a distance enough to allocate a volume of 1 cm
3 of fluid. The distance travelled will
therefore be 1 cm
3 /10 cm
2 = 0.1 cm.
The force on the output piston was increased 10 times, but the path through
which this force was applied was reduced by 1/10. The total work (given by the
product of force by distance) obtained from the hydraulic system remained constant
(e.g., Asimov 1993).
A2.4.2 Buoyancy
Bodies submerged in a fluid appear to weigh less than outside it. A huge rock,
which under normal conditions can hardly be moved, is more easily lifted if it is
underwater. When the moving rock reaches the water surface it appears to weigh
more. Other materials, such as wood, may float on liquid’s surface. In each of these
situations, there is an upward force, buoyancy, inherent to the liquid, which opposes
the downward gravity force.
Buoyancy occurs because the pressure of a fluid at rest increases with depth. In
this way, an upward pressure force exerted by the fluid on the lower surface of a
submerged solid body is greater than the downward force exerted on the upper body
surface. The buoyancy is the upward force resulting from the balance of these two
forces. For example, for a cylindrical body of height h, with the upper and lower
heights h 1 and h 2 , a cross sectional area A and subject to pressures P 1 and P 2 , the
resulting buoyancy F I , from F 1 = P 1 A and F 2 = P 2 A, on the upper and lower
surfaces, respectively, becomes:
F ¼ F 2 À F 1 ¼ q f gA h 2 À h 1
ð
Þ¼q f gAh ¼ q f gV ¼ m f V
ðA2:30Þ
where V is the volume of the cylinder. The term m f V corresponds to the weight of
the fluid with a volume equal to the volume of the cylinder. In this way, buoyancy
is equal to the weight of fluid displaced by the immersed body.
Generally, submersion of any irregular solid body in a liquid contained in a
vessel causes a displacement of an equal volume of liquid that rises to a level
suitable with the displaced volume. It follows that the immersed body exerts a
downward force enough to compensate for the weight of the displaced liquid and
that, by Newton’s third law, the liquid will exert an upward reaction, equivalent to
the weight of the same volume of liquid. The force of impulsion, exerted on a body
submerged in a fluid, is equal to the weight of the fluid, displaced by that body
(Archimedes Principle).
The weight of the submerged body is equal to the product of its volume V and
density D. The weight of the displaced liquid is equal to the product between its
volume (equal to that of the submerged body) and its density d 1 .
The weight of the body after submersion, W, is equal to the original weight,
minus the weight of the displaced water:
Annex A2: Basic Topics on Laws of Motion and Evaporation
347
3 of fluid. The distance travelled will
therefore be 1 cm
3 /10 cm
2 = 0.1 cm.
The force on the output piston was increased 10 times, but the path through
which this force was applied was reduced by 1/10. The total work (given by the
product of force by distance) obtained from the hydraulic system remained constant
(e.g., Asimov 1993).
A2.4.2 Buoyancy
Bodies submerged in a fluid appear to weigh less than outside it. A huge rock,
which under normal conditions can hardly be moved, is more easily lifted if it is
underwater. When the moving rock reaches the water surface it appears to weigh
more. Other materials, such as wood, may float on liquid’s surface. In each of these
situations, there is an upward force, buoyancy, inherent to the liquid, which opposes
the downward gravity force.
Buoyancy occurs because the pressure of a fluid at rest increases with depth. In
this way, an upward pressure force exerted by the fluid on the lower surface of a
submerged solid body is greater than the downward force exerted on the upper body
surface. The buoyancy is the upward force resulting from the balance of these two
forces. For example, for a cylindrical body of height h, with the upper and lower
heights h 1 and h 2 , a cross sectional area A and subject to pressures P 1 and P 2 , the
resulting buoyancy F I , from F 1 = P 1 A and F 2 = P 2 A, on the upper and lower
surfaces, respectively, becomes:
F ¼ F 2 À F 1 ¼ q f gA h 2 À h 1
ð
Þ¼q f gAh ¼ q f gV ¼ m f V
ðA2:30Þ
where V is the volume of the cylinder. The term m f V corresponds to the weight of
the fluid with a volume equal to the volume of the cylinder. In this way, buoyancy
is equal to the weight of fluid displaced by the immersed body.
Generally, submersion of any irregular solid body in a liquid contained in a
vessel causes a displacement of an equal volume of liquid that rises to a level
suitable with the displaced volume. It follows that the immersed body exerts a
downward force enough to compensate for the weight of the displaced liquid and
that, by Newton’s third law, the liquid will exert an upward reaction, equivalent to
the weight of the same volume of liquid. The force of impulsion, exerted on a body
submerged in a fluid, is equal to the weight of the fluid, displaced by that body
(Archimedes Principle).
The weight of the submerged body is equal to the product of its volume V and
density D. The weight of the displaced liquid is equal to the product between its
volume (equal to that of the submerged body) and its density d 1 .
The weight of the body after submersion, W, is equal to the original weight,
minus the weight of the displaced water:
Annex A2: Basic Topics on Laws of Motion and Evaporation
347