CHE-42

kLa estimate

Aeration mass-transfer coefficient.

Reading speed

GoverningkLa estimate

Governing equation

k_L a=0.026(P/V)^{0.4} u_g^{0.5}

$PV \in \left[50, 4000\right]$

where

PV: PV (W/m³)
ug: ug (m/s)
kla: kLa estimate (1/s)

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

k_L a=0.026(P/V)^{0.4} u_g^{0.5}

$PV \in \left[50, 4000\right]$

$PV = 50$ $kla = 0.018$

Along the curve

②

Domain of the variable — blue

PV_{\min} = 50,\quad PV_{\max} = 4000

$PV \in \left[50, 4000\right]$

$PV = 50$ $PV = 50$

Along the curve

③

Response curve — green

k_L a=0.026(P/V)^{0.4} u_g^{0.5}

$PV \in \left[50, 4000\right]$

$PV = 50$ $kla = 0.018$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}kla}{\mathrm{d}PV}

$PV \in \left[50, 4000\right]$

$PV = 74.84$ $kla^{\prime} = 1.12\times 10^{-4}$

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-42 — kLa estimate) is the form associated with kLa estimate. Working symbols: $PV$ , $ug$ $\rightarrow$ $kla$ . Aeration mass-transfer coefficient. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

kla

from

PV

ug

in Chemical engineering via

k_L a=0.026(P/V)^{0.4} u_g^{0.5}

Aeration mass-transfer coefficient. 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

PV = 400.000\,\mathrm{W/m^{3}}

ug = 0.020\,\mathrm{m/s}

, the governing relation

k_L a=0.026(P/V)^{0.4} u_g^{0.5}

yields

kla = 0.040\,\mathrm{1/s}

. 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

PV PV400 W/m³ug ug0.02 m/s

Outputs

kLa estimate kla0.040 1/s

Reading speed

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Narration of this film

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

Aeration mass-transfer coefficient. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube