CHE-44

Weber number

Inertia over surface tension.

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GoverningWeber number

Governing equation

We=\rho u^2 L/\sigma

$u \in \left[0.1, 20\right]$

where

rho: rho (kg/m³)
u: u (m/s)
L: L (m)
sig: sig (N/m)
We: Weber number (—)

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

We=\rho u^2 L/\sigma

$u \in \left[0.1, 20\right]$

$u = 0.1$ $We = 1.389$

Along the curve

②

Domain of the variable — blue

u_{\min} = 0.1,\quad u_{\max} = 20

$u \in \left[0.1, 20\right]$

$u = 0.1$ $u = 0.1$

Along the curve

③

Response curve — green

We=\rho u^2 L/\sigma

$u \in \left[0.1, 20\right]$

$u = 0.1$ $We = 1.389$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}We}{\mathrm{d}u}

$u \in \left[0.1, 20\right]$

$u = 0.225$ $We^{\prime} = 62.54$

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-44 — Weber number) is the form associated with Weber number. Working symbols: $rho$ , $u$ , $L$ , $sig$ $\rightarrow$ $We$ . Inertia over surface tension. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

We

from

rho

u

L

sig

in Chemical engineering via

We=\rho u^2 L/\sigma

Inertia over surface tension. 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 = 2.000\,\mathrm{m/s}

L = 0.010\,\mathrm{m}

sig = 0.072\,\mathrm{N/m}

, the governing relation

We=\rho u^2 L/\sigma

yields

We = 555.556\,\mathrm{—}

. 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

rho rho1000 kg/m³u u2 m/sL L0.01 msig sig0.072 N/m

Outputs

Weber number We555.556 —

Reading speed

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Narration of this film

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

Inertia over surface tension. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube