FLD-04

Stokes drag

F = 6π μ r v. Linear drag on a slow sphere, Re ≪ 1.

Reading speed

FluidsStokes

Governing equation

F_d=6\pi\mu r v

where

\mu: Viscosity (Pa·s)
r: Radius (mm)
v: Speed (m/s)
F_d: Drag force (µN)

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-04 — Stokes drag) is the form associated with Stokes. Working symbols: $\mu$ , $r$ , $v$ $\rightarrow$ $F_d$ . Creeping-flow solution of Navier–Stokes around a sphere. Millikan used it.

Purpose

Purpose: compute

F_d

from

\mu

r

v

in Fluid physics via

F_d=6\pi\mu r v

F = 6π μ r v. Linear drag on a slow sphere, Re ≪ 1. 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

\mu = 0.001\,\mathrm{Pa·s}

r = 0.500\,\mathrm{mm}

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

, the governing relation

F_d=6\pi\mu r v

yields

F_d = 0.188\,\mathrm{\mu N}

. A sphere, a viscous halo, a linear force arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Viscosity \mu0.001 Pa·sRadius r0.5 mmSpeed v0.02 m/s

Outputs

Drag force F_d0.188 µN

Reading speed

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Narration of this film

A sphere, a viscous halo, a linear force arrow.

Creeping-flow solution of Navier–Stokes around a sphere. Millikan used it.

Reading speed

Watch on YouTube