Strouhal Number & Karman Vortex-Shedding Frequency Formula

Use a supplied Strouhal number

The scaling relation is St=fD/V, or f=St×V/D. B2 supplies St, B3 flow-speed magnitude in m/s and B4 cylinder diameter in metres. E2 returns hertz without rounding.

St=0.2 is an illustrative circular-cylinder approximation, not a constant for all geometries or flows. Reynolds number, surface condition, nearby boundaries and body motion can alter shedding. This workbook does not calculate Reynolds number or determine whether periodic shedding exists.

Compute the nominal frequency-match speed

E3 evaluates Vmatch=fn×D/St using the positive natural frequency in B5. With St=0.2, D=1.2 m and fn=2.6 Hz, Vmatch=15.6 m/s. At V=15 m/s, E2=2.5 Hz and the frequency ratio E4 is approximately0.961538.

This is where the supplied stationary-body scaling equals a selected natural frequency. It is not an exact lock-in speed. Fluid–structure interaction can synchronize shedding and motion over a range; damping and structural properties matter.

=IF(COUNT(B2,B4:B5)<>3,"Enter numeric St,diameter,natural frequency",IF(OR(B2<=0,B4<=0,B5<=0),"Require St,diameter,natural frequency>0",B5*B4/B2))

Choose an explicit comparison tolerance

B6 is a fractional comparison tolerance, initially0.2 for±20%. E5 checks abs(f/fn−1)<=tolerance. This band is chosen for the spreadsheet exercise, not a universal physical lock-in boundary or a design-code requirement.

The initial point is inside that band. V=6 m/s gives f=1 Hz and is outside. Neither label means “safe” or proves a damaging response. The calculation does not estimate vibration amplitude, fatigue, stresses or mitigation requirements.

=IF(NOT(ISNUMBER(E4)),E4,IF(NOT(ISNUMBER(B6)),"Enter numeric fractional tolerance",IF(OR(B6<0,B6>=1),"Require tolerance from 0 to less than 1",IF(ABS(E4-1)<=B6,"Within chosen comparison band","Outside chosen comparison band"))))

Check inputs and scaling

All required inputs must be numeric. St, diameter and natural frequency must be positive; speed may be zero as an algebraic limit. The tolerance must satisfy0<=tolerance<1. Zero speed returns zero frequency but is not evidence of vortex shedding.

Double speed while holding other inputs fixed: estimated frequency doubles. Doubling diameter halves frequency and doubles match speed. E3 remains available when speed is missing because match speed does not use that input.

=IF(COUNT(B2:B4)<>3,"Enter numeric St,speed,diameter",IF(OR(B2<=0,B3<0,B4<=0),"Require St,diameter>0 and speed>=0",B2*B3/B4))

Further reading

• Harvard Natural Sciences — Vortex Shedding in Water
• ASME — Strouhal Number for Vortex-Induced Vibration Excitation of Long Slender Structures