91Ó°ÊÓ

Elephants under pressure. An elephant can swim or walk with its chest several meters underwater while the animal breathes through its trunk, which remains above the water surface and acts like a snorkel. The elephant's tissues are at an increased pressure due to the surrounding water, but the lungs are at atmospheric pressure because they are connected to the air through the trunk. Figure 13.47 shows the gauge pressures in an elephant's lungs and abdomen when the elephant's chest is submerged to a particular depth in a lake. In this situation, the elephant's diaphragm, which separates the lungs from the abdomen, must maintain the difference in pressure between the lungs and the abdomen. The diaphragm of an elephant is typically \(3.0 \mathrm{~cm}\) thick and \(120 \mathrm{~cm}\) in diameter. The maximum force the muscles of the diaphragm can exert is \(24,000 \mathrm{~N}\). What maximum pressure difference can the diaphragm withstand? A. \(160 \mathrm{~mm} \mathrm{Hg}\) B. \(760 \mathrm{~mm} \mathrm{Hg}\) C. \(920 \mathrm{~mm} \mathrm{Hg}\) D. \(5000 \mathrm{~mm} \mathrm{Hg}\)

Step by step solution

01

Understand the Problem

We need to determine the maximum pressure difference the diaphragm of an elephant can withstand, given the maximum force it can exert and the physical dimensions of the diaphragm.

02

Calculate Diaphragm Area

The diaphragm can be treated as a circular area. The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius. Given that the diameter is 120 cm, the radius is \( r = \frac{120}{2} = 60 \) cm, or 0.6 m. Thus, the area is:\[ A = \pi (0.6)^2 = \pi \times 0.36 = 1.131 \text{ m}^2 \]

03

Apply Pressure Force Relationship

Given that pressure is force per unit area, \( P = \frac{F}{A} \), where \( F = 24,000 \) N is the maximum force the diaphragm can exert and \( A = 1.131 \text{ m}^2 \) is the area we calculated. Substitute the values to find the pressure:\[ P = \frac{24,000}{1.131} \approx 21,224.1 \text{ Pa} \]

04

Convert Pressure to mm Hg

We need to convert the pressure from pascals to mm Hg. The conversion factor is \( 1 \text{ mm Hg} = 133.322 \text{ Pa} \). Therefore:\[ P = \frac{21,224.1}{133.322} \approx 159.15 \text{ mm Hg} \]

05

Select Closest Answer

The calculated maximum pressure difference the diaphragm can withstand is approximately 159.15 mm Hg, which is closest to option A: 160 mm Hg.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Pressure Difference

The concept of pressure difference is crucial in understanding how the elephant’s diaphragm manages the varying pressures between its lungs and abdomen when submerged in water.
When an elephant is underwater, its body tissues experience increased pressure from the surrounding water. However, the pressure inside the elephant’s lungs remains at atmospheric pressure due to the air flowing through the trunk.
This scenario creates a pressure differential across the diaphragm, which must be balanced for the elephant to breathe effectively.

• The difference in pressure can be calculated using the formula for pressure: \( P = \frac{F}{A} \) where \( F \) is the force and \( A \) is the area.
• The diaphragm must withstand this pressure difference, ensuring no collapse occurs in the lungs.

Understanding these principles helps explain how large animals like elephants can survive and adapt to their environments.

Elephant Adaptation

Elephants are fascinating creatures that have developed unique adaptations to thrive in diverse environments—such as breathing through a trunk when submerged.
This adaptation allows elephants to venture into deeper waters while keeping their lungs at atmospheric pressure.

• The trunk acts like a snorkel, providing a conduit for air from above the water surface.
• It enables the animal to focus its energy on other tasks, like swimming, without worrying about respiratory issues.

This particular adaptation also involves structural changes in the diaphragm and muscular systems to better manage the pressure differentials over extended periods.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us and is a constant factor influencing many natural phenomena, including how living beings like elephants breathe.
In the context of our exercise, when the elephant is underwater but breathing through its trunk, its lungs are still exposed to atmospheric pressure.

• Atmospheric pressure is approximately 101,325 Pa at sea level.
• It influences how mammals regulate their respiratory processes, and elephants must maintain this pressure for gas exchange effectively.

This continuous exposure to atmospheric pressure, regardless of body position or environmental conditions, is critical for the survival of many terrestrial and semi-aquatic animals.

Biophysics Concepts

Biophysics combines physics and biology to decipher how organisms work, explaining complex processes like the ones seen in elephants using physical principles.
These concepts help illustrate how elephants manage large pressure differentials using their diaphragm without compromising lung function.

• Biophysics applies mechanical equations to biological systems to explore the resilience and adaptability of organisms like elephants.
• It involves calculating pressure forces and understanding the physiological demands placed on the elephant’s muscular system.

Through biophysics, we gain insights into how elephants' bodies are equipped physically to deal with their environmental challenges and physiological limits.