A diver thinks that if a typical snorkel tube of 0.13 m length works, then a tube of length 6.2 m should also work. When trying to use such a tube, what is the pressure difference between the external pressure on the diver's chest and the air pressure in the lungs of the diver? Assume seawater density is 1.025 g/cm3 Express the result in the unit [Pa].

Question

A diver thinks that if a typical snorkel tube of 0.13 m length works, then a tube of length 6.2 m should also work. When trying to use such a tube, what is the pressure difference between the external pressure on the diver's chest and the air pressure in the lungs of the diver? Assume seawater density is 1.025 g/cm3 Express the result in the unit [Pa].

Answer 1

To determine the pressure difference between the external pressure on the diver's chest and the air pressure in the lungs, we can use Pascal's law, which states that the pressure difference between two points in a fluid is directly proportional to the density of the fluid, the gravitational constant, and the difference in height between the two points:

ΔP = ρgh

Where:
ΔP is the pressure difference in Pascals (Pa)
ρ is the density of the fluid (seawater) in kg/m^3
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height difference (the difference in lengths of the snorkel tubes) in meters

First, we need to convert the density of seawater from grams per cubic centimeter (g/cm^3) to kilograms per cubic meter (kg/m^3):
1.025 g/cm^3 * 1000 kg/m^3 / 1 g/cm^3 = 1025 kg/m^3

Now, we can calculate the pressure difference:
ΔP = 1025 kg/m^3 * 9.8 m/s^2 * (6.2 m - 0.13 m)

ΔP = 1025 kg/m^3 * 9.8 m/s^2 * 6.07 m

ΔP ≈ 59601.86 Pa

Therefore, the pressure difference between the external pressure on the diver's chest and the air pressure in the lungs is approximately 59601.86 Pascal (Pa).