ansewer the questions below:

Question

A. Patrick is snorkeling (surface swimming with a tube in his mouth to maintain breathing while his face is
in the water). The snorkel tube is 40 cm in length and 1.2 cm in radius. How does this affect Patrick's
breathing? Calculate the increase in relative resistance contributed by the snorkel tube.
B. What is dead space and how does that affect snorkeling? Explain your answer, assuming the snorkel tube
is a round cylinder and cylinder volume is pr2L. How does the snorkel tube affect alveolar ventilation
(assume a ventilation rate of 12 breaths/min, tidal volume of 500 mL, and normal dead space volume of 150
mL)? If normal alveolar ventilation is 4200 mL/min, how must Patrick breathe during snorkeling compared
to normal?
C. Patrick loves snorkeling, but wishes he could go a little deeper. He decides to create a longer snorkel tube
to try to achieve this desire. He isn't sure how radius figures in, so he makes two tubes of 60 cm length, one
with a 1.2 cm radius and the other with a 2 cm radius. What are the relative resistances of these two new
tubes? Do you think he will be able to snorkel well with either of these tubes? Explain.

Answer 1

A. The snorkel tube effectively increases the total length of the respiratory passage, which increases the resistance
to air flow (R L?/r4); this makes Patrick work harder to breathe. Resistance increases proportionally to
L/r4: 40/1.24 = 19.
B. Dead space is the volume of air that enters the respiratory structures but does not reach the alveoli and cannot
contribute to gas exchange. The snorkel tube increases the amount of dead space by p 1.22 × 40 = 181 mL, which
more than doubles the dead space to 331 mL. Alveolar ventilation = ventilation rate × (tidal volume - dead space) =
12/min × (500 mL - 331 mL) = 2028 mL/min; this is less than half of normal alveolar ventilation. To maintain 4200
mL/min, Patrick could increase his ventilation rate to 25 breaths/min (4200/(500 - 331)). Alternatively, he could
increase his ventilation depth to 681 mL/breath (4200/12 + 331). Or he could alter both rate and depth.
C. Tube 1: 60/1.24 = 29. Tube 2: 60/24 = 3.75. The first tube would require significantly more effort to use than the
tube in part A, so he would not be able to snorkel as long, if at all. The second tube sounds desirable, but dead
space must be considered. The snorkel tube adds an additional p 2cm2 × 60 cm = 754 mL of dead space, which is
greater than normal tidal volume and would reduce alveolar ventilation. Neither tube is practical.