ENV-46

Food-to-microorganism

Activated-sludge loading.

Reading speed

GoverningFood-to-microorganism

Governing equation

F/M=(S_0 Q)/(X V)

$X \in \left[500, 6000\right]$

where

S0: S0 (mg/L)
Q: Q (m³/d)
X: X (mg/L)
V: V (m³)
fm: Food-to-microorganism (1/d)

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

F/M=(S_0 Q)/(X V)

$X \in \left[500, 6000\right]$

$X = 500$ $fm = 2$

Along the curve

②

Domain of the variable — blue

X_{\min} = 500,\quad X_{\max} = 6000

$X \in \left[500, 6000\right]$

$X = 500$ $X = 500$

Along the curve

③

Response curve — green

F/M=(S_0 Q)/(X V)

$X \in \left[500, 6000\right]$

$X = 500$ $fm = 2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}fm}{\mathrm{d}X}

$X \in \left[500, 6000\right]$

$X = 534.6$ $fm^{\prime} = -0.004$

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-46 — Food-to-microorganism) is the form associated with Food-to-microorganism. Working symbols: $S0$ , $Q$ , $X$ , $V$ $\rightarrow$ $fm$ . Activated-sludge loading. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

fm

from

S0

Q

X

V

in Environmental via

F/M=(S_0 Q)/(X V)

Activated-sludge loading. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

S0 = 200.000\,\mathrm{mg/L}

Q = 4000.000\,\mathrm{m^{3}/d}

X = 2500.000\,\mathrm{mg/L}

V = 800.000\,\mathrm{m^{3}}

, the governing relation

F/M=(S_0 Q)/(X V)

yields

fm = 0.400\,\mathrm{1/d}

. 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

S0 S0200 mg/LQ Q4000 m³/dX X2500 mg/LV V800 m³

Outputs

Food-to-microorganism fm0.400 1/d

Reading speed

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Narration of this film

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

Activated-sludge loading. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube