Terminal Velocity in The Presence of Buoyancy Force
When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero. When the terminal velocity is reached the weight of the object is exactly balanced by the upward buoyancy force and drag force. That is
where
- = weight of the object,
- = buoyancy force acting on the object, and
- = drag force acting on the object.
If the falling object is spherical in shape, the expression for the three forces are given below:
where
- diameter of the spherical object
- gravitational acceleration,
- density of the fluid,
- density of the object,
- projected area of the sphere,
- drag coefficient, and
- characteristic velocity (taken as terminal velocity, ).
Substitution of equations (2–4) in equation (1) and solving for terminal velocity, to yield the following expression
- .
Read more about this topic: Terminal Velocity
Famous quotes containing the words terminal, presence, buoyancy and/or force:
“All sin tends to be addictive, and the terminal point of addiction is what is called damnation.”
—W.H. (Wystan Hugh)
“There are twenty ways of going to a point, and one is the shortest; but set out at once on one. A man who has that presence of mind which can bring to him on the instant all he knows, is worth for action a dozen men who know as much, but can only bring it to light slowly.”
—Ralph Waldo Emerson (1803–1882)
“She keeps
The Topic over intellectual deeps
In buoyancy afloat. They see no ghost.
With sparkling surface-eyes we ply the ball:
It is in truth a most contagious game:
Hiding the Skeleton, shall be its name.”
—George Meredith (1828–1909)
“The primacy of the word, basis of the human psyche, that has in our age been used for mind-bending persuasion and brain-washing pulp, disgraced by Goebbels and debased by advertising copy, remains a force for freedom that flies out between all bars.”
—Nadine Gordimer (b. 1923)