The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/21 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 1048 kg/m3.
To determine how far below the water the diver can swim using a snorkel, we need to consider the pressure difference between the outside and inside of the lungs.
The pressure difference that the human lungs can handle is given as 1/21 of an atmosphere. We will convert this into SI units, as it will be easier to work with.
1 atmosphere (atm) is approximately equal to 101,325 Pascals (Pa). Therefore, the pressure difference that the lungs can handle is:
Pressure difference = 1/21 * 101,325 Pa
Now, let's calculate the pressure difference:
Pressure difference = 1/21 * 101,325 Pa
Pressure difference = 4,825 Pa
Next, we need to understand how pressure changes with depth in a fluid. The relationship between pressure and depth in a fluid is given by the hydrostatic pressure equation:
Pressure = density * gravity * depth
Where:
- Pressure is the pressure at a certain depth,
- Density is the density of the fluid (given as 1048 kg/m^3 for saltwater),
- Gravity is the acceleration due to gravity (approximately 9.8 m/s^2),
- Depth is the distance below the surface of the water.
Given that the pressure difference that the lungs can handle is 4,825 Pa and the density of saltwater is 1048 kg/m^3, we can rearrange the hydrostatic pressure equation to calculate the depth the diver can swim:
Depth = Pressure difference / (density * gravity)
Plugging in the values:
Depth = 4,825 Pa / (1048 kg/m^3 * 9.8 m/s^2)
Depth ≈ 0.0487 meters
Therefore, the diver using a snorkel can swim approximately 0.0487 meters (or 4.87 centimeters) below the water surface.