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If a scuba diver descends too quickly into the sea, the internal pressure on each eardrum remains at atmospheric pressure, while the external pressure increases due to the increased water depth. At sufficient depths, the difference between the external and internal pressures can rupture an eardrum. Eardrums can rupture when the pressure difference is as little as \(35\) \(\mathrm{kPa}\). What is the depth at which this pressure difference could occur? The density of seawater is \(1025\) \(\mathrm{kg} /\mathrm{m}^{3}\).

Short Answer

Expert verified
The depth at which the eardrum could rupture is approximately 3.47 meters.

Step by step solution

01

Understanding the Problem

We need to find the depth at which the pressure difference between the internal (atmospheric) and external (water) pressure becomes 35 kPa. This involves applying the hydrostatic pressure formula.
02

Apply Hydrostatic Pressure Formula

The pressure due to a column of fluid is given by the formula: \( P = \rho g h \), where \( \rho \) is the density of the fluid, \( g \) is the acceleration due to gravity (approximately \(9.81\, \text{m/s}^2\)), and \( h \) is the height (or depth in this case) of the fluid column.
03

Set Up the Equation

We need the external pressure (caused by water) minus atmospheric pressure to equal 35 kPa. Since the atmospheric pressure is constant, we focus on the pressure due to the water. Set \( \rho g h = 35,000\, \text{Pa} \) (since 1 kPa = 1000 Pa).
04

Substitute Known Values

Substitute \( \rho = 1025\, \text{kg/m}^3 \) and \( g = 9.81\, \text{m/s}^2 \) into the equation: \[ 1025 \times 9.81 \times h = 35,000 \].
05

Solve for Depth \( h \)

Rearrange to solve for \( h \): \[ h = \frac{35,000}{1025 \times 9.81} \]. Calculate this to find \( h \).
06

Calculate the Result

Perform the calculation: \( h = \frac{35,000}{1025 \times 9.81} \approx 3.47 \text{ m} \). This is the depth at which the pressure difference could occur.

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Key Concepts

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

Scuba Diving
Scuba diving takes you into the fascinating underwater world where pressure plays a significant role in your experience and safety. As you descend underwater, you are entering a different pressure environment. At sea level, you are under the influence of what is known as atmospheric pressure. However, with each meter you dive deeper, the pressure increases due to the weight of the water above you.
While scuba diving, it's crucial to be aware of how this pressure affects your body, specifically your eardrums. Those tiny structures in our ears are incredibly sensitive to pressure changes, and they have to continuously adjust as you move through different depths. This adjustment process is called "equalizing," and failing to do so can lead to discomfort or even injury.
Understanding the impacts of pressure helps divers maintain safety and avoid common complications such as ear injuries. Diving instructors will always emphasize the importance of controlling your rate of descent to allow your body—including your ears—the time it needs to adjust to increasing pressure.
Pressure Difference
Pressure difference is a critical concept when scuba diving. This is the variation between the pressure inside your body and the water pressure outside. At sea level, your body is acclimated to atmospheric pressure, but in the ocean, water pressure increases with depth.
The formula governing this phenomenon in fluids, such as water, is given by the hydrostatic pressure equation: \( P = \rho g h \). Here, \( P \) represents the pressure, \( \rho \) is the density of sea water (measured as \(1025 \text{ kg/m}^3\)), \( g \) signifies gravity (about \(9.81 \text{ m/s}^2\)), and \( h \) is the water depth.
When diving, if the pressure outside exceeds the atmospheric pressure inside by as much as \(35 \text{ kPa}\), it can be problematic. Calculating this pressure difference is pivotal to determine safe diving depths and to prevent issues like eardrum ruptures. Knowing how to compute and anticipate these changes is part of essential diving training, highlighting the need for awareness and caution.
Eardrum Rupture
Eardrum rupture is a potential risk for scuba divers, usually caused by a rapid change in pressure. This sensitive membrane in our ear is extremely delicate, and while it can withstand some pressure, beyond a \(35 \text{ kPa}\) difference, it risks tearing.
Such ruptures may occur when a diver descends too quickly without proper equalization. Symptoms can include sharp pain, dizziness, and hearing loss, signaling damage that can take weeks to heal. The rupture occurs because the external pressure from water increases quickly, while the internal pressure remains constant if not properly adjusted.
To prevent eardrum ruptures
  • Descend slowly to allow for gradual pressure equalization.
  • Regularly perform equalizing techniques like swallowing, yawning, or gently blowing while pinching the nose.
  • Do not dive if experiencing a cold or an ear infection, as these can hinder equalization.
Ensuring these practices can keep your diving experiences both safe and enjoyable.

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Most popular questions from this chapter

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