Answer
$13.26\%$
Work Step by Step
Let the airspeed through the trachea is $v$
The volume flow rate can be defined as
$R = vA$
where A is the cross-sectional area of the trachea
If d be diameter of the trachea, then
$R = \frac{v\times\pi d^2}{4}$
or, $v=\frac{4R}{\pi d^2}$
Here, $R = 7.0\times10^{–3}\;m^3$ and $d=14\times10^{-3}\;m$
Substituting the above values we obtain:
$v=\frac{4\times7.0\times10^{–3}}{\pi \times(14\times10^{-3})^2}$
or, $v=45.47\;m/s$
Now we will find the ratio $\frac{v}{v_s}$
$\frac{v}{v_s}=\frac{45.47}{343}=13.26\%$
The airspeed through the trachea is $13.26\%$ of the speed of sound.
