·1 ILW A fish maintains its depth in fresh water by...

$\cdot 1$ ILW A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed. a fish has a density of $1.08 \mathrm{~g} / \mathrm{cm}^{3}$. To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water?

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Key Concepts

Neutral Buoyancy

Neutral buoyancy occurs when an object's density equals that of the ambient fluid, allowing it to remain suspended without rising or sinking. Achieving neutral buoyancy typically involves adjusting the object's composition—often by incorporating a low-density material like air—to match the fluid's density.

Density

Density is the measure of mass per unit volume. In physics and fluid mechanics, it determines how an object interacts with a surrounding fluid. When the mass remains constant but additional volume is added (such as inflating parts with air), the overall density is reduced, which is critical in achieving buoyancy.

Volume Fraction

The volume fraction represents the proportion of the total volume occupied by a particular component. In the context of adjusting an object's overall density, determining the necessary volume fraction of a low-density material (such as air) is essential; a specific fraction must be incorporated to reach the desired average density.

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