3.9 Gravity and the Buoyancy Force
35
in the Cartesian coordinate system and has vector components (0, 0, −g), where g =
9.81 m/s
2
is called acceleration due to gravity.
If an object of a certain mass M obj and volume V obj is released in the water column, instead of the full gravity force, it will experience only a reduced gravity force,
called buoyancy force, that makes it sink at a slower rate or even rise in dependence
of the density of the ambient medium. Imagine an air-fille plastic ball that will pop
up if released in water.
According to Archimedes’ Principle, the resultant buoyancy force is proportional
to the difference between the object’s mass with the mass of the flui replaced by the
object’s volume. See Stein (1999) for a biography of Archimedes. The constant of
proportionality is acceleration due to gravity. Accordingly, the resultant buoyancy
force (per unit mass of the object) is given by:
Buoyancy force = −g
(M obj − M amb )
M obj
where M amb is the mass of the ambient flui replaced by the object. After a few
manipulations, this formula can be expressed in terms of densities, yielding:
Buoyancy force = −g
(ρ obj − ρ amb )
ρ obj
(3.14)
where ρ amb is the density of the ambient fluid Note that the buoyancy force has a
negative sign and is directed downward if the object’s density exceeds that of the
surrounding fluid Now it will be not that difficul for the reader to tell why ships
made from steel usually stay at the sea surface (unless capsizing).
3.9.2 Reduced Gravity
In physical oceanography, the negative of the buoyancy force (per unit mass) is
commonly termed reduced gravity. This quantity carries the symbol g
and is given
by:
g
= g
(ρ obj − ρ amb )
ρ obj
(3.15)
It should be noted that buoyancy is not only restricted to objects of a solid skin.
The object of interest can be a flui parcel itself.
3.9.3 Stability Frequency
Vertical density gradients can be expressed in terms of the stability frequency N ,
traditionally called Brunt – V¨ ais¨ al¨ a frequency with appreciation of early works by
35
in the Cartesian coordinate system and has vector components (0, 0, −g), where g =
9.81 m/s
2
is called acceleration due to gravity.
If an object of a certain mass M obj and volume V obj is released in the water column, instead of the full gravity force, it will experience only a reduced gravity force,
called buoyancy force, that makes it sink at a slower rate or even rise in dependence
of the density of the ambient medium. Imagine an air-fille plastic ball that will pop
up if released in water.
According to Archimedes’ Principle, the resultant buoyancy force is proportional
to the difference between the object’s mass with the mass of the flui replaced by the
object’s volume. See Stein (1999) for a biography of Archimedes. The constant of
proportionality is acceleration due to gravity. Accordingly, the resultant buoyancy
force (per unit mass of the object) is given by:
Buoyancy force = −g
(M obj − M amb )
M obj
where M amb is the mass of the ambient flui replaced by the object. After a few
manipulations, this formula can be expressed in terms of densities, yielding:
Buoyancy force = −g
(ρ obj − ρ amb )
ρ obj
(3.14)
where ρ amb is the density of the ambient fluid Note that the buoyancy force has a
negative sign and is directed downward if the object’s density exceeds that of the
surrounding fluid Now it will be not that difficul for the reader to tell why ships
made from steel usually stay at the sea surface (unless capsizing).
3.9.2 Reduced Gravity
In physical oceanography, the negative of the buoyancy force (per unit mass) is
commonly termed reduced gravity. This quantity carries the symbol g
and is given
by:
g
= g
(ρ obj − ρ amb )
ρ obj
(3.15)
It should be noted that buoyancy is not only restricted to objects of a solid skin.
The object of interest can be a flui parcel itself.
3.9.3 Stability Frequency
Vertical density gradients can be expressed in terms of the stability frequency N ,
traditionally called Brunt – V¨ ais¨ al¨ a frequency with appreciation of early works by