Download Buoyancy - MISC Lab

Teaching Sciences by Ocean Inquiry
SMS 491/ EDW 472
Spring 2008
Buoyancy
What keeps a heavy ocean liner afloat? What determines if water masses in the ocean
will sink or rise? How do submarines function and why do you need a scuba BC when
diving? The common answer to all these questions is buoyancy.
All you need to know about buoyancy:
I. When an object is immersed in a fluid it displaces water (in other words, water is
displaced to “make room” for the object; e.g., when you get into the bath the water level
rises). The amount of water an object displaces when fully submerged is equal to its own
volume (e.g., when you measure the density of rocks in class, you immersed the rocks in
water and measured the volume that was displaced)
II. The immersed object is subjected to two forces:
1. A downward force- the gravity force. This force increases with the mass of the
object; the heavier an object is the strongest the gravitational force pulling it
downwards.
2. An upward force –the buoyancy force
The buoyancy force arises from an imbalance in the pressure exerted on the object by the
fluid; because pressure increases with depth, the bottom of the immersed object
experiences a higher pressure compared to its top and therefore a net upward force. The
net force upward is equal to the weight of the fluid which is displaced (Archimedes
principle).
When the downward gravitational force is larger than the upward buoyancy force it will
sink; otherwise it will float. In other words, if the weight of an object (in air) is greater
than the weight of the fluid it displaces it will sink; if its weight is less than the weight of
the fluid it displaces it will float (recall: weight ≠ mass; weight is a force (= mg)). Since
weight = mg = ρVg (where ρ is the density), it is the same as saying that if an object is
denser than water it will sink and vice versa and if it is less dense it will float.
III. More quantitatively, the two forces can be written as (from Newton’s second law of
motion):
Fbuoyancy = m fluid g = ρ fluid Vdisplaced g
and
Fgravity = mobject g = ρ objectVobject g
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Where mfluid and mobject are the mass of the fluid displaced and the object, respectively, g
is the gravitational acceleration constant, ρfluid and ρobject are the densities of the fluid and
the body respectively, and Vdisplaced and Vobject are the volumes of the displaced water and
body, respectively (when the body is fully immersed Vdisplaced = Vobject and recall m = ρV).
The difference between the forces will determine if the body will sink, rise, or remain
neutrally buoyant.
ΔF = Fgravity − Fbuoyancy = Vobject g ( ρ object − ρ fluid )
When
ΔF > 0 the body will sink
ΔF < 0 the body will rise
ΔF = 0 the body will remain at its depth (it is neutrally buoyant, ρobject = ρfluid )
So, the key to keeping a ship afloat, whether it is made out of wood, steel, or concrete, is
to make it displace a volume of water that weighs at least as much as the ship’s weight.
Marine science and buoyancy
Buoyancy is one of three dominant forces in ocean dynamics (the other two being
gravity and wind stress) and key for the understanding of density-driven circulation.
Ocean circulation is produced in response to atmospheric forcing:(1) Wind stress that acts
on the ocean’s surface (2) Buoyancy flux (of heat and freshwater) between air and water
that act to alter the density of seawater. Cooling and evaporation makes ocean water
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denser (making the surface waters less buoyant); warming and precipitation decrease the
density of ocean water (making surface water more buoyant). The oceanic thermohaline
circulation, for example, is attributed to latitudinal differences in buoyancy forcing.
The level at which a solid floats in a liquid depends on the balance between
gravitational force and the buoyancy force. Lithospheric plates float on the asthenosphere
(the upper mantle) at an equilibrium level (a buoyant equilibrium which is called
“isostasy”). Changes in density of lithospheric plates (as a result of various processes
(e.g., cooling of new lithosphere in mid-ocean ridges, glacial melt on continental plates)
disrupt the equilibrium between the two forces and the crust will sink or rise until a new
buoyant equilibrium is reached (this processes is termed “isostatic leveling”, and is a very
slow process). Changes in buoyant equilibrium of continental crust result in the rise or
fall of sea level in that section of the coast associated with the plate. For example, about
14,000 years ago Maine was covered with thick ice sheets, and sea level of Maine was
below the local sea level at that time. As ice retreated, the release of the weight of the ice
allowed rebound of the land mass, causing sea level to fall. [Note: buoyancy (isostatic)
leveling is only one (and very slow) process affecting sea level. Two other processes are
thermal expansion and changes in water volume as a result of land-based ice melt. We
will discuss these processes in the unit about heat and temperature].
Many marine organisms face the challenge of buoyancy regulations. Proteins,
connective tissues, skeletons and shells all have densities that are larger than the density
of seawater. Higher body density can result in the removal of an organism from its
comfort- zone by sinking (e.g., phytoplankton sinking away from the photic zone),
exposure to changes in pressure and temperature, and may affect the energy consumption
of the organism. Marine organisms developed a variety of strategies to control their
buoyancy, and hence regulate their position in the water column. Examples include the
exchange of heavier ions for lighter ions, the storage of fat and lipids and the use of gas
filled spaces.
Buoyancy is a fundamental principle in the design of boats, ships, submarines,
and autonomous underwater vehicles, with the latter being the state-of-the-art in ocean
technology and exploration. For example, buoyancy-driven gliders and floats are used to
sample the ocean. These vehicles carry a variety of sensors (e.g., temperature, salinity,
and biochemical sensors) and can sample the water column by changing their density,
and thus the buoyancy force applied on them. By pumping a fluid into/out of an
incompressible reservoir (such as a scuba bottle) to one that is compressible (e.g., a
balloon), the vehicle changes its volume (while its mass remains constant) and hence its
density. For an example visit: http://www.argo.ucsd.edu/FrHow_Argo_floats.html.
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Last updated: 2/4/08
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