Patrick is snorkeling surface swimming with a tube in his mo

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, show calculations and equations 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 pi r^2L. 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? 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.

Solution

The tube resistance is said to be directly proportional to the length of the tube and viscousity of the blood and inversely proportional to the fourth powoer of the radius.

R=L X V/ r⁴= 40 X 2.35/1.2⁴=45.33 taking viscousity of blood 2.35 mPa.s at temperature 42 degree.

Here Patrick will be able to breathe comfortably as length of the tube is according to the specified parameters for snorkeling.

Dead space in snorkeling refers to the amount of air which gets inhaled again (once after exhaled and gets stuck in the snorkeling tube) with the fresh breath of inhaled air, as a result the amount of fresh air gets reduced, making the amount of carbon dioxide higher in the blood and can prove fatal. The fresh air needs to reach alveoli through trachea with the snorkeling tube connected to the mouth of a person.

Alveolar ventilation can be defined as the volume of air expired from the alveoli to the outside of a body per minute. It can be calculated by the product of ventilation rate and difference of tidal volume and dead space volume.

Alveolar ventilation= ventilation rate X (V_T-V_D)=12 X(500-150)=12 X 350=1050 mL/minute.

Change in alveolar ventilation=Normal ventilation rate - new ventilation rate=4200mL-1050mL=3150mL

As it is clear that alveolar ventilation has dropped down by 3150 mL, so Patrick has to breathe more forcefully as compared to normal. We know that, more the volume of the tube the smaller is the tidal volume.

Longer snorkeling tube means length of trachea is increased hence increasing the passage of air from inside to outside and vice versa which makes difficult to breath and air just gets shunted into and out of the tube without fresh air replacing this. The radius plays an important role here as smaller radius reduces the dead volume hence making breathing easier by keeping the alveolar ventilation high.

Using the above formula the relative resistance of first tube is 67.997 and second tube is 8.8125

He will not be able to snorkel well with either of these tubes because by increasing their length, the dead space is increased which makes breathing difficult unless he specifically exhales out of the snorkeling tube.