ENV-37

Chick–Watson disinfection

N/N0 = exp(−k C^n t). Chick first-order with Watson concentration power.

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KineticsChick–Watson

Governing equation

N/N_0=\exp(-k C^n t)

$t \in \left[1, 180\right]$

where

k: Rate k (L^n/(mg^n·min))
C: Residual (mg/L)
n: Watson n (—)
t: Contact time (min)
N/N_0: Survival ratio (—)

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

N/N_0=\exp(-k C^n t)

$t \in \left[1, 180\right]$

$t = 1$ $N/N_0 = 0.549$

Along the curve

②

Domain of the variable — blue

t_{\min} = 1,\quad t_{\max} = 180

$t \in \left[1, 180\right]$

$t = 1$ $t = 1$

Along the curve

③

Response curve — green

N/N_0=\exp(-k C^n t)

$t \in \left[1, 180\right]$

$t = 1$ $N/N_0 = 0.549$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}N/N_0}{\mathrm{d}t}

$t \in \left[1, 180\right]$

$t = 2.126$ $N/N_0^{\prime} = -0.181$

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-37 — Chick–Watson disinfection) is the form associated with Chick–Watson. Working symbols: $k$ , $C$ , $n$ , $t$ $\rightarrow$ $N/N_0$ . Chick observed exponential die-off; Watson made the rate a power of residual disinfectant. CT tables rest on this.

Purpose

Purpose: compute

N/N_0

from

k

C

n

t

in Environmental via

N/N_0=\exp(-k C^n t)

N/N0 = exp(−k C^n t). Chick first-order with Watson concentration power. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 0.500\,\mathrm{L^n/(mg^n·min)}

C = 1.200\,\mathrm{mg/L}

n = 1.000\,\mathrm{—}

t = 30.000\,\mathrm{min}

, the governing relation

N/N_0=\exp(-k C^n t)

yields

N/N_0 = 1.523e-8\,\mathrm{—}

. A contact tank, a decaying N, a CT product. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Rate k k0.5 L^n/(mg^n·min)Residual C1.2 mg/LWatson n n1 —Contact time t30 min

Outputs

Survival ratio N/N_00.0000 —

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Narration of this film

A contact tank, a decaying N, a CT product.

Chick observed exponential die-off; Watson made the rate a power of residual disinfectant. CT tables rest on this.

Reading speed

Watch on YouTube