ENV-41

Gaussian plume centreline

Ground-level Gaussian centreline.

Reading speed

GoverningGaussian plume centreline

Governing equation

C=\frac{Q}{\pi u\sigma_y\sigma_z}

$sy \in \left[10, 400\right]$

where

Q: Q (g/s)
u: u (m/s)
sy: sy (m)
sz: sz (m)
C: Gaussian plume centreline (mg/m³)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

C=\frac{Q}{\pi u\sigma_y\sigma_z}

$sy \in \left[10, 400\right]$

$sy = 10$ $C = 5.305$

Along the curve

②

Domain of the variable — blue

sy_{\min} = 10,\quad sy_{\max} = 400

$sy \in \left[10, 400\right]$

$sy = 10$ $sy = 10$

Along the curve

③

Response curve — green

C=\frac{Q}{\pi u\sigma_y\sigma_z}

$sy \in \left[10, 400\right]$

$sy = 10$ $C = 5.305$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}C}{\mathrm{d}sy}

$sy \in \left[10, 400\right]$

$sy = 12.45$ $C^{\prime} = -0.356$

Along the curve

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-41 — Gaussian plume centreline) is the form associated with Gaussian plume centreline. Working symbols: $Q$ , $u$ , $sy$ , $sz$ $\rightarrow$ $C$ . Ground-level Gaussian centreline. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

C

from

Q

u

sy

sz

in Environmental via

C=\frac{Q}{\pi u\sigma_y\sigma_z}

Ground-level Gaussian centreline. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Q = 20.000\,\mathrm{g/s}

u = 3.000\,\mathrm{m/s}

sy = 80.000\,\mathrm{m}

sz = 40.000\,\mathrm{m}

, the governing relation

C=\frac{Q}{\pi u\sigma_y\sigma_z}

yields

C = 0.663\,\mathrm{mg/m^{3}}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Q Q20 g/su u3 m/ssy sy80 msz sz40 m

Outputs

Gaussian plume centreline C0.663 mg/m³

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Ground-level Gaussian centreline. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube