Speed of a Sneeze: Solve Homework Statement

[Goatsenator]

Homework Statement

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 5.3 x 10-3 m3/s. What multiple of the speed of sound xs (= 343 m/s) is the airspeed through the trachea if the trachea diameter (a) remains its normal value of 19 mm and (b) contracts to 7.8 mm?




2. Homework Equations / Solution Attempt

I applied the definition of volume flow rate = (area)(velocity) then divided that answer by 343 m/s to get the ratio but it says that it's wrong.

 

[miniradman]

I applied the definition of volume flow rate = (area)(velocity) then divided that answer by 343 m/s to get the ratio but it says that it's wrong.

What was the answer?

Have you tried working backwards? it might help ; )