hello, I hope you can help...
A diver accustomed to standard snorkel tubing of length 25 cm tries a self-made tube of length 8.6 m. During the attempt, what is the pressure difference (in kPa) between the external pressure on the diver's chest and the air pressure in the diver's lungs?
I've been trying rigerously with pascal's law to figure this out and I feel as though it doesn't work. I'm very stuck, please help.
hello (again)
8.6 meters is 860 cm
if you picture a stack of 860 cm cubes of water, what is the force at the bottom?
... 860 gm * g
... this is the force on one cm^2
.86 kg * 9.8 m/s^2 = f
a Pascal is one Newton per m^2
... a kPa is .001 N per cm^2
I hadn't seen your answer the first time until after I posted this one, your reply to both helped! thanks so much scott!
Of course, I'll be happy to help you with that! To determine the pressure difference between the external pressure on the diver's chest and the air pressure in the diver's lungs, we can use Pascal's law along with the concept of hydrostatic pressure.
Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container. This means that the pressure is the same at all points within a fluid at a given depth.
To solve this problem, we need to consider the difference in depths between the two tube lengths. In the case of the standard snorkel tube, the length is 25 cm, and in the self-made tube, the length is 8.6 m.
First, let's convert the length of the self-made tube to centimeters:
8.6 m * 100 cm/m = 860 cm
Now, we need to calculate the pressure difference by subtracting the pressure at the chest level from the pressure in the lungs level. This can be done using the equation for hydrostatic pressure:
ΔP = ρgh
Where:
ΔP is the pressure difference
ρ is the density of the fluid (in this case, air, which is approximately 1.2 kg/m³ or 0.0012 g/cm³)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the difference in height (in this case, the change in depth)
Let's calculate the pressure difference:
For the standard snorkel tube:
ΔP₁ = ρg * 25 cm
For the self-made tube:
ΔP₂ = ρg * 860 cm
Now, we can substitute the values and convert to kilopascals (kPa).
For the standard snorkel tube:
ΔP₁ = 0.0012 g/cm³ * 9.8 m/s² * 25 cm = 0.294 kPa
For the self-made tube:
ΔP₂ = 0.0012 g/cm³ * 9.8 m/s² * 860 cm = 10.4112 kPa
To find the pressure difference, we subtract ΔP₁ from ΔP₂:
ΔP = ΔP₂ - ΔP₁
= 10.4112 kPa - 0.294 kPa
≈ 10.1172 kPa
Therefore, the pressure difference between the external pressure on the diver's chest and the air pressure in the diver's lungs is approximately 10.1172 kPa.