Calculating Pressure Differences in Diving: A Snorkeling Dilemma Explained

[chiurox]

Homework Statement

A novice diver swimming in a lake at a depth of 6m tries to breathe with a snorkel tube that reaches to just above the surface of the water. Assume that the lake water density equal 1000kg/m³

1) What is the pressure difference between the external pressure on him and the air pressure in his lungs?

2) Do you think it's possible for the diver to breathe through a snorkel at such a depth as in (1)? Explain.

3) At another time, the diver changes surfaces while holding his breathe. The difference between the air pressure and the pressure in his lungs as he reaches the surface is 9000Pa. From what depth did he start?

4) Do you think that the diver's action in (3) is hazardous to his health? Explain.

Homework Equations

Pressure=pgh
P=F/A
m=pV

The Attempt at a Solution

Okay, so after I read the first part of the question: Difference between the external pressure on him and the air pressure in his lungs... I got a little confused. How can I calculate the pressure difference if the swimmer and the swimmer's lungs are in the same distance from the water surface? Or is this somehow a "trick question" where the answer is that there is no difference?
Could anyone confirm?
Thanks

 

[Daiquiri]

1) Think about this: the external pressure acting on swimmer's body is the water static pressure at that given depth. But if his lungs are in contact with the air above the water surface (via that snorkel tube), then the pressure inside his lungs is... ?

2) Now that you know the pressure difference acting on his lungs, you have to find the surface on which that differential pressure acts. pressure times surface gives you a force.
Now you could lay down on the ground and try to breathe with an equivalent weight on your chest. You will soon find out the correct answer to the question 2.
If after the experiment you're still able to tell someone about it, the answer is "yes". Otherwise, it's "no".

3) Here you have a $$\Delta$$h. Knowing the equation for the hydrstatic pressure, the answer is straightforward.

4) SCUBA divers know about that one very well. Try this:
http://en.wikipedia.org/wiki/Barotrauma

 

[chiurox]

1) Hm... so the pressure inside his lungs is not affected by the depth he's in? Or is it a summation of the water pressure at that given depth and the air above the water surface?

 

[Daiquiri]

Think of the snorkel immersed in the water from the surface to that given depth. Imagine that snorkel having a form of a cylinder closed at the bottom. The top of the cylinder is above the surface, open to the air.
That's the same situation you have here. Diver's lungs are just the terminal part of that open cylinder. Think about the air pressure inside that cylinder. If the air at the bottom end of the cylinder was at the same pressure as the water at 6 m depth and the air at the open end of the cylinder was at the atmospheric pressure, would that be an equlibrium situation?

It would be like a kind of air gun - a fraction of second after pulling the trigger, wouldn't it? ;)

 

[chiurox]

1)So, the pressure at 6m underwater would be (1000)(9.8)(6) which is around 59000 Pa... and the atm pressure is the standard of 1.013*10^5. Then the pressure difference is about 42000 Pa, is that right?

2) I think that the diver wouldn't be able to breathe under 6m through that snorkel tube because in order to make his diaphragm expand, his body muscles would have to overcome the deep water pressure which is not possible... (and I also checked snorkeling on wikipedia which said that the maximum usable length of a snorkeling tube is around 40cm... ^_^ and I also googled similar type of questions and one said that we can only breathe if the difference in pressure is no more than 1/20 of the standard atmospheric pressure)

3)would the answer be 11.25meters?

 

[chiurox]

4)For this part, I think that the question is a little bit unclear. If he started at 11.26m, did he inhale while being 11.26m deep through a Scuba tank? Or did he inhale at the surface and dove 11.26m then came back? (hm... but then that wouldn't create the difference in pressure... so I think the diver inhaled through an equipment)
Considering that he inhaled through an equipment, then that would mean that the air in his lungs is very pressurized, and by ascending from 11.26m, his lung would burst at the surface 0_0! is that right?

 

[Daiquiri]

1)So, the pressure at 6m underwater would be (1000)(9.8)(6) which is around 59000 Pa... and the atm pressure is the standard of 1.013*10^5. Then the pressure difference is about 42000 Pa, is that right?

Wrong!
Remember that hydrostatic pressure equation says that
$$p = p0 + \rho g \Delta h$$
where p0 is the atmospheric pressure (about 101300 Pa).
So, the pressure at 6 m underwater is not 59000 Pa but is
101300 + 59000 = 160300 Pa
and the pressure difference $$p - p0 = \rho g \Delta h$$ is 59000 Pa.

2) I think that the diver wouldn't be able to breathe under 6m through that snorkel tube because in order to make his diaphragm expand, his body muscles would have to overcome the deep water pressure which is not possible...

Sounds ok, but I tend not to use the word "impossible" ever since I've learned that men have walked on the Moon. :biggrin
Maybe Arnold Schwarzenegger in his best days would have been able to do it...

I also googled similar type of questions and one said that we can only breathe if the difference in pressure is no more than 1/20 of the standard atmospheric pressure)

I would like to know where did you find this one, for my personal info.

3)would the answer be 11.25meters?
...
4)For this part, I think that the question is a little bit unclear.

It seems very clear to me.
It says that when he gets to the surface, the pressure difference p-p0 is 9000 Pa. It's the difference between the pressure in his lungs and the atmospheric pressure at the surface.
Since $$p - p0 = \rho g \Delta h$$ then
$$\Delta h = 9000 / (\rho g) = 0.92 m$$ - about 3 ft.
It's about 9% lung volume increase - you can calculate it through the Boyle-Mariotte law (pV=const.)
I'm not really sure it can make a damage to diver's lungs. During our everyday easy respiration our lungs expand to about 15% of their maximum capacity.
But I can tell you that a general SCUBA diving rule says. "NEVER CHANGE DIVING LEVEL WITH YOUR MOUTH SHUT, WHATEVER THE LEVEL DIFFERENCE!"
So, let's be cautious and say that he shouldn't have done it.

 

[chiurox]

wow, so many mistakes I made...
Thanks for taking the time and pointing them out and explaining. =)

Regarding that info about us only being able to breathe when the pressure difference is 1/20... I got that from a question enunciation I found through google.
The thing is that I can't find answers to these questions (it's an online AP Physics course, in other words, self-studying), and there's no textbook that comes with it and the material that comes with it is too limited...So my options are physics forums and online lectures...