11.2 Buoyancy in Marine Animals
355
For example, when non-swim bladder components have an average density of
Pb = 1080 kg/m 3 and sea water density is Pw = 1026 kg/m 3 , then the fraction
OO eq = 0.05.
When an animal starts to swim upwards, the surrounding fluid pressure decreases. According to the ideal gas equation pV = Const (p is the pressure and
V is the volume in which the gas is confined), the volume of the swim bladder
must increase to some fraction a > OO eq of the total animal volume. Therefore,
the animal weight becomes:
[1 - (OO eq + 00- ooeq)] PbgV =
(1 - ooeq) PbgV - (a - ooeq ) PbgV.
(11.3)
Equating animal weight to buoyancy force gives an effective force, Feff:
=0
F~ff
PwgV - (1 - a) PbgV = IPwgV - (1 - ooeq) Pb9V]+
+ (a - ooeq) PbgV = (a - ooeq) PbgV > O.
(11.4)
As the fraction a > a eq , the additional force (a - a eq ) Pbg V causes the animal
to ascend further. The ascent is even faster if the animal moves into a region
of decreasing ambient pressure, which again induces an increase in the volume
of the swim bladder a. Further movement of the fish towards the surface may
be catastrophic for the animal, unless quickly controlled by some means.
The situation is quite opposite if the animal initially starts to move down.
As surrounding pressure increases, the swim bladder is compressed and its
volume a decreases below the a eq value. Therefore, the effective force, Feff
in Eq. (11.4), becomes negative, causing the animal to sink further. Because
the volume of the swim bladder is inversely proportional to the surrounding
pressure, the change in volume is less for higher pressures. Thus, for a fish
living at great depth, a difference in swim bladder volume (a - ooeq) is easier
to correct. In general, the time for proper adjustment of the swim bladder is
of the order of hours (Denny, 1993). However, details of the physiology of the
adjustment mechanisms are beyond the scope of this book.
A second method of adjustment of the buoyancy mechanism which involves a
gas chamber is to have a chamber with rigid walls. The chamber walls have to
sustain the difference in pressure between the external hydrostatic pressure and
the pressure of gas within the chamber. The chamber contains both gas and
liquid. For example, the cuttlefish uses its cuttlebone, and the pearly Nautilus
uses its shell to control its buoyancy. When they try to sink, liquid is pumped
into the cuttlebone in the case of the cuttlefish, or into the shell in the case of
the Nautilus, and the volume of the gas decreases. The liquid is pumped out of
the chamber when the animal ascends. In fact, this mechanism is very similar,
in principle, to that used by submarines. The mechanism for pumping water
355
For example, when non-swim bladder components have an average density of
Pb = 1080 kg/m 3 and sea water density is Pw = 1026 kg/m 3 , then the fraction
OO eq = 0.05.
When an animal starts to swim upwards, the surrounding fluid pressure decreases. According to the ideal gas equation pV = Const (p is the pressure and
V is the volume in which the gas is confined), the volume of the swim bladder
must increase to some fraction a > OO eq of the total animal volume. Therefore,
the animal weight becomes:
[1 - (OO eq + 00- ooeq)] PbgV =
(1 - ooeq) PbgV - (a - ooeq ) PbgV.
(11.3)
Equating animal weight to buoyancy force gives an effective force, Feff:
=0
F~ff
PwgV - (1 - a) PbgV = IPwgV - (1 - ooeq) Pb9V]+
+ (a - ooeq) PbgV = (a - ooeq) PbgV > O.
(11.4)
As the fraction a > a eq , the additional force (a - a eq ) Pbg V causes the animal
to ascend further. The ascent is even faster if the animal moves into a region
of decreasing ambient pressure, which again induces an increase in the volume
of the swim bladder a. Further movement of the fish towards the surface may
be catastrophic for the animal, unless quickly controlled by some means.
The situation is quite opposite if the animal initially starts to move down.
As surrounding pressure increases, the swim bladder is compressed and its
volume a decreases below the a eq value. Therefore, the effective force, Feff
in Eq. (11.4), becomes negative, causing the animal to sink further. Because
the volume of the swim bladder is inversely proportional to the surrounding
pressure, the change in volume is less for higher pressures. Thus, for a fish
living at great depth, a difference in swim bladder volume (a - ooeq) is easier
to correct. In general, the time for proper adjustment of the swim bladder is
of the order of hours (Denny, 1993). However, details of the physiology of the
adjustment mechanisms are beyond the scope of this book.
A second method of adjustment of the buoyancy mechanism which involves a
gas chamber is to have a chamber with rigid walls. The chamber walls have to
sustain the difference in pressure between the external hydrostatic pressure and
the pressure of gas within the chamber. The chamber contains both gas and
liquid. For example, the cuttlefish uses its cuttlebone, and the pearly Nautilus
uses its shell to control its buoyancy. When they try to sink, liquid is pumped
into the cuttlebone in the case of the cuttlefish, or into the shell in the case of
the Nautilus, and the volume of the gas decreases. The liquid is pumped out of
the chamber when the animal ascends. In fact, this mechanism is very similar,
in principle, to that used by submarines. The mechanism for pumping water