Chapter 20, Problem 43A

It is easy to breathe when snorkeling with only your face beneath the surface of the water, but quite difficult to breathe when you are submerged nearly a meter, and nearly impossible when you are more than a meter deep (even if your snorkel tube reaches to the surface). Figure out why, and explain carefully.

To determine

To Explain: It is very difficult for someone to breathe inside the water.

Explanation of Solution

Introduction:

The fluid pressure is a pressure at any point inside the fluid due to weight of fluid. The pressure applied by the atmosphere of earth is known as atmospheric pressure. The magnitude of pressure applied by the atmosphere at the sea level is $1\text{ atm}$ or $760\text{ mm}$ of mercury.

The variation of pressure with depth is:

  $P=P_0+\rho gh$

Where, $P_0$ = atmospheric pressure

  $\rho$ = density of fluid

  $h$ = depth

  $g$ = acceleration due to gravity

Snorkeling tube is a type of plastic tube or rubber tube which is fitted in the swimmer's mouth for taking breath under water.

As swimmer goes inside the water and depth increases, the pressure acting on body also changes. The variation of pressure with depth is:

  $P=P_0+\rho gh$

From above equation, pressure increases with depth $\left(h\right)$ and practically it is approximately estimated that for change in every $10$ m depth, the increase in pressure is approximately $1$ atm.

Therefore, it is very difficult for chest to expand as the force acting on chest increases with depth. According to data, human lungs can operate only up to an external pressure of $0.05$ atm or less, which means lungs will not able to suck air once swimmer go beyond depth of $0.5$ m.

Conclusion:

Thus, it is very difficult to breathe after depth of $1\text{ m}$ due to external force of water.