How Deep Can a Snorkeler Dive with a 1/20 Atmosphere Lung Pressure Difference?

[thatgirlyouknow]

Homework Statement

The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/20 of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1029 kg/m3.

Homework Equations

1 atm = 1.013e5 Pa
1/20 atm = 5065 Pa
P1 + P2 = gauge pressure
P = density*gravity*height
P = Force/Area

The Attempt at a Solution

So the pressure in the lungs minus the pressure outside the lungs must be less than 5065 Pa. If
P1-P2 = 5065 and
P2 = 1029*height
these should just be combined somehow. However, how do I know what the pressure is inside the lungs? If I use 1 atm,
1.013e5 - 1029(g)(h) = 5065
96235 = 1029(9.8)(h)
h = 9.54 m
But this is not correct. Does anyone have a suggestion?

 

[Kurdt]

I would expect the pressure under water to be greater so I'd take the under water pressure away from the pressure in the lungs. The difference is not that great however.

 

[thatgirlyouknow]

Ok so any other ideas?

 

[stewartcs]

I came up with about 0.5 meters.