FLD-11

Weber number

We = ρ v² L / σ. Inertia versus surface tension.

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FluidsWeber

Governing equation

We=\dfrac{\rho v^2 L}{\sigma}

where

\rho: Density (kg/m³)
v: Speed (m/s)
L: Length (mm)
\sigma: Surface tension (N/m)
We: Weber (—)

Lecture brief

Historical brief

Bernoulli, Navier–Stokes, Reynolds (1883) and Stokes drag made continuum flow a dimensionless craft. The sheets compute head, drag, Re and a pedagogical NS snapshot. This sheet (FLD-11 — Weber number) is the form associated with Weber. Working symbols: $\rho$ , $v$ , $L$ , $\sigma$ $\rightarrow$ $We$ . Droplet breakup, atomisation and capillary waves. We ≫ 1 means inertia wins.

Purpose

Purpose: compute

We

from

\rho

v

L

\sigma

in Fluid physics via

We=\dfrac{\rho v^2 L}{\sigma}

We = ρ v² L / σ. Inertia versus surface tension. Use it when a real fluid physics 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}}

v = 2.000\,\mathrm{m/s}

L = 2.000\,\mathrm{mm}

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

, the governing relation

We=\dfrac{\rho v^2 L}{\sigma}

yields

We = 111.11\,\mathrm{—}

. A drop, a stretching ligament, a splash. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density \rho1000 kg/m³Speed v2 m/sLength L2 mmSurface tension \sigma0.072 N/m

Outputs

Weber We111.11 —

Reading speed

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Narration of this film

A drop, a stretching ligament, a splash.

Droplet breakup, atomisation and capillary waves. We ≫ 1 means inertia wins.

Reading speed

Watch on YouTube