The bodies of some fish contain porous bones or air-filled bladders which allow

Question

The bodies of some fish contain porous bones or air-filled bladders which allow them to float in water without expended any energy. One such example is the cuttlefish, which has porous bones with density = 0.62 g/cm3 while the rest of its body has density = 1.067 g/cm3. Answer the following questions, assuming sea water has density = 1.026 g/cm3: (a) If the cuttlefish lives 150 m below the sea, what is the water pressure on the cuttlefish? (b) For a cuttlefish with cross-sectional area A and thickness h, what must its average density be in order to remain at a depth of 150 m? Express your answer in terms of A and h. You can approximate the shape of the cuttlefish as a box. (c) What percentage of its body volume must be composed of porous bone?

Explanation / Answer

a) Pressure = _water*gH = (1.026*10^3)*9.81*150 = 1509759 Pa

b) Buoyant force = _water*V*g

Weight of fish = _fish*V*g

Equating both, _fish = _water = 1.026 g/cm3

c) x*0.62 + (1-x)*1.067 = 1.026

So, x = 0.0917 = 9.17 %

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