How Deep Can a Diver Go with a Snorkel Based on Lung Pressure Differential?

[Moe*]

Homework Statement

THe human lungs can operate w a pressure differential of abt 1/20 of an atmosphere. If a diver uses a snorkle for breathing, about how far below the water level can they swim?

Homework Equations

P=P(i) + pgh

where p is ro, density.

The Attempt at a Solution

1026kPa=101.3kPa + (0.001g/l)(9.8m/s^2)(h)

I isolated for h, but the number i get is way larger than the diameter of earth.

My problem is this: the units don't seemt o cancel out properly. the units for height work out to be L/m^2

 

[rohanprabhu]

You are not using a proper set of units here. Use the S.I system throughout. For pressure, use Pascals (Pa), not kPa. 1 Pa = 1 N/m² . For density, use kg/m³. Density of water is: 1000 kg/m³. You have used the right units for gravitational acceleration and your 'h' should come out in meters.

You have used the density of water as 0.001 g/l. It is actually 1000 g/l. [or 1000 kg/m³].

As for the unit dimensions, you are getting it as L/m². 'L' is litres, so it has the dimension, [Length]³, and the denominator has dimension, [Length]². When it cancels out, you get the height's dimensions as [Length].. so there is no error in the dimensional analysis.

 

[Moetasim]

, which doesn't make sense.

I would first check my calculations to make sure I didn't make any mistakes. I would also double check the units to make sure they are consistent throughout the equation. If there are any discrepancies, I would go back and make sure I am using the correct units and that they are cancelling out properly.

Additionally, I would also consider the other factors that could affect the pressure differential in the lungs, such as the depth of the water and the lung capacity of the diver. I may also research and compare the pressure differentials of different types of breathing apparatus, such as a snorkel versus a scuba tank, to see how they may affect the maximum depth a diver can reach.

Furthermore, I would also consider the safety and physiological limitations of the human body when diving to certain depths. While the lungs may be able to operate at a pressure differential of 1/20 of an atmosphere, there may be other factors such as air consumption, nitrogen absorption, and oxygen toxicity that could limit the depth a diver can safely reach.

In conclusion, as a scientist, I would thoroughly analyze the problem and consider all relevant factors before providing a response. Proper calculations, consistent units, and consideration of physiological limitations are all important in finding a solution to this fluid problem.