/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 There is a maximum depth at whic... [FREE SOLUTION] | 91Ó°ÊÓ

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There is a maximum depth at which a diver can breathe through a snorkel tube (\(\textbf{Fig. E12.17}\) ) 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 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.)

Short Answer

Expert verified
The external-internal pressure difference is approximately 59841 Pa.

Step by step solution

01

Understand the Pressure Concept

The pressure exerted by a column of fluid is due to the weight of the fluid above the point in question. This pressure increases with depth in the fluid because more water is above the point. The key is to find the pressure difference between the external pressure (at the depth of the lungs) and internal pressure (atmospheric pressure when using a snorkel).
02

Identify the Relevant Formula

The pressure difference due to water depth can be calculated using the formula: \( \Delta P = \rho g h \), where \( \Delta P \) is the pressure difference, \( \rho \) is the density of water (for freshwater, \( 1000 \ \text{kg/m}^3 \)), \( g \) is the acceleration due to gravity (approximately \( 9.81 \ \text{m/s}^2 \)), and \( h \) is the depth of the water column (6.1 m in this case).
03

Plug in the Values and Compute

Substitute the values into the formula: \( \Delta P = 1000 \ \text{kg/m}^3 \times 9.81 \ \text{m/s}^2 \times 6.1 \ \text{m} \). Calculate to get \( \Delta P \).
04

Calculate the Result

Perform the calculation: \( \Delta P = 1000 \times 9.81 \times 6.1 = 59841 \ \text{Pa} \). Therefore, the pressure difference is approximately 59841 Pa.

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Key Concepts

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

Snorkeling Physics
When you go snorkeling, you're essentially exploring the water surface while still breathing air from the atmosphere. Snorkeling physics revolves around understanding how pressure changes with depth. Because a snorkel tube connects your lungs to the air above water, the pressure inside your lungs remains at atmospheric pressure, no matter how deep you are. However, the water exerts additional pressure on your body. As you swim deeper, this pressure increases and can compress your lungs beyond what's comfortable or safe. This is why snorkeling usually limits you to stay near the water surface, unlike scuba diving that uses tanks to breathe compressed air.
Pressure Difference Formula
The concept of pressure difference is central when discussing how submerged objects experience forces. The pressure difference formula, \( \Delta P = \rho g h \), is key to solving many fluid mechanics problems. In this equation, \( \Delta P \) is the pressure difference between the water and your lungs. \(\rho\) represents the water’s density, \( g \) is the gravitational acceleration, and \( h \) is the depth below the water surface. By inserting the values for freshwater (\( 1000 \, \text{kg/m}^3\) for density, \( 9.81 \, \text{m/s}^2\) for gravitational acceleration), and the depth of 6.1 meters, you can find how much more pressure there is from the water compared to the atmospheric pressure in your lungs, which is crucial for understanding safe snorkeling depths.
Fluid Mechanics Concepts
Fluid mechanics is a branch of physics concerning the behavior of fluids (liquids and gases) and the forces on them. In snorkeling, it explains how pressure changes with depth in a liquid. A fundamental aspect of this field is how the pressure at any point in a static fluid is due to the weight of the fluid above it. This is why, as you move deeper into water, the pressure increases. Moreover, while atmospheric pressure is fairly constant, water pressure increases significantly with each meter you descend. Understanding these principles helps in estimating how deep a snorkeler can go safely and why scuba diving requires pressurized tanks to match increased external pressure.

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