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.)

Verified step by step guidance

1. Step 1: Identify the given data: depth of the diver (h) = 6.1 m, density of fresh water (ρ) = 1000 kg/m³, and acceleration due to gravity (g) = 9.8 m/s².
2. Step 2: Use the hydrostatic pressure formula to calculate the pressure exerted by the water at the given depth: P = ρgh.
3. Step 3: Substitute the given values into the formula: P = (1000 kg/m³)(9.8 m/s²)(6.1 m).
4. Step 4: Calculate the pressure difference between the external water pressure and the internal atmospheric pressure: ΔP = P - P_atm, where P_atm is the atmospheric pressure (approximately 101,325 Pa).
5. Step 5: Express the final pressure difference ΔP in Pascals (Pa).

Key Concepts

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, calculated using the formula P = ρgh, where P is pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the depth. For freshwater, the pressure increases approximately by 9.81 kPa for every meter of depth.

Pressure Difference

The pressure difference between two points is crucial in understanding fluid dynamics and breathing mechanics. In the context of diving, the external pressure (from the water) increases with depth, while the internal pressure (in the diver's lungs) remains at atmospheric pressure. This difference can lead to lung collapse if the external pressure exceeds the internal pressure significantly.

Breathing Mechanics in Diving

Breathing mechanics in diving involve the relationship between lung pressure and external water pressure. A snorkeler relies on atmospheric pressure to breathe, which limits their depth due to increasing external pressure. In contrast, scuba divers use tanks that provide compressed air, allowing them to equalize internal lung pressure with external water pressure, enabling deeper dives without the same risk of lung collapse.