BIO. There is a maximum depth at which a diver can breathe through a snorkel tube (Fig. E12.17) because as the depth increases, so does the pressure difference, which tends to collapse the diver's lungs. Since the snorkel connects the air in the lungs to the atmosphere at the surface, the pressure inside the lungs is atmospheric pressure. What is the external– internal pressure difference when the diver's lungs are at a depth of 6.1 m (about 20 ft)? Assume that the diver is in fresh-water. (A scuba diver breathing from compressed air tanks can operate at greater depths than can a snorkeler, since the pressure of the air inside the scuba diver's lungs increases to match the external pressure of the water.)
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Identify the given information: The diver is at a depth of 6.1 m in fresh water. The pressure inside the lungs is atmospheric pressure, which is approximately 101,325 Pa (Pascals).
Understand the concept: The pressure difference between the external water pressure and the internal lung pressure is what we need to calculate. The external pressure at a depth in a fluid is given by the hydrostatic pressure formula.
Use the hydrostatic pressure formula: The pressure at a depth in a fluid is given by the equation \( P = P_0 + \rho g h \), where \( P_0 \) is the atmospheric pressure, \( \rho \) is the density of the fluid (for fresh water, \( \rho \approx 1000 \text{ kg/m}^3 \)), \( g \) is the acceleration due to gravity (approximately \( 9.81 \text{ m/s}^2 \)), and \( h \) is the depth (6.1 m in this case).
Calculate the external pressure: Substitute the known values into the hydrostatic pressure formula to find the pressure at 6.1 m depth. This will give you the total pressure exerted by the water at that depth.
Determine the pressure difference: Subtract the atmospheric pressure from the total pressure calculated in the previous step to find the external-internal pressure difference experienced by the diver's lungs.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hydrostatic Pressure
Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases with depth in a fluid, such as water, and is calculated using the formula P = ρgh, where ρ is the fluid density, g is the acceleration due to gravity, and h is the depth. This concept is crucial for understanding the pressure experienced by a diver underwater.
The pressure difference between the inside and outside of the diver's lungs is critical for understanding the limits of breathing through a snorkel. At a depth of 6.1 meters, the external pressure from the water is greater than the atmospheric pressure inside the lungs, creating a pressure difference that can lead to lung collapse if it becomes too large.
Atmospheric pressure is the pressure exerted by the weight of the atmosphere above a surface. At sea level, it is approximately 101,325 Pa (Pascals). When a diver uses a snorkel, the air pressure inside their lungs remains at atmospheric pressure, which is why the pressure difference with increasing water depth becomes a concern for safe breathing.
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