Diving Depth for 1/20 Atmospheric Pressure Differential

[bpw91284]

Homework Statement

A diver with a snorkle can handle a pressure differential of 1/20 atmospheric pressure between his the oustide of his lungs and the inside. How deep can he dive? The water's density is 1025 kg/m^3.

Homework Equations

P=P_0+pgh

The Attempt at a Solution

I assumed P_atm = 101325 PA and the density of air is 1.29 kg/m^3.

I came up with P_(outside lungs)-P_(inside lungs)=(1/20)P_atm

P(outside lungs) = P_atm + pgh = 101325 + 1025*9.8*h
P(inside lungs) = P_atm + pgh = 101325 + 1.29*9.8*h

Solving for h I got 0.5 meters... Just seems way to shallow.

 

[chroot]

Your solution is correct; a diver would not be able to inhale through a snorkel at a depth of more than just a few feet.

By the way, you don't need to concern yourself with the pressure or density of the air. What matters here is the gauge pressure, which is the pressure experienced by the diver over and above that of the air he's trying to breath through the snorkel.

- Warren

 

[bpw91284]

Your solution is correct; a diver would not be able to inhale through a snorkel at a depth of more than just a few feet.

By the way, you don't need to concern yourself with the pressure or density of the air. What matters here is the gauge pressure, which is the pressure experienced by the diver over and above that of the air he's trying to breath through the snorkel.

- Warren

Just curious, how would you solve it differently then? In my solution the atmospheric pressures cancel out any way, so would your solution be the same as mine?

 

[louie3006]

this may sound weird, but how or where did you get "101325" from?

 

[bpw91284]

this may sound weird, but how or where did you get "101325" from?

1 Atm = 101325 Pascals

 

[ChillyWilly]

This explains why when I tried to use one of those "noodles" (flotation devices for pools and lakes , mostly for fun not safety) which was about 5 - 6 feet long (Looks like a giant straw) I felt the air being sucked out of me no matter how hard I tried.

 

[chroot]

Just curious, how would you solve it differently then? In my solution the atmospheric pressures cancel out any way, so would your solution be the same as mine?

Yep, the fact that the atmospheric pressure cancels out is evidence that it doesn't matter in the first place.

- Warren