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 1037 kg/m3.
hey, I did the one about the eardrums.
how can I see the answer?
To answer this question, we need to understand the concept of pressure and how it changes with depth.
In a fluid, pressure increases with depth due to the weight of the fluid above it. This relationship is described by the equation:
P = P0 + ρgh
Where:
- P is the total pressure at a certain depth
- P0 is the pressure at the surface (usually atmospheric pressure)
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the depth below the surface
In this case, we are given that the pressure difference between the outside and inside of the lungs can be 1/21 of an atmosphere. One atmosphere is approximately equal to 101325 Pa. Therefore, the pressure difference is (1/21) * 101325 = 4825 Pa.
Now, let's assume that the diver is using a snorkel, which allows her to breathe air at the surface. This means the pressure inside her lungs is equal to atmospheric pressure, which we'll assume to be 101325 Pa.
To find out how deep she can swim, we can use the equation mentioned earlier. We know the density of salt water is 1037 kg/m^3, and we can assume the acceleration due to gravity is approximately 9.8 m/s^2. We need to solve for h, the depth below the surface.
4825 = 0 + (1037 * 9.8 * h)
Simplifying the equation:
4825 = 10136.6h
Dividing both sides by 10136.6:
h = 0.476 meters (or approximately 0.5 meters)
Therefore, the diver can swim approximately 0.5 meters below the surface using a snorkel before the pressure difference exceeds the limit at which the lungs can function satisfactorily.