It is known that when a steady wind blows past a bluff body, vortices may develop

on the downwind side that are shed in a regular fashion at some definite frequency.

Since these vortices can create harmful periodic forces acting on the structure, it is

important to determine their shedding frequency. For a specific structure of

interest, D$=0\mathrm{.}1$m$,$H$=0\mathrm{.}3$m$,$ and the representative wind velocity, V$,$ is

$50$km$//$hr$.$ Air at standard temperature and pressure can be assumed.

The vortex shedding frequency is to be determined through the use of a small$-$scale

model that is to be tested in a water tunnel, with the water also being at standard

temperature and pressure. For the model D$\_($m$)=20$mm$.$

a$)$ List the parameters which influence the shedding frequency, omega, and then use the

Buckingham pi$-$theorem to find the non$-$dimensional groups for this problem.

b$)$ Determine the model dimension, H$\_($m$),$ and velocity, V$\_($m$),$ at which the test should

be performed.

c$)$ If the shedding frequency for the model is found to be $49\mathrm{.}9$ Hz $,$ determine the

corresponding frequency of the prototype.