Suppose a fish has an average density of 1030 kg/m3, compared to the density of the surrounding water, 1000 k/m3. One way the fish can keep from slowly sinking is by using an air bladder (the density of air is 1.2 kg/m3). What fraction of the fish’s total volume must be air in order for the fish to be neutrally buoyant (the buoyant force is equal and opposite to the weight). Assume that the volume V of the fish’s tissue is fixed, so in order to increase the volume U of the air bladder, the total volume of the fish V + U must increase.

Physics for Scientists and Engineers: Foundations and Connections
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ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter15: Fluids
Section: Chapter Questions
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Suppose a fish has an average density of 1030 kg/m3, compared to the density of the surrounding water, 1000 k/m3. One way the fish can keep from slowly sinking is by using an air bladder (the density of air is 1.2 kg/m3). What fraction of the fish’s total volume must be air in order for the fish to be neutrally buoyant (the buoyant force is equal and opposite to the weight). Assume that the volume V of the fish’s tissue is fixed, so in order to increase
the volume U of the air bladder, the total volume of the fish V + U must increase.

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