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 1052 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.
The pressure difference between the outside and inside of the lungs is equivalent to the pressure exerted by a column of water above the diver. This pressure is dependent on the depth of the water.
The pressure at a certain depth in a liquid is given by the formula:
P = ρgh
Where:
P is the pressure (in Pascals),
ρ is the density of the liquid (in kg/m^3),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
h is the depth of the liquid (in meters).
In this case, we can calculate the depth of water the diver can swim by equating the pressure difference to 1/21 of an atmosphere, or approximately 4,752 Pascals:
1/21 atm = 4,752 Pa
Let's rearrange the formula to solve for h:
h = P / (ρg)
Plugging in the given values:
h = 4,752 / (1052 * 9.8)
Calculating this expression, we can determine the depth a diver can swim using a snorkel.
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.
Given:
Pressure difference limit = 1/21 atm
Density of saltwater (ρ) = 1052 kg/m^3
Step 1: Convert pressure difference to SI unit (Pa)
1 atm = 101325 Pa
Pressure difference limit = (1/21) * 101325 Pa
Step 2: Convert density to SI unit (kg/m^3)
Density of saltwater = 1052 kg/m^3
Step 3: Use the hydrostatic pressure formula
Pressure = ρgh
where:
ρ = density (kg/m^3)
g = acceleration due to gravity (9.8 m/s^2)
h = depth (m)
Step 4: Set up the equation
(1/21) * 101325 = 1052 * 9.8 * h
Step 5: Solve for h
h = (1/21) * 101325 / (1052 * 9.8)
Calculating the above, we find:
h ≈ 4.78 meters
Therefore, a diver using a snorkel can safely swim approximately 4.78 meters below the water.
This question is very misleading because in fact free diving with a snorkel you can go down many, many meters. However you do not breathe while doing so, but hold your breath and your lungs get smaller compressing the air inside. (Your buoyancy also decreases and the deeper you go the faster your descent.
That said:
1 atm = 10^5 Pascal or Newton/m^2
water per meter pressure =rho g
= 1052 kg * 9.81 = 10,320 N/m^3
so
10,320 d = (1/21)10^5
216,722 d = 10^5 = 100,000
d = .461 meters
By the way, that is an awfully long snorkel