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Chapter 15: Problem 8

A mountain stream, frothy with entrained air bubbles, presents a serious hazard to hikers who fall into it, for they may sink in the stream where they would float in calm water. Why?

Short Answer

Expert verified
The presence of entrained air bubbles in a mountain stream reduces the density of the water. This means that a hiker submerged in the stream displaces less weight of the fluid and hence experiences less buoyant force than in calm water. This could cause the hiker to sink where they would normally float.

Step by step solution

01

Understanding buoyancy

The first key concept in this exercise is understanding buoyancy. Buoyancy is the force exerted on an object that is submerged in a fluid, counteracting the force of gravity. This force is caused by the pressure difference in the fluid when the object is submerged. The magnitude of this force is equal to the weight of the fluid displaced by the object. Hence, a hiker will float in water if they displace water weight greater than their own weight.
02

Effect of air bubbles on buoyancy

The second crucial point is understanding the impact of entrained air bubbles on the buoyant force. When a stream is filled with air bubbles, it is less dense than calm water because the overall volume contains less water and more air, which is less dense. Hence, the weight of the fluid displaced by a hiker submerged in a frothy stream is less than that in calm water.
03

Identifying the danger to hikers

Given that the buoyant force depends on the weight of the water displaced, when air bubbles decrease the weight of the water displaced, the buoyant force is also reduced. Therefore, hikers may face the risk of submersion in a frothy mountain stream as opposed to calm water. A hiker's body may displace less water mass in a bubbly stream than in regular water; therefore, the buoyant force may not be enough to keep the hiker afloat, leading to the hiker sinking.

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