Strouhal number
Encyclopedia
In dimensional analysis
, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal
, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding
and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics
.
The Strouhal number is often given as
where
is the dimensionless Strouhal number, 
is the frequency of vortex
shedding
,
is the characteristic length (for example hydraulic diameter) and 
is the velocity of the fluid.
For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10−4 and below), the high-speed, quasi steady state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.
For spheres in uniform flow in the Reynolds number range of 800 < Re < 200,000 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake and is independent of the Reynolds number Re and is approximately equal to 0.2. The higher frequency Strouhal number is caused by small-scale instabilities from the separation of the shear layer.
In metrology
, specifically axial-flow turbine meters, the Strouhal number is used in combination with the Roshko number
to give a correlation between flow rate and frequency. The advantage of this method over the freq/viscosity versus K-factor method is that it takes into account temperature effects on the meter.
f = meter frequency,
U = flow rate,
C = linear coefficient of expansion for the meter housing material
This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C3, resulting in units of pulses/volume (same as K-factor).
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...
, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal
Vincenc Strouhal
Vincenc Strouhal was a Austrian physicist specializing in experimental physics. He was one of the founders of the Physics department at Charles University.-Further reading:* *...
, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding
Vortex shedding
Vortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...
and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
.
The Strouhal number is often given as
where
is the dimensionless Strouhal number, is the frequency of vortexVortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
shedding
Vortex shedding
Vortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...
,
is the characteristic length (for example hydraulic diameter) and is the velocity of the fluid.For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10−4 and below), the high-speed, quasi steady state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.
For spheres in uniform flow in the Reynolds number range of 800 < Re < 200,000 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake and is independent of the Reynolds number Re and is approximately equal to 0.2. The higher frequency Strouhal number is caused by small-scale instabilities from the separation of the shear layer.
In metrology
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...
, specifically axial-flow turbine meters, the Strouhal number is used in combination with the Roshko number
Roshko number
In fluid mechanics, the Roshko number is a dimensionless number describing oscillating flow mechanisms. It is named after the American Professor of Aeronautics Anatol Roshko...
to give a correlation between flow rate and frequency. The advantage of this method over the freq/viscosity versus K-factor method is that it takes into account temperature effects on the meter.
f = meter frequency,
U = flow rate,
C = linear coefficient of expansion for the meter housing material
This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C3, resulting in units of pulses/volume (same as K-factor).