Scruton number

{{Short description|Dimensionless number in fluid mechanics}}

{{Use dmy dates|date=May 2022}}

{{complex|date=January 2017}}

The Scruton number (Sc) is an important parameter for vortex-induced vibration (excitation) of structures, vibrations caused by rain or wind, dry inclined cable galloping, and wake galloping, the unstable airflow that forms around bridge cables and other cylindrically-structured buildings.{{Cite web|url=https://www.fhwa.dot.gov/publications/research/infrastructure/bridge/05083/chap3.cfm|title=MECHANICS OF WIND-INDUCED VIBRATIONS|date=August 2007|website=Federal Highway Administration Research and Technology|access-date=17 January 2017}} It is named after Christopher "Kit" Scruton, a British industrial dynamics engineer.{{Cite book|url=https://books.google.com/books?id=pclv2jOWBx8C&q=Kit+scruton%2C+scruton+number&pg=PA464|title=Health Monitoring of Bridges|last=Wenzel|first=Helmut|publisher=Wiley|year=2008|isbn=978-0-470-74018-7|pages=464}}{{cite book|author1=Ted Stathopoulos|author2=Charalambos C. Baniotopoulos|title=Wind Effects on Buildings and Design of Wind-Sensitive Structures|url=https://books.google.com/books?id=m49tRzY4Va8C&pg=PA45|date=31 December 2007|publisher=Springer Science & Business Media|isbn=978-3-211-73076-8|page=45}}

It is defined by:{{cite conference

|author-first=Svend O.

|author-last=Hansen

|url=https://www.eurocodes.fi/wp-content/uploads/1991/1991-1-4/Hansen_2007.pdf

|title=Vortex-induced vibrations of structures

|date=2-7 November 2007

|access-date=5 March 2021

|conference=Structural Engineers World Congress 2007

|location=Bangalore, India}}

:$\backslash mathrm\{Sc\}\; =\; \backslash frac\{2\backslash delta\_sm\_e\}\{\backslash rho\; b^2\_\backslash text\{ref\}\},$

where

:

$\backslash delta\_s$	is the structural damping expressed by the logarithmic damping decrement,
$m\_e$	is the effective mass per unit length,
$\backslash rho$	is the density of the air, or liquid,
$b\_\backslash text\{ref\}$	is the characteristic width of the structure.