ENV-45

Hydraulic retention

Reactor mean residence time.

Reading speed

GoverningHydraulic retention

Governing equation

\theta=V/Q

$Q \in \left[20, 4000\right]$

where

V: V (m³)
Q: Q (m³/d)
th: Hydraulic retention (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

\theta=V/Q

$Q \in \left[20, 4000\right]$

$Q = 20$ $th = 40$

Along the curve

②

Domain of the variable — blue

Q_{\min} = 20,\quad Q_{\max} = 4000

$Q \in \left[20, 4000\right]$

$Q = 20$ $Q = 20$

Along the curve

③

Response curve — green

\theta=V/Q

$Q \in \left[20, 4000\right]$

$Q = 20$ $th = 40$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}th}{\mathrm{d}Q}

$Q \in \left[20, 4000\right]$

$Q = 45.03$ $th^{\prime} = -0.571$

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-45 — Hydraulic retention) is the form associated with Hydraulic retention. Working symbols: $V$ , $Q$ $\rightarrow$ $th$ . Reactor mean residence time. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

th

from

V

Q

in Environmental via

\theta=V/Q

Reactor mean residence time. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

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

Q = 400.000\,\mathrm{m^{3}/d}

, the governing relation

\theta=V/Q

yields

th = 2.000\,\mathrm{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

V V800 m³Q Q400 m³/d

Outputs

Hydraulic retention th2.000 d

Reading speed

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Narration of this film

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

Reactor mean residence time. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube