FLD-12

Strouhal number

St = f L / v. Shedding frequency of a bluff body.

Reading speed

FluidsStrouhal

Governing equation

St=f L/v

$v \in \left[0.1, 40\right]$

where

f: Frequency (Hz)
L: Length (m)
v: Speed (m/s)
St: Strouhal (—)

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

St=f L/v

$v \in \left[0.1, 40\right]$

$v = 0.1$ $St = 6$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0.1,\quad v_{\max} = 40

$v \in \left[0.1, 40\right]$

$v = 0.1$ $v = 0.1$

Along the curve

③

Response curve — green

St=f L/v

$v \in \left[0.1, 40\right]$

$v = 0.1$ $St = 6$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}St}{\mathrm{d}v}

$v \in \left[0.1, 40\right]$

$v = 0.351$ $St^{\prime} = -9.969$

Along the curve

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-12 — Strouhal number) is the form associated with Strouhal. Working symbols: $f$ , $L$ , $v$ $\rightarrow$ $St$ . A cylinder sheds at St ≈ 0.2 over a wide Re. Aeolian tones and vortex-induced vibration.

Purpose

Purpose: compute

St

from

f

L

v

in Fluid physics via

St=f L/v

St = f L / v. Shedding frequency of a bluff body. 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

f = 12.000\,\mathrm{Hz}

L = 0.050\,\mathrm{m}

v = 3.000\,\mathrm{m/s}

, the governing relation

St=f L/v

yields

St = 0.200\,\mathrm{—}

. A cylinder, a von Karman street, a ticking f. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency f12 HzLength L0.05 mSpeed v3 m/s

Outputs

Strouhal St0.200 —

Reading speed

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Narration of this film

A cylinder, a von Karman street, a ticking f.

A cylinder sheds at St ≈ 0.2 over a wide Re. Aeolian tones and vortex-induced vibration.

Reading speed

Watch on YouTube