Long Snorkel: Inhalation of a breath occurs when the muscles surrounding the hum

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 3910 Pa. Consider the longest snorkel that a human can operate. The minimum pressure difference needed to take in a breath is about 278 Pa. Find the depth h that a person could swim to and still breathe with this snorkel.

Explanation / Answer

Hi,

In this case, we have to remember how to calculate the pressure as a fluid column:

The problem says the maximum pressure difference that our muscles can produce. Besides, it says the minimum pressure difference we need in order to breath, so the pressure difference we have to consider is:

P = Pmax - Pmin = 3910 Pa - 278 Pa = 3632 Pa

As we are underwater, this pressure should be expressed in meters (or other unit of distance) of said fluid, so:

P = pgh ; where p is the water density (1000 kg/m3) and g is the acceleration due to gravity (9.8 m/s2)

h = P/pg = 3632 Pa/(9.8 m/s2 * 1000 kg/m3) = 0.37 m

So, the longest snorkel should have a length of 37 cm, which is a little more than one foot.

I hope it helps.

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