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.
the weight of a 1 meter tube of water h meters high...
weight=9.8*1025*h*1m^2 N
pressure= 9.8*1025*h Pa
lung pressure=1/20*101.3 kPa
set them equal
.05*101.3e^3 Pa=9.8*1025*h
h= .... about a half meter.
To determine how far below the water a diver can swim using a snorkel, we need to calculate the maximum pressure difference the lungs can handle and then convert that into a depth.
First, we are given that the lungs can function satisfactorily up to a pressure difference of 1/20 of an atmosphere. To convert this into standard units, we need to convert atmospheres to Pascals, as pressure is commonly measured in Pascals.
1 atmosphere is equal to 101325 Pascals (Pa). So, 1/20 of an atmosphere is equal to (1/20) * 101325 Pa, which gives us 5066.25 Pa.
Next, we can use the concept of pressure in a fluid to relate this pressure difference to a depth. The pressure at a specific depth in a fluid is given by the equation:
pressure = density * gravity * depth,
where density is the density of the fluid, gravity is the acceleration due to gravity, and depth is the depth below the surface of the fluid.
In this case, we are given that the diver is in salt water with a density of 1025 kg/m^3. The acceleration due to gravity can be assumed to be approximately 9.8 m/s^2.
We can rearrange the equation and solve for depth:
depth = pressure / (density * gravity).
Substituting in the given values, we have:
depth = 5066.25 Pa / (1025 kg/m^3 * 9.8 m/s^2).
Performing the calculation:
depth = 5066.25 / (1025 * 9.8) = 0.496 meters.
Therefore, the diver can swim up to a depth of approximately 0.496 meters below the water using a snorkel in salt water.