ENV-44

Overflow rate

Clarifier surface overflow.

Reading speed

GoverningOverflow rate

Governing equation

v=Q/A

$Q \in \left[200, 20000\right]$

where

Q: Q (m³/d)
A: A (m²)
v: Overflow rate (m/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

v=Q/A

$Q \in \left[200, 20000\right]$

$Q = 200$ $v = 0.8$

Along the curve

②

Domain of the variable — blue

Q_{\min} = 200,\quad Q_{\max} = 20000

$Q \in \left[200, 20000\right]$

$Q = 200$ $Q = 200$

Along the curve

③

Response curve — green

v=Q/A

$Q \in \left[200, 20000\right]$

$Q = 200$ $v = 0.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}Q}

$Q \in \left[200, 20000\right]$

$Q = 324.5$ $v^{\prime} = 0.004$

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-44 — Overflow rate) is the form associated with Overflow rate. Working symbols: $Q$ , $A$ $\rightarrow$ $v$ . Clarifier surface overflow. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

v

from

Q

A

in Environmental via

v=Q/A

Clarifier surface overflow. 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 = 4000.000\,\mathrm{m^{3}/d}

A = 250.000\,\mathrm{m^{2}}

, the governing relation

v=Q/A

yields

v = 16.000\,\mathrm{m/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

Q Q4000 m³/dA A250 m²

Outputs

Overflow rate v16.000 m/d

Reading speed

Watch on YouTube

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Narration of this film

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

Clarifier surface overflow. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube