The alveoli are the biological membranes responsible for res

The alveoli are the biological membranes responsible for respiration (the exchange (diffusion) of CO2 and O2 between the air we breathe and blood) in our lungs. A typical diameter for the alveoli is 200 micrometers (200 x 10^-6m , 0.0002m). Science fiction movies like Honey I shrunk the kid, and the Fantastic voyage have depicted shrinking people down to the size of ants, and human blood cells, respectively.

b.Using the ratio of length scales, areas and volumes, and knowing that a human of size ~2m has a lung surface area of 80m² f an ant is approximately 2cm and a blood vessel is 8 micrometers, for shrinking to each size, what is the new diameter(s) of the alveoli assuming geometric similarity?

c.What physical limit(s) would you, a fluid mechanics expert, worry about regarding the ability of tiny humans to breathe as their alveoli get smaller and smaller? What information would you need to gather to help you compute a recommendation for a safest ‘minimum’ size to shrink a person based on this physical limits?

Solution

B) Assuming alveoli as a spherical shaped structures given is

Human size - 2m= 200cm, lung surface area- 80m2, alveoli diameter - 200micrometers

As human shrunk to ant size having size - 2cm = 0.02m, and blood vessel size - 8 200micrometers

In general computing the mathematics the size of the human reduced from 2m to 0.02m so approximate diameter of alveoli which was 200 micrometers= 0.0002m, was reduced to 0.000002m.

C) As the healthy lung having 80m2 surface area intakes approximately 6 litres of air in it. The volume of the lung is reduced by approximately 100 times so the air capacity will also be reduced by 100 times. The safest minimum size of the shrinked individual will depend upon the height, sex and physical condition of the individual.