91Ó°ÊÓ

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 \(\mathrm{m}\) (about 20 \(\mathrm{ft}\) )? Assume that the diver is in freshwater. (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.)

Step by step solution

01

Understand the Problem

The problem involves calculating the pressure difference between the pressure outside of a diver's lungs at a certain depth in water and atmospheric pressure inside the lungs. We need to use the depth of the diver to find this pressure difference.

02

Recall the Pressure Formula

The pressure in a fluid increases with depth according to the formula: \( P = P_0 + \rho gh \), where \( P_0 \) is the atmospheric pressure, \( \rho \) is the density of the fluid (freshwater in this case), \( g \) is the acceleration due to gravity, and \( h \) is the depth.

03

Identify the Values

For freshwater, the density \( \rho \approx 1000 \, \mathrm{kg/m^3} \), \( g = 9.8 \, \mathrm{m/s^2} \), and the depth \( h = 6.1 \, \mathrm{m} \). Atmospheric pressure \( P_0 \approx 101325 \, \mathrm{Pa} \).

04

Calculate Pressure at Depth

The pressure at depth due to the water column is \( P_w = \rho gh = 1000 \, \mathrm{kg/m^3} \times 9.8 \, \mathrm{m/s^2} \times 6.1 \, \mathrm{m} \). Simplifying gives us \( P_w = 59780 \, \mathrm{Pa} \).

05

Determine the Pressure Difference

The external-internal pressure difference is the pressure at depth minus atmospheric pressure (internal pressure remains atmospheric). Thus, the pressure difference \( \Delta P = P_w - P_0 = 59780 \, \mathrm{Pa} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Snorkeling

Snorkeling is an enjoyable water activity where a person swims on or through the water wearing a diving mask and breathing through a snorkel tube. This allows for underwater observation for extended periods while remaining near the water's surface.
The snorkel itself is a simple piece of equipment—a tube that connects the diver’s mouth to the air above water.

• The primary function is to enable breathing while the diver’s face is submerged.
• It allows for easy exploration of underwater life.

However, there are limitations to how deep one can snorkel, largely due to pressure differences as one goes deeper into the water. This is a crucial factor as the human body can only withstand so much pressure exerted by water, which increases with depth.

Fluid Pressure Calculation

Calculating fluid pressure is key in understanding how pressures change in a submerged environment. The fundamental formula used is \( P = P_0 + \rho gh \). This formula helps us calculate the pressure exerted by a fluid at any given depth.

Let's break it down:

• \( P_0 \): Atmospheric pressure at the surface.
• \( \rho \): Density of the fluid—in this case, freshwater, approximately 1000 \( \mathrm{kg/m^3} \).
• \( g \): Acceleration due to gravity, which is about \( 9.8 \, \mathrm{m/s^2} \).
• \( h \): Depth of the fluid, or how far below the surface the object is—in this example, \( 6.1 \, \mathrm{m} \).

Using this formula provides the pressure due to the water column at a specific depth. Understanding how to apply this equation is essential for various applications in diving and marine activities.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the atmosphere. It acts uniformly in all directions and decreases as we move to higher altitudes. At sea level, it is approximately \( 101325 \, \mathrm{Pa} \) (Pascal).

In the context of diving, atmospheric pressure is the baseline.

• When a diver is at the surface, their lungs experience this pressure only.
• Once submerged, the diver's lungs still have air at atmospheric pressure due to the air in the lungs or snorkel tube being from above the surface.

Understanding atmospheric pressure is vital since it is a constant factor that does not change much with minor height variations above the sea level. It is a reference point when considering pressure differences underwater.

Diving Physics

Diving physics revolves around the principles of pressure, buoyancy, and fluid dynamics as they apply to underwater activities.

When diving, the pressure a diver feels underwater is the combination of atmospheric pressure and the pressure from the water itself. The deeper you dive, the more pressure is exerted on your body due to the increased weight of the water column above.

• This increased pressure affects your lungs, which naturally want to equalize pressure with the water outside.
• For snorkelers, the pressure difference is more pronounced because they rely solely on atmospheric pressure air.
• Scuba divers use compressed air tanks to breathe under higher pressure conditions, allowing them to dive deeper without pressure-related issues.

Understanding diving physics ensures safety and comfort in water activities by respecting the limits of natural pressure resistance the human body can safely handle.