The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/19 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 1046 kg/m3.
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.
We know that the human lungs can function satisfactorily when the pressure difference is 1/19 of an atmosphere. In other words, the pressure inside the lungs should be 1/19 of an atmosphere lower than the pressure outside.
Given that the density of saltwater is 1046 kg/m^3, we can use the hydrostatic pressure formula to calculate the pressure at a certain depth below the water's surface.
The formula for hydrostatic pressure is:
P = ρgh
Where:
P is the pressure
ρ is the density of the fluid (saltwater)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the depth below the surface
To find the depth at which the pressure difference is 1/19 of an atmosphere, we can set up the following equation:
1/19 atm = ρgh
Let's rearrange the equation to solve for h:
h = (1/19 atm) / (ρg)
Now we can substitute the density of saltwater (1046 kg/m^3) and the acceleration due to gravity (9.8 m/s^2) into the equation:
h = (1/19 atm) / (1046 kg/m^3 * 9.8 m/s^2)
Calculating the numerical value gives us:
h ≈ 0.0000549 m
Therefore, a diver using a snorkel can swim approximately 0.0000549 meters (or 0.0549 millimeters) below the surface of saltwater while maintaining a pressure difference of 1/19 of an atmosphere.