Strouhal number

Physical key figure
Surname	Strouhal number
Formula symbol	${\displaystyle {\mathit {Sr}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Sr}}={\frac {f\cdot L}{v}}}$
${\displaystyle f}$ Vortex shedding frequency ${\displaystyle L}$ characteristic length ${\displaystyle v}$ Flow velocity
Named after	Vincent Strouhal
scope of application	oscillating currents

The Strouhal number is a dimensionless number used in fluid mechanics . In the case of unsteady flow processes, it can be used to determine the shedding frequency of eddies , as can be observed, for example, in a Karman vortex street . It is named after the Czech physicist Vincent Strouhal (1850–1922), who first used it in 1878. ${\displaystyle {\mathit {Sr}}}$

Definition and values

Kármán vortex street behind a cylinder with a flow around it

The Strouhal number is defined as:

${\displaystyle {\mathit {Sr}}={\frac {f\cdot L}{v}}}$

With

• Vortex shedding frequency ${\displaystyle f}$
• Size of the flow around the obstacle, e.g. B. diameter of a cylinder ${\displaystyle L}$
• Flow velocity . ${\displaystyle v}$

Dependence of the Strouhal number on the Reynolds number for a long cylinder

The diagram shows the dependence of the Strouhal number on the Reynolds number for a cylinder with a flow around it. For most practical applications, the approximation applies:

${\displaystyle {\mathit {Sr}}\approx 0{,}21.}$

With this the frequency of the vortex shedding can be calculated:

${\displaystyle f={\frac {{\mathit {Sr}}\cdot v}{L}}}$

Examples

If the wind blows around a cable with a diameter of 0.01 m at a speed of 20 m / s, one hears the singing of the wires , also called aeolian tones , with a frequency of 0.21 · 20 m / s: 0.01 m = 420 Hz.

Air bombs strike from a height of 2000 m at a speed of approx. 200 m / s. With a diameter of a few decimeters, they produce a high-pitched whistling tone, the pitch of which is additionally modulated by the Doppler effect .

Web links

• Measured values ​​for Sr (R) (English)
• Strouhal, Vincenz: About a special kind of sound excitation. In: Annals of Physics and Chemistry. Leipzig, 1878. NF. Vol. V, H. 10, S. 216-251 (Link German Text Archive).