Question

Long Snorkel: Inhalation of a breath occurs when the muscles surrounding the human lungs move to increase the volume of the lungs, thereby reducing the air pressure in the lungs. The difference between the reduced pressure in the lungs and outside atmospheric pressure causes a flow of air into the lungs. The maximum reduction in air pressure that muscles of the chest can produce in the lungs against the surrounding air pressure on the chest and body is about 3740 Pa. Consider the longest snorkel that a human can operate. The minimum pressure difference needed to take in a breath is about 188 Pa. Find the depth h that a person could swim to and still breathe with this snorkel

Answer 1

h = 0.362 m

Step-by-step explanation:

The pressure equation with depth is

P₂ =
`P_(atm)` +ρ g h

The gauge pressure is

P2 -
`P_(atm)` = ρ g h

This is the pressure that muscles can create

P₂ -
`P_(atm)`= 3740 Pa

But still the person needs a small pressure for the transfer of gases, so

P₂ -
`P_(atm)` = 3740 - 188 = 3552 Pa

This is the maximum pressure difference, where the person can still breathe,

Let's clear the height

h = 3552 / ρ g

h = 3552 / (1000 9.8)

h = 0.362 m

This is the maximum depth where the person can still breathe normally.