Fish buoyancy

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In order to stay at a constant depth, an aquatic organism needs to be neutrally buoyant.  To achieve this, the animal must have an average density that is equal to that of water, so that the mass of its body is equal to the mass of the volume of water being displaced. 

One of the complications underwater to maintaining neutral buoyancy is the fact that pressure changes with depth.  Since air volume is inversely proportional to pressure, the volume of air in a fish’s swim bladder or a mammal’s lungs decreases with depth, changing the animal’s overall volume and hence its density. The following example explores some of the effects of these changes.

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1. Consider a freshwater fish (swimming in water of density $\mathrm{1000 \; kg/m^3}$).  Assume that the average density of its tissues is $\mathrm{1070 \; kg/m^3}$ and its swim bladder makes up 7% of the animal’s total volume at the surface.  Calculate the density of the fish at the surface.

2. What happens to the fish’s density as it descends to 20 m?  What would happen to the fish if it did nothing? (Assume a constant temperature.)

3. What volume of air does it have to add to its swim bladder to remain neutrally buoyant at a depth of 20 m? 

Karen Carleton