CHE-41

Ergun packed bed

Packed-bed pressure drop.

Reading speed

GoverningErgun packed bed

Governing equation

\Delta P/L=150\mu(1-\epsilon)^2 u/(\epsilon^3 d^2)+1.75\rho(1-\epsilon)u^2/(\epsilon^3 d)

$u \in \left[0.001, 0.2\right]$

where

mu: mu (Pa·s)
eps: eps (—)
u: u (m/s)
d: d (mm)
rho: rho (kg/m³)
dP: Ergun packed bed (Pa/m)

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

\Delta P/L=150\mu(1-\epsilon)^2 u/(\epsilon^3 d^2)+1.75\rho(1-\epsilon)u^2/(\epsilon^3 d)

$u \in \left[0.001, 0.2\right]$

$u = 0.001$ $dP = 99.22$

Along the curve

②

Domain of the variable — blue

u_{\min} = 0.001,\quad u_{\max} = 0.2

$u \in \left[0.001, 0.2\right]$

$u = 0.001$ $u = 0.001$

Along the curve

③

Response curve — green

\Delta P/L=150\mu(1-\epsilon)^2 u/(\epsilon^3 d^2)+1.75\rho(1-\epsilon)u^2/(\epsilon^3 d)

$u \in \left[0.001, 0.2\right]$

$u = 0.001$ $dP = 99.22$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}dP}{\mathrm{d}u}

$u \in \left[0.001, 0.2\right]$

$u = 0.002$ $dP^{\prime} = 1.18\times 10^{5}$

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-41 — Ergun packed bed) is the form associated with Ergun packed bed. Working symbols: $mu$ , $eps$ , $u$ , $d$ , $rho$ $\rightarrow$ $dP$ . Packed-bed pressure drop. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

dP

from

mu

eps

u

d

rho

in Chemical engineering via

\Delta P/L=150\mu(1-\epsilon)^2 u/(\epsilon^3 d^2)+1.75\rho(1-\epsilon)u^2/(\epsilon^3 d)

Packed-bed pressure drop. 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

mu = 0.001\,\mathrm{Pa·s}

eps = 0.400\,\mathrm{—}

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

d = 3.000\,\mathrm{mm}

rho = 1000.000\,\mathrm{kg/m^{3}}

, the governing relation

\Delta P/L=150\mu(1-\epsilon)^2 u/(\epsilon^3 d^2)+1.75\rho(1-\epsilon)u^2/(\epsilon^3 d)

yields

dP = 4062.500\,\mathrm{Pa/m}

. 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

mu mu0.001 Pa·seps eps0.4 —u u0.02 m/sd d3 mmrho rho1000 kg/m³

Outputs

Ergun packed bed dP4062.500 Pa/m

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Narration of this film

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

Packed-bed pressure drop. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube