ENV-48

Hardness as CaCO3

Equivalent CaCO3 hardness.

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GoverningHardness as CaCO3

Governing equation

H=2.5\\,[Ca]+4.1\\,[Mg]

$Ca \in \left[1, 200\right]$

where

Ca: Ca (mg/L)
Mg: Mg (mg/L)
H: Hardness as CaCO3 (mg/L)

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

H=2.5\\,[Ca]+4.1\\,[Mg]

$Ca \in \left[1, 200\right]$

$Ca = 1$ $H = 51.7$

Along the curve

②

Domain of the variable — blue

Ca_{\min} = 1,\quad Ca_{\max} = 200

$Ca \in \left[1, 200\right]$

$Ca = 1$ $Ca = 1$

Along the curve

③

Response curve — green

H=2.5\\,[Ca]+4.1\\,[Mg]

$Ca \in \left[1, 200\right]$

$Ca = 1$ $H = 51.7$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}H}{\mathrm{d}Ca}

$Ca \in \left[1, 200\right]$

$Ca = 2.252$ $H^{\prime} = 2.5$

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-48 — Hardness as CaCO3) is the form associated with Hardness as CaCO3. Working symbols: $Ca$ , $Mg$ $\rightarrow$ $H$ . Equivalent CaCO3 hardness. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

H

from

Ca

Mg

in Environmental via

H=2.5\\,[Ca]+4.1\\,[Mg]

Equivalent CaCO3 hardness. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Ca = 40.000\,\mathrm{mg/L}

Mg = 12.000\,\mathrm{mg/L}

, the governing relation

H=2.5\\,[Ca]+4.1\\,[Mg]

yields

H = 149.200\,\mathrm{mg/L}

. 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

Ca Ca40 mg/LMg Mg12 mg/L

Outputs

Hardness as CaCO3 H149.200 mg/L

Reading speed

Watch on YouTube

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Narration of this film

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

Equivalent CaCO3 hardness. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube