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 1025 kg/m3.
didn't I respond to this earlier? What did you not understand on that?
Actually I did not understand why and how did you calculate the wight.
weight of the water column=density*gravityforce*height*area
gravity force=9.8N/kg
density=mass/volume
area is area of a mythical column 1m x 1m, height is water above where you want to measure pressure.
then pressure is weight/area, so
pressure= density*9.8*height (in N/m^2 or Pascals)
set that equal to 1/20 th of normal atmospheric pressure (101.3 kPa), solve for h.
Thanks a lot
To determine how far below the water a diver can swim using a snorkel, we need to consider the pressure difference between the outside and inside of the lungs.
The pressure difference required for the human lungs to function satisfactorily is 1/20 of an atmosphere. This means that the pressure inside the lungs should be 1/20 of an atmosphere higher than the pressure outside the lungs.
Now let's calculate the pressure difference in terms of the pressure units commonly used for such calculations - pascals (Pa).
1 atmosphere is approximately equal to 101,325 Pa. Therefore, 1/20 of an atmosphere is:
Pressure difference = (1/20) x (101,325 Pa) = 5,066.25 Pa
The pressure at a certain depth in a fluid can be calculated using the formula:
Pressure = Density x Gravitational acceleration x Depth
Since the diver is in saltwater, with a density of 1025 kg/m³, and the gravitational acceleration is approximately 9.8 m/s², we can rearrange the formula to solve for depth:
Depth = Pressure / (Density x Gravitational acceleration)
Substituting the values into the equation:
Depth = 5,066.25 Pa / (1025 kg/m³ x 9.8 m/s²)
Simplifying the equation:
Depth = 0.4965 meters
Therefore, the diver can swim approximately 0.4965 meters (or about 49.65 cm) below the water surface while using a snorkel and still have satisfactory lung function.