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)
“Man is fallen; nature is erect, and serves as a differential thermometer, detecting the presence or absence of the divine sentiment in man.”
—Ralph Waldo Emerson (1803–1882)
“The boatmen appeared to lead an easy and contented life, and we thought that we should prefer their employment ourselves to many professions which are much more sought after. They suggested how few circumstances are necessary to the well-being and serenity of man, how indifferent all employments are, and that any may seem noble and poetic to the eyes of men, if pursued with sufficient buoyancy and freedom.”
—Henry David Thoreau (1817–1862)
“Power acquired by violence is only a usurpation, and lasts only as long as the force of him who commands prevails over that of those who obey.”
—Denis Diderot (1713–1784)