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# Strouhal number

In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. Often, it is given as:

$\mathrm{St}= {f L\over V}$

where St is the dimensionless Strouhal number, f is the frequency of vortex shedding, L is the characteristic length (for example hydraulic diameter) and V is the velocity of the fluid.

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 (Kim and Durbin, 1988 and Sakamoto and Haniu, 1990).

The Strouhal number is named after Vincenc Strouhal and is an integral part of the fundamentals of fluid mechanics.

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.

$\mathrm{St}= {f\over U}{C^3}$

f = meter frequency, U = flow rate, C = linear coefficient of expansion for the meter housing material

This relationship leaves Strouhal unitless, although a unitless approximation is often used for C^3, resulting in units of pulses/volume (same as K-factor).

## References

Kim, K. J. and Durbin, P. A. (1988) "Observations of the frequencies in a sphere wake and drag increase by acoustic excitation," Physics of Fluids, 31, pp. 3260-3265.

Sakamoto, H. and Haniu, H. (1990) "A study on vortex shedding from spheres in uniform flow," Journal of Fluids Engineering, 112(December), pp. 386-392.