CHE-36

Residence / space time

τ = V / v0. Space time based on inlet volumetric flow.

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ReactorsSpace time

Governing equation

\tau=V/v_0

$V \in \left[0.05, 40\right]$

where

V: Volume (m³)
v_0: Inlet flow (m³/h)
\tau: Space time (h)

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

\tau=V/v_0

$V \in \left[0.05, 40\right]$

$V = 0.05$ $\tau = 0.013$

Along the curve

②

Domain of the variable — blue

V_{\min} = 0.05,\quad V_{\max} = 40

$V \in \left[0.05, 40\right]$

$V = 0.05$ $V = 0.05$

Along the curve

③

Response curve — green

\tau=V/v_0

$V \in \left[0.05, 40\right]$

$V = 0.05$ $\tau = 0.013$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\tau}{\mathrm{d}V}

$V \in \left[0.05, 40\right]$

$V = 0.301$ $\tau^{\prime} = 0.25$

Along the curve

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-36 — Residence / space time) is the form associated with Space time. Working symbols: $V$ , $v_0$ $\rightarrow$ $\tau$ . Space time is the holding time of the feed volume. Mean residence time equals τ only for constant density.

Purpose

Purpose: compute

\tau

from

V

v_0

in Chemical engineering via

\tau=V/v_0

τ = V / v0. Space time based on inlet volumetric flow. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 2.000\,\mathrm{m^{3}}

v_0 = 4.000\,\mathrm{m^{3}/h}

, the governing relation

\tau=V/v_0

yields

\tau = 0.500\,\mathrm{h}

. A tank, a volume V, an inlet v0. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Volume V2 m³Inlet flow v_04 m³/h

Outputs

Space time \tau0.500 h

Reading speed

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Narration of this film

A tank, a volume V, an inlet v0.

Space time is the holding time of the feed volume. Mean residence time equals τ only for constant density.

Reading speed

Watch on YouTube