CHE-29

Packed-bed Reynolds number

Rep = ρ u dp / [μ (1−ε)]. Particle Reynolds of a packed bed.

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Packed bedsErgun Re

Governing equation

Re_p=\dfrac{\rho u d_p}{\mu(1-\varepsilon)}

$u \in \left[0.001, 2\right]$

where

\rho: Fluid density (kg/m³)
u: Superficial velocity (m/s)
d_p: Particle diameter (mm)
\mu: Viscosity (Pa·s)
\varepsilon: Void fraction (—)
Re_p: Particle Reynolds (—)

The figure, part by part

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①

Governing law — red

Re_p=\dfrac{\rho u d_p}{\mu(1-\varepsilon)}

$u \in \left[0.001, 2\right]$

$u = 0.001$ $Re_p = 5$

Along the curve

②

Domain of the variable — blue

u_{\min} = 0.001,\quad u_{\max} = 2

$u \in \left[0.001, 2\right]$

$u = 0.001$ $u = 0.001$

Along the curve

③

Response curve — green

Re_p=\dfrac{\rho u d_p}{\mu(1-\varepsilon)}

$u \in \left[0.001, 2\right]$

$u = 0.001$ $Re_p = 5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Re_p}{\mathrm{d}u}

$u \in \left[0.001, 2\right]$

$u = 0.014$ $Re_p^{\prime} = 5000$

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-29 — Packed-bed Reynolds number) is the form associated with Ergun Re. Working symbols: $\rho$ , $u$ , $d_p$ , $\mu$ , $\varepsilon$ $\rightarrow$ $Re_p$ . The interstitial velocity u/(ε) and the hydraulic diameter ~ε dp/(1−ε) combine into this conventional packed-bed Reynolds.

Purpose

Purpose: compute

Re_p

from

\rho

u

d_p

\mu

\varepsilon

in Chemical engineering via

Re_p=\dfrac{\rho u d_p}{\mu(1-\varepsilon)}

Rep = ρ u dp / [μ (1−ε)]. Particle Reynolds of a packed bed. 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

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

u = 0.050\,\mathrm{m/s}

d_p = 3.000\,\mathrm{mm}

\mu = 0.001\,\mathrm{Pa·s}

\varepsilon = 0.400\,\mathrm{—}

, the governing relation

Re_p=\dfrac{\rho u d_p}{\mu(1-\varepsilon)}

yields

Re_p = 250.0\,\mathrm{—}

. A bed of spheres, a seepage arrow, an Re tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Fluid density \rho1000 kg/m³Superficial velocity u0.05 m/sParticle diameter d_p3 mmViscosity \mu0.001 Pa·sVoid fraction \varepsilon0.4 —

Outputs

Particle Reynolds Re_p250.0 —

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Narration of this film

A bed of spheres, a seepage arrow, an Re tick.

The interstitial velocity u/(ε) and the hydraulic diameter ~ε dp/(1−ε) combine into this conventional packed-bed Reynolds.

Reading speed

Watch on YouTube