Halliday, Resnick & Walker — Fluids: Problem Problem_84

When you cough, you expel air at high speed through the trachea and upper bronchi so that the air will remove excess mucus lining the pathway. You produce the high speed by this procedure: You breathe in a large amount of air, trap it by closing the glottis (the narrow opening in the larynx), increase the air pressure by contracting the lungs, partially collapse the trachea and upper bronchi to narrow the pathway, and then expel the air through the pathway by suddenly reopening the glottis. Assume that during the expulsion the volume flow rate is \(7.0 \times 10^{-3} \text{ m}^3/\text{s}\). What multiple of \(343 \text{ m/s}\) (the speed of sound \(v_s\)) is the airspeed through the trachea if the trachea diameter (a) remains its normal value of \(14 \text{ mm}\) and (b) contracts to \(5.2 \text{ mm}\)?