuses instead of guessing.

Run it your way. environmental-engineering-ai999x comes as the AI999X desktop app and as the command-line program environmental-engineering for Windows and Linux, runs in your browser as WebAssembly, and installs as a Python package. The desktop app, the command line and the browser run the same compiled Rust program on your own device: offline, no Python needed.

Get it

Way to run it	For	Get it
AI999X Environmental Engineering desktop app 1.2.0	Windows, Linux — this model in its own app: search, ask in words, forms, live figures, explanations, offline	Windows (x86-64) · Linux (x86-64)
AI999X desktop app 1.2.0	Windows, Linux — every AI999X model in one app: search, ask in words, forms, live figures, explanations, offline	Windows (x86-64) · Linux (x86-64)
Command line (environmental-engineering)	Windows, Linux — one program per model, offline, no Python	Windows (x86-64) · Linux (x86-64)
In your browser	any device — nothing to install	Compute on the model page
Python	Python 3.10+	pip install environmental-engineering-ai999x

Checksums: SHA256SUMS · every version: https://www.ai999x.com/downloads/desktop/latest/ · install guide: desktop & command line

Rust versions

Environmental Engineering also comes as native programs compiled from Rust, version 1.2.0 of the AI999X desktop app and command line: they run offline on your computer and need no Python. Each file is in this repository's rust/ folder, on the GitHub release v1.0.0 and on the website.

Program	System	File	Size	Download	Use
Desktop app (Environmental Engineering)	Windows x86-64	ai999x-environmental-engineering-1.2.0-windows-x86_64.zip	7.2 MB	Hub · GitHub · website	unzip, then double-click ai999x-environmental-engineering.exe (no installer)
Desktop app (Environmental Engineering)	Linux x86-64	ai999x-environmental-engineering-1.2.0-linux-x86_64.tar.gz	8.2 MB	Hub · GitHub · website	extract, then run ./ai999x-environmental-engineering (X11 or Wayland desktop)
Command line (environmental-engineering)	Windows x86-64	ai999x-environmental-engineering-cli-1.2.0-windows-x86_64.zip	3.0 MB	Hub · GitHub · website (all models)	unzip, then environmental-engineering.exe ask "<question>" or environmental-engineering.exe solve <capability> name=value
Command line (environmental-engineering)	Linux x86-64	ai999x-environmental-engineering-cli-1.2.0-linux-x86_64.tar.gz	2.9 MB	Hub · GitHub · website (all models)	extract, then ./environmental-engineering ask "<question>" or ./environmental-engineering solve <capability> name=value

The command-line archive holds environmental-engineering with a README of its commands and examples, the licence and the notice. Checksums: rust/SHA256SUMS (sha256sum -c SHA256SUMS).

Quick start

Desktop app

Download AI999X Environmental Engineering for your system (above), unpack it and start it; type a question in words or pick a capability, fill in the form and press Compute. Figures and an explanation of the answer appear beside it. The AI999X desktop app has the same, with Environmental Engineering among all AI999X models.

Linux, from a terminal:

curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/ai999x-environmental-engineering-1.2.0-linux-x86_64.tar.gz
curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/SHA256SUMS
sha256sum -c --ignore-missing SHA256SUMS
tar xzf ai999x-environmental-engineering-1.2.0-linux-x86_64.tar.gz
./ai999x-environmental-engineering-1.2.0-linux-x86_64/ai999x-environmental-engineering

Command line

Linux:

curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/ai999x-cli-1.2.0-linux-x86_64.tar.gz
curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/SHA256SUMS
sha256sum -c --ignore-missing SHA256SUMS
mkdir -p ~/.local/share && tar xzf ai999x-cli-1.2.0-linux-x86_64.tar.gz -C ~/.local/share
echo 'export PATH="$HOME/.local/share/ai999x-cli-1.2.0-linux-x86_64:$PATH"' >> ~/.bashrc && source ~/.bashrc
environmental-engineering --version

Windows (PowerShell):

$F = "ai999x-cli-1.2.0-windows-x86_64.zip"
Invoke-WebRequest "https://www.ai999x.com/downloads/desktop/1.2.0/$F" -OutFile $F
Invoke-WebRequest "https://www.ai999x.com/downloads/desktop/1.2.0/SHA256SUMS" -OutFile SHA256SUMS
(Get-FileHash $F -Algorithm SHA256).Hash.ToLower() -eq ((Select-String -SimpleMatch $F SHA256SUMS).Line -split ' ')[0]
Expand-Archive $F -DestinationPath "$env:LOCALAPPDATA\AI999X" -Force
$D = "$env:LOCALAPPDATA\AI999X\ai999x-cli-1.2.0-windows-x86_64"; $env:Path += ";$D"
[Environment]::SetEnvironmentVariable("Path", [Environment]::GetEnvironmentVariable("Path", "User") + ";$D", "User")
environmental-engineering --version

Every command below was run as shown; the text under it is what the program printed.

Ask in words — Write the question as you would say it: the program reads the quantities and their units, picks the capability and answers.

$ environmental-engineering ask "Streeter-Phelps oxygen deficit: kd = 0.23 1/d, ka = 0.46 1/d, L0 = 10 mg/L, D0 = 1 mg/L, t = 2 d, DOsat = 9.1 mg/L"
Read as: Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time
D = 0.002726165085 kg/m^3
DO = 0.006373834915 kg/m^3
D_mgL = 2.726165085
DO_mgL = 6.373834915
  by: Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time  (D = kd L0/(ka - kd) (e^(-kd t) - e^(-ka t)) + D0 e^(-ka t); for ka = kd, D = (kd L0 t + D0) e^(-kd t))
  D0 = 0.001 kg/m^3
  DOsat = 0.0091 kg/m^3
  L0 = 0.01 kg/m^3
  ka = 5.324074074e-06 1/s
  kd = 2.662037037e-06 1/s
  t = 172800 s
  assumes: first-order deoxygenation and reaeration; plug flow; deficit stays below saturation

What a capability needs — The equation or method, every input and output with its SI unit. Read this before solve: it tells you the input names.

$ environmental-engineering info enveng_streeter_phelps_deficit
Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time
  D = kd L0/(ka - kd) (e^(-kd t) - e^(-ka t)) + D0 e^(-ka t); for ka = kd, D = (kd L0 t + D0) e^(-kd t)
  in   kd       deoxygenation rate constant [1/s]
  in   ka       reaeration rate constant [1/s]
  in   L0       ultimate BOD of the mixed river water at the outfall [kg/m^3]
  in   D0       oxygen deficit at the outfall (DOsat - DO) [kg/m^3]
  in   t        travel time from the outfall [s]
  in   DOsat    saturation dissolved oxygen [kg/m^3]
  out  D        oxygen deficit at t [kg/m^3]
  out  DO       dissolved oxygen at t [kg/m^3]
  out  D_mgL    deficit in mg/L []
  out  DO_mgL   dissolved oxygen in mg/L []

Solve — Inputs as name=value, each with any unit of the right kind. The answer lists every output, the method used, each input converted to SI, and the conditions the answer assumes.

$ environmental-engineering solve enveng_streeter_phelps_deficit "kd=0.23 1/day" "ka=0.46 1/day" "L0=10 mg/L" "D0=1 mg/L" "t=2 day" "DOsat=9.1 mg/L"
D = 0.002726165085 kg/m^3
DO = 0.006373834915 kg/m^3
D_mgL = 2.726165085
DO_mgL = 6.373834915
  by: Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time  (D = kd L0/(ka - kd) (e^(-kd t) - e^(-ka t)) + D0 e^(-ka t); for ka = kd, D = (kd L0 t + D0) e^(-kd t))
  kd = 2.662037037e-06 1/s
  ka = 5.324074074e-06 1/s
  L0 = 0.01 kg/m^3
  D0 = 0.001 kg/m^3
  t = 172800 s
  DOsat = 0.0091 kg/m^3
  assumes: first-order deoxygenation and reaeration; plug flow; deficit stays below saturation

Many questions at once — One JSON request per line in, one JSON answer per line out, in order: for scripts, notebooks and agents (the program starts once). In PowerShell: Get-Content cases.jsonl | environmental-engineering batch

cases.jsonl:

{"key": "enveng_streeter_phelps_deficit", "inputs": {"kd": "0.23 1/day", "ka": "0.46 1/day", "L0": "10 mg/L", "D0": "1 mg/L", "t": "2 day", "DOsat": "9.1 mg/L"}}
{"key": "enveng_briggs_plume_rise", "inputs": {"vs": "15 m/s", "d": "3 m", "Ts": "420 K", "Ta": "288 K", "u": "5 m/s", "hs": "100 m"}}

$ environmental-engineering batch < cases.jsonl
{"outcome":"SOLVED","message":"","value":0.00637383491469,"unit":"kg/m^3","solved_for":"DO","si":[["kd",2.662037037037037e-6],["ka",5.324074074074074e-6],["L0",0.01],["D0",0.001],["t",172800.0],["DOsat",0.0091]],"values":[["D",0.00272616508531,"kg/m^3"],["DO",0.00637383491469,"kg/m^3"],["D_mgL",2.72616508531,""],["DO_mgL",6.37383491469,""]],"target":"DO","phrase":"oxygen deficit at t","assumptions":["first-order deoxygenation and reaeration","plug flow","deficit stays below saturation"],"name":"Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time","equation":"D = kd L0/(ka - kd) (e^(-kd t) - e^(-ka t)) + D0 e^(-ka t); for ka = kd, D = (kd L0 t + D0) e^(-kd t)"}
{"outcome":"SOLVED","message":"","value":125.637535501,"unit":"m","solved_for":"dh","si":[["vs",15.0],["d",3.0],["Ts",420.0],["Ta",288.0],["u",5.0],["hs",100.0]],"values":[["F",104.0205375,""],["x_f",762.771747653,"m"],["dh",125.637535501,"m"],["H",225.637535501,"m"]],"target":"dh","phrase":"buoyancy flux, m^4/s^3","assumptions":["Ts > Ta","neutral or unstable air (classes A-D)","buoyancy-dominated plume"],"name":"Briggs plume rise and effective stack height (neutral or unstable air)","equation":"F = g vs d^2 (Ts - Ta)/(4 Ts); x_f = 49 F^(5/8) (F < 55) or 119 F^(2/5); dh = 1.6 F^(1/3) x_f^(2/3)/u"}

In your browser

Open Environmental Engineering on ai999x.com, choose a capability and press Compute: the model runs on your own device as WebAssembly; nothing is sent anywhere. Change any input (any unit of the right kind) and the answer, its explanation and the figures follow.

In your own page: environmental_engineering_ai999x.wasm and the loader ax-wasm.js (https://www.ai999x.com/compute/rust/ax-wasm.js).

Python

pip install environmental-engineering-ai999x

Worked examples in every form

The same worked example from the command line, from Python and in the browser. Each command-line output is what the program printed.

Box model of an air basin (well-mixed, time-dependent)

The concentration over a city treated as a well-mixed box: emission flux per area, wind through a box of length L under a mixing height, background air; the concentration after time t and at steady state.

Command line:

$ environmental-engineering solve enveng_box_model "q=4 ug/(m^2*s)" "L=15000 m" "u=3 m/s" "Hm=600 m" "Cb=20 ug/m^3" "C0=20 ug/m^3" "t=2 h"
C = 4.543574138e-08 kg/m^3
C_ss = 5.333333333e-08 kg/m^3
C_ugm3 = 45.43574138
  by: Box model of an air basin (well-mixed, time-dependent)  (dC/dt = q/Hm - u (C - Cb)/L, so C = Css + (C0 - Css) e^(-u t/L) with Css = Cb + q L/(u Hm))
  q = 4e-09 kg/(m^2*s)
  L = 15000 m
  u = 3 m/s
  Hm = 600 m
  Cb = 2e-08 kg/m^3
  C0 = 2e-08 kg/m^3
  t = 7200 s
  assumes: well-mixed box; constant wind, mixing height and emissions

Python:

import environmental_engineering_ai999x as m

a = m.solve("enveng_box_model", q="4 ug/(m^2*s)", L="15000 m", u="3 m/s", Hm="600 m", Cb="20 ug/m^3", C0="20 ug/m^3", t="2 h")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

Briggs dispersion coefficients sigma_y and sigma_z

The horizontal and vertical plume spreads (Pasquill-Gifford curves in Briggs' formulas) at a downwind distance for a stability class, open-country or urban.

Command line:

$ environmental-engineering solve enveng_briggs_dispersion_coefficients "x=1000 m" cls=d terrain=rural
sigma_y = 76.27700714 m
sigma_z = 37.94733192 m
  by: Briggs dispersion coefficients sigma_y and sigma_z  (Briggs (1973) interpolation formulas sigma = a x (1 + b x)^p for each class and terrain)
  x = 1000 m
  cls = d
  terrain = rural
  assumes: 100 m <= x <= 10 km

Python:

import environmental_engineering_ai999x as m

a = m.solve("enveng_briggs_dispersion_coefficients", x="1000 m", cls="d", terrain="rural")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

Briggs plume rise and effective stack height (neutral or unstable air)

The buoyancy flux, the final plume rise by Briggs' 2/3 law (neutral or unstable air) and the effective stack height.

Command line:

$ environmental-engineering solve enveng_briggs_plume_rise "vs=15 m/s" "d=3 m" "Ts=420 K" "Ta=288 K" "u=5 m/s" "hs=100 m"
F = 104.0205375
x_f = 762.7717477 m
dh = 125.6375355 m
H = 225.6375355 m
  by: Briggs plume rise and effective stack height (neutral or unstable air)  (F = g vs d^2 (Ts - Ta)/(4 Ts); x_f = 49 F^(5/8) (F < 55) or 119 F^(2/5); dh = 1.6 F^(1/3) x_f^(2/3)/u)
  vs = 15 m/s
  d = 3 m
  Ts = 420 K
  Ta = 288 K
  u = 5 m/s
  hs = 100 m
  assumes: Ts > Ta; neutral or unstable air (classes A-D); buoyancy-dominated plume

Python:

import environmental_engineering_ai999x as m

a = m.solve("enveng_briggs_plume_rise", vs="15 m/s", d="3 m", Ts="420 K", Ta="288 K", u="5 m/s", hs="100 m")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

Briggs plume rise in stable air

The final rise of a buoyant plume in stable air (classes E, F) from the buoyancy flux, wind speed and potential-temperature gradient, and the effective stack height.

Command line:

$ environmental-engineering solve enveng_briggs_stable_plume_rise "vs=15 m/s" "d=3 m" "Ts=420 K" "Ta=288 K" "u=4 m/s" "dtheta=0.02 K/m" "hs=100 m"
F = 104.0205375
s = 0.0006810173611
dh = 87.55352869 m
H = 187.5535287 m
  by: Briggs plume rise in stable air  (s = (g/Ta) dtheta/dz; dh = 2.6 (F/(u s))^(1/3))
  vs = 15 m/s
  d = 3 m
  Ts = 420 K
  Ta = 288 K
  u = 4 m/s
  dtheta = 0.02 K/m
  hs = 100 m
  assumes: Ts > Ta; stable air: dtheta/dz > 0

Python:

import environmental_engineering_ai999x as m

a = m.solve("enveng_briggs_stable_plume_rise", vs="15 m/s", d="3 m", Ts="420 K", Ta="288 K", u="4 m/s", dtheta="0.02 K/m", hs="100 m")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

Documentation

• Rust user guide — the command line, every capability with a command and what it printed: PDF · Markdown
• Python guide — every capability with a Python example: PDF · Markdown
• Desktop app & command line — downloads, install, ask and search, figures, offline use, checksums: https://www.ai999x.com/desktop-cli/
• Model page — compute in your browser, every capability explained: https://www.ai999x.com/models/environmental-engineering-ai999x/

Highlights

• Verified, not generated. Every answer is computed by a certified environmental engineering capability and checked (substituted back, dimension-checked or compared with an independent computation) before it is returned.
• Zero wrong answers by design. Seven explicit outcomes — SOLVED, NEEDS_INPUT, AMBIGUOUS, INVALID_INPUT, OUT_OF_SCOPE, UNRECOGNIZED_FORMAT, INTERNAL_ERROR — never a silent guess. Every one of its 613 documented answers is reproduced exactly on every tested platform.
• Plain-English questions and a guaranteed typed interface. ask() reads documented question forms; solve(capability_id, **inputs) always solves a supported task with valid inputs.
• Explains itself. Steps, formulas in LaTeX, units, assumptions and the model used, ready for notebooks, tutoring apps and homework checkers.
• Native and in the browser. Every capability also computes natively in Rust: the desktop app and the environmental-engineering command line for Windows and Linux, and WebAssembly on the model page — no Python, no network.
• Small and portable. Pure Python (sympy, mpmath); identical answers on Windows and Linux (Python 3.10, 3.11, 3.12, 3.13, 3.14).
• Coverage: air pollution dispersion, water quality, water and wastewater treatment, gas transfer, noise and solid waste.

Model overview

Property	Value
Package	environmental-engineering-ai999x 1.0.0 (import environmental_engineering_ai999x)
Type	Deterministic neuro-symbolic environmental engineering engine (rule-based reading + certified symbolic capabilities)
Capabilities	99 certified procedures
Knowledge pack	version 1.0.0
Golden answers	613 documented answers, identical on every tested platform
Platforms tested	Windows (Python 3.13), Linux x86-64 (Python 3.10, 3.11, 3.12, 3.13, 3.14)
Runtime	CPU only, offline; no GPU, no network, no API key
License	Apache-2.0
Creator / engineer	Ibnul Jaif Farabi
Organization	AI999X

Python quick start

pip install environmental-engineering-ai999x
# or straight from this repository:
pip install https://huggingface.co/AI999X/environmental-engineering-ai999x/resolve/main/dist/environmental_engineering_ai999x-1.0.0-py3-none-any.whl

import environmental_engineering_ai999x as environmental_engineering

environmental_engineering.ask("Streeter-Phelps oxygen deficit: kd = 0.23 1/d, ka = 0.46 1/d, L0 = 10 mg/L, D0 = 1 mg/L, t = 2 d, DOsat = 9.1 mg/L").show()
# -> SOLVED — D = 0.00272617, DO = 0.00637383, D_mgL = 2.72617, DO_mgL = 6.37383  (enveng_streeter_phelps_deficit)
environmental_engineering.ask("Briggs plume rise: vs = 15 m/s, d = 3 m, Ts = 420 K, Ta = 288 K, u = 5 m/s, hs = 100 m").show()
# -> SOLVED — F = 104.021, x_f = 762.772, dh = 125.638, H = 225.638  (enveng_briggs_plume_rise)
environmental_engineering.solve("enveng_gaussian_plume_concentration", Q=0.1, u=4.0, sigma_y=60.0, sigma_z=30.0, H=50.0, y=20.0, z=0.0).show()
# -> SOLVED — C = 1.04281e-06, C_ugm3 = 1042.81  (enveng_gaussian_plume_concentration)
environmental_engineering.ask("Activated sludge complete-mix design: Y = 0.5, k = 5 1/d, Ks = 60 mg/L, kd = 0.06 1/d, SRT = 10 d, HRT = 6 h, S0 = 250 mg/L").show()
# -> SOLVED — S = 0.00410256, S_mgL = 4.10256, X = 3.07372, X_mgL = 3073.72  (enveng_activated_sludge_cstr_design)
environmental_engineering.solve("enveng_decibel_addition", L=[85.0, 85.0, 90.0]).show()
# -> SOLVED — L_total = 92.1284  (enveng_decibel_addition)
environmental_engineering.ask("Who created you?").message
# -> environmental-engineering-ai999x was created and engineered by Ibnul Jaif Farabi at AI999X.

The Python package also installs a Python command, environmental-engineering-ai999x "<question>"; for the native program use environmental-engineering (above). The outputs above were produced by running this exact code on environmental-engineering-ai999x 1.0.0.

How every answer is verified

1. Reading — the question is turned into typed quantities (value, unit, kind, role) and one asked quantity; every stated number must be used or the question is refused.
2. Planning — only certified capabilities may answer; a capability applies only under the conditions the wording states (for example a pendulum, a liquid at rest, boiling).
3. Computing — exact symbolic or high-precision numeric evaluation.
4. Checking — dimensions, substitution back into the defining equation, and agreement between independent readings; any disagreement becomes a refusal, never a number.

Capabilities are certified before they ship: each must reproduce hand-worked reference cases, reject a deliberately wrong variant (a control), and leave every benchmark answer unchanged.

Python worked examples, with their steps

Each question was put to environmental-engineering-ai999x; the answer is the one it returned, with the steps it took.

Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time · Water quality

Streeter-Phelps oxygen deficit: kd = 0.23 1/d, ka = 0.46 1/d, L0 = 10 mg/L, D0 = 1 mg/L, t = 2 d, DOsat = 9.1 mg/L

→ D = 0.002726165085 kg/m^3, DO = 0.006373834915 kg/m^3, D_mgL = 2.726165085, DO_mgL = 6.373834915

Steps

• Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time: kd = 0.23 1/day, ka = 0.46 1/day, L0 = 10 mg/L, D0 = 1 mg/L, t = 2 day, DOsat = 9.1 mg/L → D = 0.002726165085 kg/m^3, DO = 0.006373834915 kg/m^3, D_mgL = 2.726165085 kg/m^3, DO_mgL = 6.373834915 kg/m^3

Briggs plume rise and effective stack height (neutral or unstable air) · Air pollution

Briggs plume rise: vs = 15 m/s, d = 3 m, Ts = 420 K, Ta = 288 K, u = 5 m/s, hs = 100 m

→ F = 104.0205375, x_f = 762.7717477 m, dh = 125.6375355 m, H = 225.6375355 m

Steps

• Briggs plume rise and effective stack height (neutral or unstable air): vs = 15 m/s, d = 3 m, Ts = 420 K, Ta = 288 K, u = 5 m/s, hs = 100 m → F = 104.0205375 m, x_f = 762.7717477 m, dh = 125.6375355 m, H = 225.6375355 m

Gaussian plume concentration at a receptor (ground reflection) · Air pollution

m.solve("enveng_gaussian_plume_concentration", Q=0.1, u=4.0, sigma_y=60.0, sigma_z=30.0, H=50.0, y=20.0, z=0.0)

→ C = 1.042805659e-06 kg/m^3, C_ugm3 = 1042.805659

Steps

• Gaussian plume concentration at a receptor (ground reflection): Q = 0.1 kg/s, u = 4 m/s, sigma_y = 60 m, sigma_z = 30 m, H = 50 m, y = 20 m, z = 0 m → C = 1.042805659e-06 kg/m^3, C_ugm3 = 1042.805659 kg/m^3

Activated sludge (complete mix) effluent substrate and biomass (Lawrence-McCarty) · Wastewater

Activated sludge complete-mix design: Y = 0.5, k = 5 1/d, Ks = 60 mg/L, kd = 0.06 1/d, SRT = 10 d, HRT = 6 h, S0 = 250 mg/L

→ S = 0.004102564103 kg/m^3, S_mgL = 4.102564103, X = 3.073717949 kg/m^3, X_mgL = 3073.717949, Y_obs = 0.3125

Steps

• Activated sludge (complete mix) effluent substrate and biomass (Lawrence-McCarty): Y = 0.5, k = 5 1/day, Ks = 60 mg/L, kd = 0.06 1/day, SRT = 10 day, HRT = 6 h, S0 = 250 mg/L → S = 0.004102564103 kg/m^3, S_mgL = 4.102564103 kg/m^3, X = 3.073717949 kg/m^3, X_mgL = 3073.717949 kg/m^3, Y_obs = 0.3125 kg/m^3

Adding sound levels in decibels · Noise

m.solve("enveng_decibel_addition", L=[85.0, 85.0, 90.0])

→ L_total = 92.1284136

Steps

• Adding sound levels in decibels: L = [85, 85, 90] → L_total = 92.1284136

Packed-tower air stripping: stripping factor, transfer units and height · Gas transfer

Air stripping tower: Qw = 0.05 m^3/s, Qa = 1.5 m^3/s, H = 0.2, Cin = 200 ug/L, Cout = 5 ug/L, HTU = 1 m

→ R = 6, NTU = 4.213854527, Z = 4.213854527 m, air_to_water_min = 4.875

Steps

• Packed-tower air stripping: stripping factor, transfer units and height: Qw = 0.05 m^3/s, Qa = 1.5 m^3/s, H = 0.2, Cin = 200 ug/L, Cout = 5 ug/L, HTU = 1 m → R = 6 m, NTU = 4.213854527 m, Z = 4.213854527 m, air_to_water_min = 4.875 m

Figures

Every point was computed by environmental-engineering-ai999x.

Briggs plume rise and effective stack height (neutral or unstable air)

dh (plume rise) against vs (stack gas exit velocity), with Ta = 288 K, Ts = 420 K, d = 3 m, hs = 100 m, u = 5 m/s. 31 points computed by environmental-engineering-ai999x; marked: vs = 15, dh = 125.638 m.

Packed-tower air stripping: stripping factor, transfer units and height

Z (packed height HTU NTU) against Qw (water flow), with Cin = 2.00e-4 kg/m^3, Cout = 5.00e-6 kg/m^3, H = 0.2, HTU = 1 m, Qa = 1.5 m^3/s. 31 points computed by environmental-engineering-ai999x; marked: Qw = 0.05, Z = 4.21385 m.

Activated sludge (complete mix) effluent substrate and biomass (Lawrence-McCarty)

S (effluent soluble substrate) against Y (true yield coefficient, kg VSS per kg BOD), with HRT = 21600 s, Ks = 0.06 kg/m^3, S0 = 0.25 kg/m^3, SRT = 8.64e5 s, k = 5.79e-5 1/s, kd = 6.94e-7 1/s. 31 points computed by environmental-engineering-ai999x; marked: Y = 0.5, S = 0.00410256 kg/m^3.

Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time

DO (dissolved oxygen at t) against kd (deoxygenation rate constant), with D0 = 0.001 kg/m^3, DOsat = 0.0091 kg/m^3, L0 = 0.01 kg/m^3, ka = 5.32e-6 1/s, t = 1.73e5 s. 31 points computed by environmental-engineering-ai999x; marked: kd = 2.66204e-06, DO = 0.00637383 kg/m^3.

Capabilities

99 certified procedures. A few of them:

• Procedures: Activated carbon dose from the Freundlich isotherm; Activated sludge (complete mix) effluent substrate and biomass (Lawrence-McCarty); Adding sound levels in decibels; Adsorbent dose from the Langmuir isotherm; BOD exerted after a time (first-order); BOD from a dilution test (with optional seed correction); BOD rate constant and ultimate BOD fitted to BOD data; Box model of an air basin (well-mixed, time-dependent); Briggs dispersion coefficients sigma_y and sigma_z; Briggs plume rise and effective stack height (neutral or unstable air); Briggs plume rise in stable air; Chlorine dose and feed rate; Clean-bed head loss through a granular filter (Ergun / Carman-Kozeny); Concentration after mixing a discharge with a river; Concentration in a well-mixed lake over time; Critical (minimum) dissolved oxygen of the oxygen sag; Cyclone cut diameter and fractional efficiency (Lapple); Day-night (Ldn) and day-evening-night (Lden) sound levels; Disinfection CT value of a contact basin; Disinfection by the Chick-Watson law; Dissolved concentration in equilibrium with a gas (Henry's law); Dissolved oxygen at a distance downstream (Streeter-Phelps); Dissolved oxygen during aeration and the transfer rate; Dissolved oxygen saturation concentration (Benson-Krause) …

environmental_engineering_ai999x.templates() lists every question form ask() reads; the capability guide (PDF, every example executed) is included in this repository.

All 99 formulas

Show every formula, by topic

Air pollution / Gaussian plume

Gaussian plume concentration at a receptor (ground reflection)

$$C=\frac{Q}{2\pi u{\sigma }_y{\sigma }_z}{e}^{-\frac{y^2}{2{\sigma }_y^2}}[e^{-\frac{(z-H{)}^2}{2{\sigma }_z^2}}+e^{-\frac{(z+H{)}^2}{2{\sigma }_z^2}}]C\; =\; \backslash frac\{Q\}\{2\backslash pi\; u\backslash sigma\_y\backslash sigma\_z\}\; e^\{-\backslash frac\{y^2\}\{2\backslash sigma\_y^2\}\}\backslash left[e^\{-\backslash frac\{(z-H)^2\}\{2\backslash sigma\_z^2\}\}\; +\; e^\{-\backslash frac\{(z+H)^2\}\{2\backslash sigma\_z^2\}\}\backslash right]$$

Gaussian plume concentration from the stability class

$$C=\frac{Q}{2\pi u{\sigma }_y(x){\sigma }_z(x)}{e}^{-\frac{y^2}{2{\sigma }_y^2}}[e^{-\frac{(z-H{)}^2}{2{\sigma }_z^2}}+e^{-\frac{(z+H{)}^2}{2{\sigma }_z^2}}]C\; =\; \backslash frac\{Q\}\{2\backslash pi\; u\backslash sigma\_y(x)\backslash sigma\_z(x)\}\; e^\{-\backslash frac\{y^2\}\{2\backslash sigma\_y^2\}\}\backslash left[e^\{-\backslash frac\{(z-H)^2\}\{2\backslash sigma\_z^2\}\}\; +\; e^\{-\backslash frac\{(z+H)^2\}\{2\backslash sigma\_z^2\}\}\backslash right]$$

Gaussian plume trapped below an inversion lid (multiple reflections)

$$C=\frac{Q{e}^{-y^2\mathrm{/}2{\sigma }_y^2}}{2\pi u{\sigma }_y{\sigma }_z}\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}[e^{-\frac{(z-H+2nL{)}^2}{2{\sigma }_z^2}}+e^{-\frac{(z+H+2nL{)}^2}{2{\sigma }_z^2}}]C\; =\; \backslash frac\{Q\; e^\{-y^2/2\backslash sigma\_y^2\}\}\{2\backslash pi\; u\backslash sigma\_y\backslash sigma\_z\}\backslash sum\_\{n=-\backslash infty\}^\{\backslash infty\}\backslash left[e^\{-\backslash frac\{(z-H+2nL)^2\}\{2\backslash sigma\_z^2\}\}\; +\; e^\{-\backslash frac\{(z+H+2nL)^2\}\{2\backslash sigma\_z^2\}\}\backslash right]$$

Ground-level centreline concentration of a plume

$$C(x,0,0)=\frac{Q}{\pi u{\sigma }_y{\sigma }_z}\exp \text{\hspace{0.17em}⁣}(-\frac{H^2}{2{\sigma }_z^2})C(x,0,0)\; =\; \backslash frac\{Q\}\{\backslash pi\; u\backslash sigma\_y\backslash sigma\_z\}\backslash exp\backslash !\backslash left(-\backslash frac\{H^2\}\{2\backslash sigma\_z^2\}\backslash right)$$

Stack plume: effective height, dispersion and ground-level concentration

$$C=\frac{Q}{\pi u{\sigma }_y{\sigma }_z}\exp \text{\hspace{0.17em}⁣}(-\frac{(h_s+\mathrm{\Delta }h{)}^2}{2{\sigma }_z^2})C\; =\; \backslash frac\{Q\}\{\backslash pi\; u\backslash sigma\_y\backslash sigma\_z\}\backslash exp\backslash !\backslash left(-\backslash frac\{(h\_s\; +\; \backslash Delta\; h)^2\}\{2\backslash sigma\_z^2\}\backslash right)$$

Air pollution / atmospheric stability

Pasquill-Turner atmospheric stability class

$$\text{class}=T(u,\text{ insolation or cloud cover})\backslash text\{class\}\; =\; T(u,\backslash \; \backslash text\{insolation\; or\; cloud\; cover\})$$

Air pollution / box model

Box model of an air basin (well-mixed, time-dependent)

$$C(t)=C_{ss}+(C_0-C_{ss})e^{-ut\mathrm{/}L},C_{ss}=C_b+\frac{qL}{u{H}_m}C(t)\; =\; C\_\{ss\}\; +\; (C\_0\; -\; C\_\{ss\})e^\{-ut/L\},\backslash quad\; C\_\{ss\}\; =\; C\_b\; +\; \backslash frac\{qL\}\{uH\_m\}$$

Air pollution / concentration units

Gas concentration: mass concentration to ppm (by volume)

$$\text{ppm}=\frac{CRT}{PM}\times {10}^6\backslash text\{ppm\}\; =\; \backslash frac\{C\; R\; T\}\{P\; M\}\backslash times10^\{6\}$$

Gas concentration: ppm (by volume) to mass concentration

$$C=\text{ppm}\times {10}^{-6}\frac{PM}{RT}C\; =\; \backslash text\{ppm\}\backslash times10^\{-6\}\backslash ,\backslash frac\{P\; M\}\{R\; T\}$$

Air pollution / dispersion coefficients

Briggs dispersion coefficients sigma_y and sigma_z

$${\sigma }_y=\frac{a_{y}x}{\sqrt{1+b_{y}x}},{\sigma }_z=a_{z}x(1+b_{z}x{)}^{p_z}\backslash sigma\_y\; =\; \backslash frac\{a\_y\; x\}\{\backslash sqrt\{1\; +\; b\_y\; x\}\},\backslash quad\; \backslash sigma\_z\; =\; a\_z\; x\backslash ,(1\; +\; b\_z\; x)^\{p\_z\}$$

Air pollution / emissions

Sulfur dioxide emission from fuel sulfur

$$E={\dot{m}}_{fuel}S\frac{M_{S{O}_2}}{M_S}(1-\eta )E\; =\; \backslash dot\; m\_\{fuel\}\backslash ,S\backslash ,\backslash frac\{M\_\{SO\_2\}\}\{M\_S\}(1-\backslash eta)$$

Air pollution / maximum concentration

Maximum ground-level concentration (constant sigma_y/sigma_z)

$$C_{max}=\frac{2Q}{\pi eu{H}^2}\frac{{\sigma }_z}{{\sigma }_y},{\sigma }_z=\frac{H}{\sqrt{2}}C\_\{max\}\; =\; \backslash frac\{2Q\}\{\backslash pi\; e\backslash ,u\; H^2\}\backslash frac\{\backslash sigma\_z\}\{\backslash sigma\_y\},\backslash quad\; \backslash sigma\_z\; =\; \backslash frac\{H\}\{\backslash sqrt\; 2\}$$

Maximum ground-level concentration and its distance (Briggs coefficients)

$$\frac{d\ln C}{dx}=-\frac{{\sigma }_y^{\mathrm{\prime }}}{{\sigma }_y}+\frac{{\sigma }_z^{\mathrm{\prime }}}{{\sigma }_z}(\frac{H^2}{{\sigma }_z^2}-1)=0\backslash frac\{d\backslash ln\; C\}\{dx\}\; =\; -\backslash frac\{\backslash sigma\_y\text{'}\}\{\backslash sigma\_y\}\; +\; \backslash frac\{\backslash sigma\_z\text{'}\}\{\backslash sigma\_z\}\backslash left(\backslash frac\{H^2\}\{\backslash sigma\_z^2\}\; -\; 1\backslash right)\; =\; 0$$

Air pollution / particulate control

Cyclone cut diameter and fractional efficiency (Lapple)

$$d_{50}=\sqrt{\frac{9\mu W}{2\pi N_e{V}_i({\rho }_p-{\rho }_g)}},\eta =\frac{1}{1+(d_{50}\mathrm{/}{d}_p{)}^2}d\_\{50\}\; =\; \backslash sqrt\{\backslash frac\{9\backslash mu\; W\}\{2\backslash pi\; N\_e\; V\_i(\backslash rho\_p\; -\; \backslash rho\_g)\}\},\backslash quad\; \backslash eta\; =\; \backslash frac\{1\}\{1\; +\; (d\_\{50\}/d\_p)^2\}$$

Electrostatic precipitator efficiency (Deutsch-Anderson)

$$\eta =1-e^{-wA\mathrm{/}Q}\backslash eta\; =\; 1\; -\; e^\{-wA/Q\}$$

Electrostatic precipitator plate area for a target efficiency

$$A=-\frac{Q}{w}\ln (1-\eta )A\; =\; -\backslash frac\{Q\}\{w\}\backslash ln(1-\backslash eta)$$

Gravity settling chamber collection efficiency

$$\eta =\frac{v_{t}LWN}{Q},v_t=\frac{g({\rho }_p-{\rho }_g)d_p^2}{18\mu }\backslash eta\; =\; \backslash frac\{v\_t\; L\; W\; N\}\{Q\},\backslash quad\; v\_t\; =\; \backslash frac\{g(\backslash rho\_p\; -\; \backslash rho\_g)d\_p^2\}\{18\backslash mu\}$$

Air pollution / plume rise

Briggs plume rise and effective stack height (neutral or unstable air)

$$F=\frac{g{v}_s{d}^2(T_s-T_a)}{4T_s},\mathrm{\Delta }h=\frac{1.6F^{1\mathrm{/}3}{x}_f^{2\mathrm{/}3}}{u}F\; =\; \backslash frac\{g\; v\_s\; d^2\; (T\_s\; -\; T\_a)\}\{4T\_s\},\backslash quad\; \backslash Delta\; h\; =\; \backslash frac\{1.6F^\{1/3\}x\_f^\{2/3\}\}\{u\}$$

Briggs plume rise in stable air

$$\mathrm{\Delta }h=2.6{\left(\frac{F}{us}\right)}^{1\mathrm{/}3},s=\frac{g}{T_a}\frac{\mathrm{\partial }\theta }{\mathrm{\partial }z}\backslash Delta\; h\; =\; 2.6\backslash left(\backslash frac\{F\}\{u\; s\}\backslash right)^\{1/3\},\backslash quad\; s\; =\; \backslash frac\{g\}\{T\_a\}\backslash frac\{\backslash partial\backslash theta\}\{\backslash partial\; z\}$$

Holland plume rise

$$\mathrm{\Delta }h=\frac{v_{s}d}{u}(1.5+2.68\times {10}^{-3}pd\frac{T_s-T_a}{T_s})\backslash Delta\; h\; =\; \backslash frac\{v\_s\; d\}\{u\}\backslash left(1.5\; +\; 2.68\backslash times10^\{-3\}\backslash ,p\backslash ,d\backslash ,\backslash frac\{T\_s\; -\; T\_a\}\{T\_s\}\backslash right)$$

Air pollution / wind profile

Wind speed at height (power law)

$$u_2=u_1{\left(\frac{z_2}{z_1}\right)}^{p}u\_2\; =\; u\_1\backslash left(\backslash frac\{z\_2\}\{z\_1\}\backslash right)^p$$

Gas transfer / Henry's law

Dissolved concentration in equilibrium with a gas (Henry's law)

$$C=\frac{p}{H}C\; =\; \backslash frac\{p\}\{H\}$$

Henry's law constant conversion between forms

$$H_{cc}=\frac{H_{pc}}{RT},H_{px}=H_{pc}{c}_w,H_{cp}=\frac{1}{H_{pc}}H\_\{cc\}\; =\; \backslash frac\{H\_\{pc\}\}\{RT\},\backslash quad\; H\_\{px\}\; =\; H\_\{pc\}\backslash ,c\_w,\backslash quad\; H\_\{cp\}\; =\; \backslash frac\{1\}\{H\_\{pc\}\}$$

Temperature dependence of Henry's constant (van 't Hoff)

$$H^{cp}(T)=H^{cp}(T_{ref})\exp \text{\hspace{0.17em}⁣}\left[B(\frac{1}{T}-\frac{1}{T_{ref}})\right]H^\{cp\}(T)\; =\; H^\{cp\}(T\_\{ref\})\backslash exp\backslash !\backslash left[B\backslash left(\backslash frac1T\; -\; \backslash frac\{1\}\{T\_\{ref\}\}\backslash right)\backslash right]$$

Gas transfer / air stripping

Packed-tower air stripping: stripping factor, transfer units and height

$$NTU=\frac{R}{R-1}\ln \text{\hspace{0.17em}⁣}\left[\frac{(C_{in}\mathrm{/}{C}_{out})(R-1)+1}{R}\right],Z=HTU\cdot NTUNTU\; =\; \backslash frac\{R\}\{R-1\}\backslash ln\backslash !\backslash left[\backslash frac\{(C\_\{in\}/C\_\{out\})(R-1)\; +\; 1\}\{R\}\backslash right],\backslash quad\; Z\; =\; HTU\backslash cdot\; NTU$$

Gas transfer / two-film theory

Overall liquid-phase transfer coefficient and flux (two-film theory)

$$\frac{1}{K_L}=\frac{1}{k_l}+\frac{1}{H{k}_g},N=K_L(C-\frac{C_g}{H})\backslash frac\{1\}\{K\_L\}\; =\; \backslash frac\{1\}\{k\_l\}\; +\; \backslash frac\{1\}\{Hk\_g\},\backslash quad\; N\; =\; K\_L\backslash left(C\; -\; \backslash frac\{C\_g\}\{H\}\backslash right)$$

Noise / community noise

Day-night (Ldn) and day-evening-night (Lden) sound levels

$$L_{dn}=10{\log }_{10}\frac{1}{24}(\sum _{day}{10}^{L_h\mathrm{/}10}+\sum _{night}{10}^{(L_h+10)\mathrm{/}10})L\_\{dn\}\; =\; 10\backslash log\_\{10\}\backslash frac\{1\}\{24\}\backslash left(\backslash sum\_\{day\}10^\{L\_h/10\}\; +\; \backslash sum\_\{night\}10^\{(L\_h+10)/10\}\backslash right)$$

Noise / decibel arithmetic

Adding sound levels in decibels

$$L=10{\log }_{10}\sum _i{10}^{L_i\mathrm{/}10}L\; =\; 10\backslash log\_\{10\}\backslash sum\_i\; 10^\{L\_i/10\}$$

Source level after removing background noise

$$L_s=10{\log }_{10}({10}^{L_t\mathrm{/}10}-{10}^{L_b\mathrm{/}10})L\_s\; =\; 10\backslash log\_\{10\}\backslash left(10^\{L\_t/10\}\; -\; 10^\{L\_b/10\}\backslash right)$$

Noise / exposure

Equivalent continuous sound level Leq

$$L_{eq}=10{\log }_{10}\frac{\sum _i{t}_i{10}^{L_i\mathrm{/}10}}{\sum _i{t}_i}L\_\{eq\}\; =\; 10\backslash log\_\{10\}\backslash frac\{\backslash sum\_i\; t\_i10^\{L\_i/10\}\}\{\backslash sum\_i\; t\_i\}$$

Noise / occupational exposure

Occupational noise dose and 8-hour TWA (OSHA, 5 dB exchange)

$$D=100\sum _i\frac{C_i}{T_i},T_i=\frac{8}{2^{(L_i-90)\mathrm{/}5}},TWA=16.61{\log }_{10}\frac{D}{100}+90D\; =\; 100\backslash sum\_i\backslash frac\{C\_i\}\{T\_i\},\backslash \; T\_i\; =\; \backslash frac\{8\}\{2^\{(L\_i-90)/5\}\},\backslash \; TWA\; =\; 16.61\backslash log\_\{10\}\backslash frac\{D\}\{100\}\; +\; 90$$

Noise / propagation

Sound level at another distance (point or line source)

$$L_2=L_1-20{\log }_{10}\frac{r_2}{r_1}\text{ (point)}L\_2\; =\; L\_1\; -\; 20\backslash log\_\{10\}\backslash frac\{r\_2\}\{r\_1\}\backslash \; \backslash text\{(point)\}$$

Sound pressure level from sound power level

$$L_p=L_W+10{\log }_{10}\frac{Q}{4\pi r^2}L\_p\; =\; L\_W\; +\; 10\backslash log\_\{10\}\backslash frac\{Q\}\{4\backslash pi\; r^2\}$$

Solid waste / energy recovery

Heating value of waste from its elemental composition (modified Dulong)

$$HHV=337C+1419(H-\frac{O}{8})+93S+23N[\mathrm{k}\mathrm{J}\mathrm{/}\mathrm{k}\mathrm{g},\mathrm{\%}]HHV\; =\; 337C\; +\; 1419\backslash left(H\; -\; \backslash frac\; O8\backslash right)\; +\; 93S\; +\; 23N\backslash \; \backslash \; [\backslash mathrm\{kJ/kg\},\backslash \; \backslash \%]$$

Solid waste / generation

Municipal solid waste generation and collection trucks

$$\dot{m}=Pr,n=\lceil \frac{\dot{m}}{\rho V_t}\rceil \backslash dot\; m\; =\; P\backslash ,r,\backslash quad\; n\; =\; \backslash left\backslash lceil\backslash frac\{\backslash dot\; m\}\{\backslash rho\; V\_t\}\backslash right\backslash rceil$$

Solid waste / landfill gas

Landfill methane generation (first-order decay, constant acceptance)

$$Q(t)={\int }_0^{\min (t,t_c)}k{L}_{0}M{e}^{-k(t-\tau )}d\tau =M{L}_0(e^{-k(t-\min (t,t_c))}-e^{-kt})Q(t)\; =\; \backslash int\_0^\{\backslash min(t,t\_c)\}\; kL\_0M\backslash ,e^\{-k(t-\backslash tau)\}d\backslash tau\; =\; ML\_0\backslash left(e^\{-k(t-\backslash min(t,t\_c))\}\; -\; e^\{-kt\}\backslash right)$$

Solid waste / landfills

Landfill life with daily cover and waste growth

$$n=\frac{\ln (1+\frac{Cg}{V_0})}{\ln (1+g)},V_0=\frac{M(1+c)}{\rho }n\; =\; \backslash frac\{\backslash ln\backslash left(1\; +\; \backslash frac\{C\; g\}\{V\_0\}\backslash right)\}\{\backslash ln(1+g)\},\backslash quad\; V\_0\; =\; \backslash frac\{M(1\; +\; c)\}\{\backslash rho\}$$

Solid waste / properties

Moisture content of mixed solid waste

$$M_{wet}=\frac{\sum m_i{w}_i}{\sum m_i}M\_\{wet\}\; =\; \backslash frac\{\backslash sum\; m\_iw\_i\}\{\backslash sum\; m\_i\}$$

Wastewater / activated sludge

Activated sludge (complete mix) effluent substrate and biomass (Lawrence-McCarty)

$$S=\frac{K_s(1+k_d{\theta }_c)}{{\theta }_c(Yk-k_d)-1},X=\frac{{\theta }_{c}Y(S_0-S)}{\theta (1+k_d{\theta }_c)}S\; =\; \backslash frac\{K\_s(1\; +\; k\_d\backslash theta\_c)\}\{\backslash theta\_c(Yk\; -\; k\_d)\; -\; 1\},\backslash quad\; X\; =\; \backslash frac\{\backslash theta\_c\; Y(S\_0\; -\; S)\}\{\backslash theta(1\; +\; k\_d\backslash theta\_c)\}$$

Food-to-microorganism ratio (F/M)

$$\frac{F}{M}=\frac{Q{S}_0}{VX}\backslash frac\; FM\; =\; \backslash frac\{QS\_0\}\{VX\}$$

Hydraulic retention time and volumetric organic loading

$$\theta =\frac{V}{Q},L_v=\frac{Q{S}_0}{V}\backslash theta\; =\; \backslash frac\; VQ,\backslash quad\; L\_v\; =\; \backslash frac\{QS\_0\}\{V\}$$

Minimum (washout) solids retention time

$$\frac{1}{{\theta }_{c,min}}=\frac{Yk{S}_0}{K_s+S_0}-k_d\backslash frac\{1\}\{\backslash theta\_\{c,min\}\}\; =\; \backslash frac\{YkS\_0\}\{K\_s\; +\; S\_0\}\; -\; k\_d$$

Oxygen requirement of an activated-sludge process

$${\dot{m}}_{O_2}=\frac{Q(S_0-S)}{f}-1.42P_x\backslash dot\; m\_\{O\_2\}\; =\; \backslash frac\{Q(S\_0\; -\; S)\}\{f\}\; -\; 1.42P\_x$$

Return activated sludge ratio

$$R=\frac{Q_r}{Q}=\frac{X}{X_r-X}R\; =\; \backslash frac\{Q\_r\}\{Q\}\; =\; \backslash frac\{X\}\{X\_r\; -\; X\}$$

Sludge volume index (SVI)

$$SVI=\frac{V_{30}}{MLSS}SVI\; =\; \backslash frac\{V\_\{30\}\}\{MLSS\}$$

Solids retention time (mean cell residence time)

$${\theta }_c=\frac{VX}{Q_w{X}_w+Q_e{X}_e}\backslash theta\_c\; =\; \backslash frac\{VX\}\{Q\_wX\_w\; +\; Q\_eX\_e\}$$

Waste biomass production (observed yield)

$$P_x=\frac{Y}{1+k_d{\theta }_c}Q(S_0-S)P\_x\; =\; \backslash frac\{Y\}\{1\; +\; k\_d\backslash theta\_c\}Q(S\_0\; -\; S)$$

Wastewater / aeration

Dissolved oxygen during aeration and the transfer rate

$$C=C_s-(C_s-C_0)e^{-K_{L}at}C\; =\; C\_s\; -\; (C\_s\; -\; C\_0)e^\{-K\_La\backslash ,t\}$$

Field (actual) oxygen transfer rate of an aeration system

$$AOTR=SOTR\alpha {\theta }^{T-20}\frac{\beta C_{s,T}F-C_L}{C_{s,20}}AOTR\; =\; SOTR\backslash ,\backslash alpha\backslash ,\backslash theta^\{T-20\}\backslash ,\backslash frac\{\backslash beta\; C\_\{s,T\}F\; -\; C\_L\}\{C\_\{s,20\}\}$$

KLa fitted to a reaeration test

$$\ln (C_s-C)=\ln (C_s-C_0)-K_{L}at\backslash ln(C\_s\; -\; C)\; =\; \backslash ln(C\_s\; -\; C\_0)\; -\; K\_La\backslash ,t$$

Overall oxygen transfer coefficient KLa from two DO readings

$$K_{L}a=\frac{\ln \frac{C_s-C_1}{C_s-C_2}}{t_2-t_1}K\_La\; =\; \backslash frac\{\backslash ln\backslash frac\{C\_s\; -\; C\_1\}\{C\_s\; -\; C\_2\}\}\{t\_2\; -\; t\_1\}$$

Wastewater / anaerobic treatment

Methane production from COD removed (anaerobic digestion)

$$Q_{C{H}_4}=\frac{\mathrm{C}\mathrm{O}\mathrm{D}-1.42P_x}{64\mathrm{g}\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}}\frac{RT}{P}Q\_\{CH\_4\}\; =\; \backslash frac\{\backslash mathrm\{COD\}\; -\; 1.42P\_x\}\{64\backslash \; \backslash mathrm\{g/mol\}\}\backslash ,\backslash frac\{RT\}\{P\}$$

Wastewater / attached growth

Trickling filter BOD removal efficiency (NRC equation)

$$E=\frac{100}{1+0.4432\sqrt{W\mathrm{/}(VF)}},F=\frac{1+R}{(1+R\mathrm{/}10{)}^2}E\; =\; \backslash frac\{100\}\{1\; +\; 0.4432\backslash sqrt\{W/(VF)\}\},\backslash quad\; F\; =\; \backslash frac\{1+R\}\{(1\; +\; R/10)^2\}$$

Wastewater / microbial kinetics

Monod specific growth rate

$$\mu =\frac{{\mu }_{max}S}{K_s+S}\backslash mu\; =\; \backslash frac\{\backslash mu\_\{max\}S\}\{K\_s\; +\; S\}$$

Wastewater / sludge handling

Sludge volume after thickening or dewatering

$$V_2=V_1\frac{P_1}{P_2}V\_2\; =\; V\_1\backslash frac\{P\_1\}\{P\_2\}$$

Volume of wet sludge from dry solids

$$V=\frac{M_s}{{\rho }_w{S}_{sl}{P}_s}V\; =\; \backslash frac\{M\_s\}\{\backslash rho\_w\; S\_\{sl\}\; P\_s\}$$

Water quality / BOD kinetics

BOD exerted after a time (first-order)

$$BO{D}_t=L_0(1-e^{-kt})BOD\_t\; =\; L\_0\backslash left(1\; -\; e^\{-kt\}\backslash right)$$

BOD rate constant and ultimate BOD fitted to BOD data

$$\underset{k,L_0}{\min }\sum _i{[y_i-L_0(1-e^{-k{t}_i})]}^2\backslash min\_\{k,L\_0\}\backslash sum\_i\backslash left[y\_i\; -\; L\_0\backslash left(1\; -\; e^\{-kt\_i\}\backslash right)\backslash right]^2$$

Temperature correction of a rate constant (theta model)

$$k_T=k_{20}{\theta }^{T-20}k\_T\; =\; k\_\{20\}\backslash ,\backslash theta^\{\backslash ,T\; -\; 20\}$$

Ultimate BOD from a BOD test

$$L_0=\frac{BO{D}_t}{1-e^{-kt}}L\_0\; =\; \backslash frac\{BOD\_t\}\{1\; -\; e^\{-kt\}\}$$

Water quality / BOD measurement

BOD from a dilution test (with optional seed correction)

$$BOD=\frac{(D_1-D_2)-(B_1-B_2)f}{P}BOD\; =\; \backslash frac\{(D\_1\; -\; D\_2)\; -\; (B\_1\; -\; B\_2)f\}\{P\}$$

Water quality / dissolved oxygen

Dissolved oxygen saturation concentration (Benson-Krause)

$$\ln C_s=-139.34411+\frac{1.575701\times {10}^5}{T}-\frac{6.642308\times {10}^7}{T^2}+\frac{1.2438\times {10}^{10}}{T^3}-\frac{8.621949\times {10}^{11}}{T^4}-S(\dots )\backslash ln\; C\_s\; =\; -139.34411\; +\; \backslash frac\{1.575701\backslash times10^5\}\{T\}\; -\; \backslash frac\{6.642308\backslash times10^7\}\{T^2\}\; +\; \backslash frac\{1.2438\backslash times10^\{10\}\}\{T^3\}\; -\; \backslash frac\{8.621949\backslash times10^\{11\}\}\{T^4\}\; -\; S(\backslash dots)$$

Water quality / lakes

Concentration in a well-mixed lake over time

$$C(t)=C_{ss}+(C_0-C_{ss})e^{-(Q\mathrm{/}V+k)t}C(t)\; =\; C\_\{ss\}\; +\; (C\_0\; -\; C\_\{ss\})e^\{-(Q/V\; +\; k)t\}$$

Steady-state concentration in a well-mixed lake (first-order decay)

$$C=\frac{W}{Q+kV}C\; =\; \backslash frac\{W\}\{Q\; +\; kV\}$$

Water quality / loads

Pollutant mass load of a flow

$$W=QCW\; =\; Q\backslash ,C$$

Water quality / mass balance

Concentration after mixing a discharge with a river

$$C=\frac{Q_w{C}_w+Q_r{C}_r}{Q_w+Q_r}C\; =\; \backslash frac\{Q\_w\; C\_w\; +\; Q\_r\; C\_r\}\{Q\_w\; +\; Q\_r\}$$

Flow-weighted mixing of several streams

$$C=\frac{\sum _i{Q}_i{C}_i}{\sum _i{Q}_i}C\; =\; \backslash frac\{\backslash sum\_i\; Q\_i\; C\_i\}\{\backslash sum\_i\; Q\_i\}$$

Water quality / oxygen demand

Theoretical oxygen demand of an organic compound

$$\text{ThOD}=\frac{(a+\frac{b}{4}-\frac{c}{2}-\frac{3d}{4})M_{O_2}}{M}\backslash text\{ThOD\}\; =\; \backslash frac\{\backslash left(a\; +\; \backslash frac\; b4\; -\; \backslash frac\; c2\; -\; \backslash frac\{3d\}\{4\}\backslash right)M\_\{O\_2\}\}\{M\}$$

Water quality / oxygen sag

Critical (minimum) dissolved oxygen of the oxygen sag

$$t_c=\frac{1}{k_a-k_d}\ln \text{\hspace{0.17em}⁣}\left[\frac{k_a}{k_d}(1-\frac{D_0(k_a-k_d)}{k_d{L}_0})\right],D_c=\frac{k_d}{k_a}{L}_0{e}^{-k_d{t}_c}t\_c\; =\; \backslash frac\{1\}\{k\_a\; -\; k\_d\}\backslash ln\backslash !\backslash left[\backslash frac\{k\_a\}\{k\_d\}\backslash left(1\; -\; \backslash frac\{D\_0(k\_a\; -\; k\_d)\}\{k\_d\; L\_0\}\backslash right)\backslash right],\backslash quad\; D\_c\; =\; \backslash frac\{k\_d\}\{k\_a\}L\_0e^\{-k\_d\; t\_c\}$$

Dissolved oxygen at a distance downstream (Streeter-Phelps)

$$D(x)=\frac{k_d{L}_0}{k_a-k_d}(e^{-k_{d}x\mathrm{/}v}-e^{-k_{a}x\mathrm{/}v})+D_0{e}^{-k_{a}x\mathrm{/}v}D(x)\; =\; \backslash frac\{k\_d\; L\_0\}\{k\_a\; -\; k\_d\}\backslash left(e^\{-k\_d\; x/v\}\; -\; e^\{-k\_a\; x/v\}\backslash right)\; +\; D\_0\; e^\{-k\_a\; x/v\}$$

Streeter-Phelps oxygen deficit and dissolved oxygen at a travel time

$$D=\frac{k_d{L}_0}{k_a-k_d}(e^{-k_{d}t}-e^{-k_{a}t})+D_0{e}^{-k_{a}t}D\; =\; \backslash frac\{k\_d\; L\_0\}\{k\_a\; -\; k\_d\}\backslash left(e^\{-k\_d\; t\}\; -\; e^\{-k\_a\; t\}\backslash right)\; +\; D\_0\; e^\{-k\_a\; t\}$$

Water quality / reaeration

Stream reaeration coefficient (O'Connor-Dobbins, Churchill, Owens-Gibbs)

$$k_a=\frac{3.93u^{0.5}}{H^{1.5}}\text{ (O’Connor-Dobbins)}k\_a\; =\; \backslash frac\{3.93\backslash ,u^\{0.5\}\}\{H^\{1.5\}\}\backslash \; \backslash text\{(O\text{'}Connor-Dobbins)\}$$

Water quality / rivers

First-order decay of a pollutant downstream (plug flow)

$$C=C_0{e}^{-kx\mathrm{/}u}C\; =\; C\_0\backslash ,e^\{-kx/u\}$$

Water treatment / adsorption

Activated carbon dose from the Freundlich isotherm

$$q_e=K{C}_e^{1\mathrm{/}n},\frac{m}{V}=\frac{C_0-C_e}{q_e}q\_e\; =\; K\; C\_e^\{1/n\},\backslash quad\; \backslash frac\{m\}\{V\}\; =\; \backslash frac\{C\_0\; -\; C\_e\}\{q\_e\}$$

Adsorbent dose from the Langmuir isotherm

$$q_e=\frac{q_{max}b{C}_e}{1+b{C}_e},\frac{m}{V}=\frac{C_0-C_e}{q_e}q\_e\; =\; \backslash frac\{q\_\{max\}bC\_e\}\{1\; +\; bC\_e\},\backslash quad\; \backslash frac\{m\}\{V\}\; =\; \backslash frac\{C\_0\; -\; C\_e\}\{q\_e\}$$

Freundlich isotherm constants fitted to adsorption data

$$\log q_e=\log K+\frac{1}{n}\log C_e\backslash log\; q\_e\; =\; \backslash log\; K\; +\; \backslash frac1n\backslash log\; C\_e$$

Langmuir isotherm constants fitted to adsorption data

$$\frac{C_e}{q_e}=\frac{1}{q_{max}b}+\frac{C_e}{q_{max}}\backslash frac\{C\_e\}\{q\_e\}\; =\; \backslash frac\{1\}\{q\_\{max\}b\}\; +\; \backslash frac\{C\_e\}\{q\_\{max\}\}$$

Water treatment / basin hydraulics

Hydraulic detention time

$$\theta =\frac{V}{Q}\backslash theta\; =\; \backslash frac\{V\}\{Q\}$$

Water treatment / disinfection

Chlorine dose and feed rate

$$\dot{m}=Q(\text{demand}+\text{residual}),{\dot{m}}_{product}=\frac{\dot{m}}{p}\backslash dot\; m\; =\; Q\backslash ,(\backslash text\{demand\}\; +\; \backslash text\{residual\}),\backslash quad\; \backslash dot\; m\_\{product\}\; =\; \backslash frac\{\backslash dot\; m\}\{p\}$$

Disinfection CT value of a contact basin

$$CT=C{t}_{10}=CBF\frac{V}{Q}CT\; =\; C\backslash ,t\_\{10\}\; =\; C\backslash ,BF\backslash ,\backslash frac\{V\}\{Q\}$$

Disinfection by the Chick-Watson law

$$\ln \frac{N}{N_0}=-k{C}^{n}t\backslash ln\backslash frac\{N\}\{N\_0\}\; =\; -k\backslash ,C^n\; t$$

Fraction of free chlorine as hypochlorous acid (pH)

$${\alpha }_{HOCl}=\frac{1}{1+{10}^{pH-p{K}_a}}\backslash alpha\_\{HOCl\}\; =\; \backslash frac\{1\}\{1\; +\; 10^\{\backslash ,pH\; -\; pK\_a\}\}$$

Log inactivation from the CT ratio

$$\text{log inactivation}=3\frac{C{t}_{10}}{C{T}_{99.9}}\backslash text\{log\; inactivation\}\; =\; 3\backslash ,\backslash frac\{C\; t\_\{10\}\}\{CT\_\{99.9\}\}$$

Log removal and percentage removal

$$LR={\log }_{10}\frac{N_0}{N}LR\; =\; \backslash log\_\{10\}\backslash frac\{N\_0\}\{N\}$$

Microbial inactivation by Chick's law (first order)

$$\frac{N}{N_0}=e^{-kt}\backslash frac\{N\}\{N\_0\}\; =\; e^\{-kt\}$$

Water treatment / filtration

Clean-bed head loss through a granular filter (Ergun / Carman-Kozeny)

$$\frac{h}{L}=\frac{150\mu (1-\epsilon {)}^{2}v}{\rho g{\epsilon }^3(\psi d{)}^2}+\frac{1.75(1-\epsilon )v^2}{g{\epsilon }^3\psi d}\backslash frac\{h\}\{L\}\; =\; \backslash frac\{150\backslash mu(1-\backslash varepsilon)^2\; v\}\{\backslash rho\; g\backslash varepsilon^3(\backslash psi\; d)^2\}\; +\; \backslash frac\{1.75(1-\backslash varepsilon)v^2\}\{g\backslash varepsilon^3\backslash psi\; d\}$$

Filter bed expansion during backwash

$${\epsilon }_e={\left(\frac{v_b}{v_s}\right)}^{0.22},L_e=\frac{L(1-\epsilon )}{1-{\epsilon }_e}\backslash varepsilon\_e\; =\; \backslash left(\backslash frac\{v\_b\}\{v\_s\}\backslash right)^\{0.22\},\backslash quad\; L\_e\; =\; \backslash frac\{L(1-\backslash varepsilon)\}\{1-\backslash varepsilon\_e\}$$

Filtration (hydraulic loading) rate with one filter out of service

$$v=\frac{Q}{NA},v^{\mathrm{\prime }}=\frac{Q}{(N-1)A}v\; =\; \backslash frac\{Q\}\{NA\},\backslash quad\; v\text{'}\; =\; \backslash frac\{Q\}\{(N-1)A\}$$

Water treatment / membranes

Membrane recovery, rejection, flux and concentrate

$$r=\frac{Q_p}{Q_f},R=1-\frac{C_p}{C_f},C_c=\frac{Q_f{C}_f-Q_p{C}_p}{Q_f-Q_p}r\; =\; \backslash frac\{Q\_p\}\{Q\_f\},\backslash \; R\; =\; 1\; -\; \backslash frac\{C\_p\}\{C\_f\},\backslash \; C\_c\; =\; \backslash frac\{Q\_fC\_f\; -\; Q\_pC\_p\}\{Q\_f\; -\; Q\_p\}$$

Osmotic pressure of a dilute solution (van 't Hoff)

$$\pi =i\frac{C}{M}RT\backslash pi\; =\; i\backslash ,\backslash frac\{C\}\{M\}\backslash ,RT$$

Water treatment / mixing and flocculation

Mean velocity gradient G (rapid mixing and flocculation)

$$G=\sqrt{\frac{P}{\mu V}}G\; =\; \backslash sqrt\{\backslash frac\{P\}\{\backslash mu\; V\}\}$$

Power needed for a target velocity gradient

$$P=G^2\mu VP\; =\; G^2\backslash mu\; V$$

Water treatment / sedimentation

Fraction of discrete particles removed in an ideal settling basin

$$R=\min (1,\frac{v_s}{v_0})R\; =\; \backslash min\backslash left(1,\; \backslash frac\{v\_s\}\{v\_0\}\backslash right)$$

Sedimentation basin sizing from overflow rate and detention time

$$A=\frac{Q}{v_0},V=Q\theta ,h=v_0\theta A\; =\; \backslash frac\{Q\}\{v\_0\},\backslash \; V\; =\; Q\backslash theta,\backslash \; h\; =\; v\_0\backslash theta$$

Stokes settling velocity of a discrete particle

$$v_s=\frac{g({\rho }_p-{\rho }_w)d^2}{18\mu }v\_s\; =\; \backslash frac\{g(\backslash rho\_p\; -\; \backslash rho\_w)d^2\}\{18\backslash mu\}$$

Surface overflow rate of a circular clarifier

$$v_0=\frac{Q}{\pi D^2\mathrm{/}4}v\_0\; =\; \backslash frac\{Q\}\{\backslash pi\; D^2/4\}$$

Terminal settling velocity in any flow regime (drag coefficient iteration)

$$v_t=\sqrt{\frac{4gd({\rho }_p-{\rho }_f)}{3C_D{\rho }_f}},C_D=\frac{24}{Re}+\frac{3}{\sqrt{Re}}+0.34v\_t\; =\; \backslash sqrt\{\backslash frac\{4g\; d(\backslash rho\_p\; -\; \backslash rho\_f)\}\{3C\_D\backslash rho\_f\}\},\backslash quad\; C\_D\; =\; \backslash frac\{24\}\{Re\}\; +\; \backslash frac\{3\}\{\backslash sqrt\{Re\}\}\; +\; 0.34$$

Weir loading rate of a circular clarifier

$$WL=\frac{Q}{\pi D}WL\; =\; \backslash frac\{Q\}\{\backslash pi\; D\}$$

Water treatment / water chemistry

Water hardness as CaCO3

$$TH=Ca\frac{50.04}{20.04}+Mg\frac{50.04}{12.15}TH\; =\; Ca\backslash ,\backslash frac\{50.04\}\{20.04\}\; +\; Mg\backslash ,\backslash frac\{50.04\}\{12.15\}$$

Out of scope

• Open-ended explanation, essay writing or tutoring dialogue: it is a solver, not a chatbot.
• Questions outside its certified environmental engineering capabilities, and any question whose stated numbers it cannot all use — it refuses with the reason instead.
• High-stakes engineering, medical or legal decisions without independent review.

Limitations

• It answers what its certified capabilities cover (air pollution dispersion, water quality, water and wastewater treatment, gas transfer, noise and solid waste); anything else is refused with a reason.
• ask() reads documented question forms and common phrasings; unusual wording may be refused — use solve() for guaranteed results.
• Results are as correct as the certified relations and their stated conditions; a certified relation is a checked model, not a claim about every physical situation.

Citation

@software{environmental_engineering_ai999x_1_0_0,
  title  = {environmental-engineering-ai999x: an offline, verified environmental engineering solver},
  author = {Farabi, Ibnul Jaif}, organization = {AI999X},
  year   = {2026}, version = {1.0.0},
  url    = {https://huggingface.co/AI999X/environmental-engineering-ai999x}
}

Contact

Questions, bug reports and requests: open a discussion on https://huggingface.co/AI999X/environmental-engineering-ai999x/discussions or visit https://ai999x.com.

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Created and engineered by Ibnul Jaif Farabi · AI999X · ai999x.com