Activity 1: Graphing Scuba Divers And Pressure

Activity 1 Graphing Scuba Divers Must Learn About Pressure Under Wate

Activity 1: Graphing scuba divers must learn about pressure underwater. At the water's surface, air exerts 1 atmosphere (atm) of pressure. Under water, the pressure increases with depth according to the equation P (atm) = 1 + d/33, where d is the depth in feet. Boyle's law states that the volume V of air varies inversely with pressure P, expressed as PV = k, where k is a constant. When holding your breath, the volume of air in your lungs increases as you ascend, due to decreasing pressure. For example, if you have 4 quarts of air at a depth of 66 ft (P=3 atm), the air will expand to 6 quarts at 33 ft (P=2 atm). Using this data, make a table and graph to demonstrate how the volume of air varies with depth and pressure.

Activity 2: When a diver ascends from deep water, the volume of air in the lungs can more than double, risking lung rupture. To prevent this, divers are instructed not to hold their breath during ascent. If a diver has 4 quarts of air at 66 ft depth (P=3 atm), how many quarts of air must be exhaled during ascent to the surface, where P=1 atm, to ensure the lungs contain only 4 quarts upon surfacing? Explain why beginning divers are advised "Don't hold your breath," referencing your tables and graphs.

Activity 3: A common scuba tank volume is 71.2 ft³ at surface pressure (1 atm). The tank's internal pressure is around 2250 lb/in². How large does a tank need to be to hold 71.2 ft³ of compressed air at this pressure? Apply Boyle's law PV = k, noting that 1 atm = 14.7 lb/in².

Activity 4: The rate at which a diver consumes air depends on factors including depth. The deeper the dive, the more quickly the air is used, and the duration is inversely proportional to the pressure. A tank lasting 60 minutes at the surface (1 atm) will last less at greater depths. How long will the air last at 99 ft (pressure of 4 atm)? Create a table to show the duration of air supply at depths of 0 ft, 20 ft, 33 ft, 40 ft, 50 ft, 66 ft, and 99 ft.

Paper For Above instruction

Introduction

Scuba diving involves understanding pressure effects underwater and how they influence a diver’s body and equipment. Boyle’s law, which describes the inverse relationship between the volume and pressure of a gas, is central to understanding the physical challenges faced by divers. This paper explores the relationship between pressure, volume, and depth, illustrating critical concepts through tables and graphs. It also examines practical implications, such as lung safety, tank sizing, and air consumption rates at various depths.

Relationship Between Pressure and Depth

Underwater pressure increases with depth, calculated through the formula P = 1 + d/33, where d is in feet. At the surface, pressure equals 1 atm, and at greater depths, pressure rises linearly. For example, at 66 ft, pressure is approximately 3 atm. This relationship highlights how pressure variation affects a diver’s lungs and equipment and underscores the importance of understanding Boyle’s law.

Boyle’s Law and Its Application

Boyle’s law states that PV = k, meaning that as pressure increases, volume decreases proportionally, assuming temperature remains constant. This inverse relationship explains why lung volume changes during a dive: as a diver descends, increased pressure compresses the air in the lungs; as the diver ascends, decreased pressure allows the air to expand. Understanding this helps prevent lung injury caused by overexpansion during ascent.

Volume and Pressure Variations with Depth

Given the initial data—that 4 quarts of air at 66 ft (P=3 atm) expands to 6 quarts at 33 ft (P=2 atm)—a complete table can be constructed to depict volume changes with depth:

This table reveals that as depth increases, pressure increases, and the volume of air decreases accordingly, in line with Boyle's law. A graph plotting depth versus volume demonstrates an inverse relationship and emphasizes the importance of managing lung volume during dives.

Implications for Diver Safety: Breathing and Lung Expansion

As a diver ascends, the reduction in pressure causes the air within the lungs to expand. If a diver holds their breath during ascent, the rapidly expanding air can cause lung rupture—a potentially fatal injury. Therefore, divers are taught to exhale continuously during ascent, preventing overexpansion of the lungs. For example, if a diver starts with 4 quarts of air at 66 ft (P=3 atm), to maintain this volume upon surfacing, they must exhale enough air during ascent. Calculations show that at the surface (P=1 atm), the lung volume should be 12 quarts (since V = 4 qt × (P at 66 ft / P at surface)). By exhaling accordingly, divers avoid lung overexpansion and injury.

Sizing of Diving Tanks

The volume of a scuba tank at surface pressure is often marked as 71.2 ft³. However, the tank's physical volume, considering internal pressure, can be calculated using Boyle’s law. Given the internal pressure of 2250 lb/in², and converting to atmospheres (1 atm = 14.7 lb/in²), the actual tank volume V_tank can be found as follows:

V_tank = V_filled × (P at surface) / P_internal = 71.2 ft³ × 1 atm / (2250 / 14.7) atm ≈ 71.2 ft³ × 14.7 / 2250 ≈ 0.466 ft³

This indicates that the physical volume of the tank is about 0.466 ft³, containing compressed air at high pressure. The actual tank size must be designed to contain this compressed volume safely.

Air Consumption and Dive Duration

The rate at which air is consumed depends on depth, with more pressure leading to faster usage. Since the duration of available air at depth is inversely proportional to pressure, the tank's duration at various depths can be calculated. For example, if a tank lasts 60 minutes at the surface (1 atm), at 99 ft (pressure of 4 atm), it will last approximately 60 / 4 = 15 minutes. A table illustrating this:

This demonstrates the critical need for divers to plan dives carefully, considering depth and air duration.

Conclusion

Understanding the relationship between pressure, volume, and depth is essential for safe scuba diving. Boyle’s law provides the framework for predicting how lung volume and tank capacity change underwater. Proper exhalation during ascent prevents lung injury caused by overexpansion, and calculating tank size and air duration ensures safe diving practices. Through the construction of tables and graphs, divers and instructors can better visualize these relationships, enhancing safety and efficiency in underwater exploration.

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