MECH $342$ Assignment $5$: Dimensional Analysis

Telephone wires are known to 'sing' in the wind. The sound produced by a telephone wire is caused by

vibration of the wire, due to shed vortices $($similar to flow past a cylinder$).$

Cross$-$section of telephone wire

$V$ is the wind velocity, $$ is the dynamic viscosity of air, $$ is the air density, $d$ is the cylinder diameter, $T$ is the

shedding period and $$ is the shedding $($and sound$)$ frequency.

Q$1.$ Assuming that $=f(V,,d,),$ use Buckingham PI theory to derive the non$-$dimensional numbers

associated with this problem. $[$Show full working$].$

Q$2.$ What are the names of these non$-$dimensional numbers? Explain what they physically represent.

Q$3.$ It turns out that the non$-$dimensional frequency $)=(0\mathrm{.}2$ is approximately constant for this problem.

Using your answer for Q$1,$ determine the singing frequency for a Reynolds number of $5000$ and diameter of

$6$ mm at sea level conditions.