Answer
$96.1\%$
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 $d=5.2\times10^{-3}\;m$
Substituting the above values we obtain:
$v=\frac{4\times7.0\times10^{–3}}{\pi \times(5.2\times10^{-3})^2}$
or, $v=329.61\;m/s$
Now we will find the ratio $\frac{v}{v_s}$
$\frac{v}{v_s}=\frac{329.61}{343}=96.1\%$
The airspeed through the trachea is $96.1\%$ of the speed of sound.
