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 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.)

Step by step solution

01

Given Data

The depth is$\mathrm{h}=6.1\mathrm{m}$.

02

Understanding the gauge pressure

In this problem, the absolute pressure can be calculated by using the sum of gauge pressure in the tube and atmospheric pressure.

03

Determining the gauge pressure

The relation of gauge pressure can be written as:

${\mathrm{P}}_{\mathrm{g}}=\mathrm{pgh}$

Here, $p$is the density of water and g is the gravitational acceleration.

Substitute 6.1 for h, 1000$\mathrm{kg}/{\mathrm{m}}^3$for p, and $9.80\mathrm{m}/{\mathrm{s}}^2$for g in the above relation.

$$\begin{gathered} {\mathrm{P}}_{\mathrm{g}}=\left(1000\mathrm{kg}/{\mathrm{m}}^3\right)\left(9.80\mathrm{m}/{\mathrm{s}}^2\right)\left(6.1\mathrm{m}\right) \\ {\mathrm{P}}_{\mathrm{g}}=59780\mathrm{Pa} \end{gathered}$$

Thus, the required pressure difference is 59780 pa.

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!