# Appendix A: Correction of Non-Dimensional Frequency for Actual Strouhal Number

The tests by Gopalkrishnan (1993) were carried out with a small cylinder. According to the standard curve for Strouhal number, as a function of Reynolds number, the Strouhal number, \(\mathrm {St}_G\), must have been approximately \(\mathrm {0.2}\) for these tests. If we have another Strouhal number and want to apply Gopalkrishnan’s results, we have to take this into account when calculating the non-dimensional frequency parameter.

**General case**: \(\mathrm {St}^*\)

Vortex shedding frequency

Non-dimensional frequency

**Gopalkrishnan’s case**: \(\mathrm {St}_G\)

Vortex shedding frequency

Non-dimensional frequency

The general case is assumed to be equivalent to Gopalkrishnan’s case if

The non-dimensional frequency can now be defined from parameters in the general case:

Hence

By using this definition for the non-dimensional frequency in all operations we can use Gopalkrishnan’s data directly.

If we calculate the reduced velocity from the standard definition

for a system with Strouhal number \(=\mathrm {St}^*\) that is different from \(\mathrm {St}_G\), and want to compare such values to values obtained from Equation (8). we have to correct \(\mathrm {U_R}\) in order to take care of the difference in Strouhal number. If we assume that the ratio \(\mathrm {\displaystyle \frac{f_0}{f_v}}\) should be constant, the correction will be as follows

With standard Strouhal number:

At a different Strouhal number:

We can now define a modified \(\mathrm {U_R}\) that will give the same ratio. This must be as follows:

By using this definition of the reduced velocity we can compare \(\mathrm {U_R^*}\) directly to values found from the standard relation between \(\mathrm {U_R}\) and the non-dimensional frequency in Gopalkrishnan’s experiments.