Bernoullian Thoughts Essay, Research Paper
Daniel Bernoulli was born into a family of
mathemeticians on February 8, 1700. He was the only person
in his family to make an impressive mark on physics.
Bernoulli became a Swiss physicist and mathmatician who made
enourmous contributions to the world of physics. He
uncovered many significant phenomena in hydrodynamics, and
in 1738, published his most famous work, Hydrodynamica,
which was a study of equilibrium, pressure, and velocity of
fluids. He proved that as the velocity of fluid flow
increases, its pressure decreases. Bernoulli?s principle
was an early formulation of the subsequent idea of ?the
conservation of energy?.
Bernoulli?s Hydrodynamica was also the first attemt to
explainof the behavior of gasses with changing pressure and
temperature. This was the beginning of the kinetic theory of
gasses. His gas model has been revived and transformed into
a powerful theory regarding the thermal and mechanical
properties of gases using the atomic hypothesis.
Bernoulli thought of the ?corpuscles? of the gas as so
minute that there were ?practically an infinite number?
under ordinary conditions, even in a small container. In
their rapid motion, these corpuscles collide with each other
and also with the rigid walls of the closed vessel. The
collisions, however, can be assumed to be perfectly elastic;
therefore, the kinetic energy of the particles is conserved
and the motion can continue undiminished. Therefore, the
pressure which the gas is expected to exert against all
sides of the container is caused by the incessant impact of
millions of high speed particles; hence the name ?impact
theory? of gas pressure.
Imagine a gas filled cylindrical container with the top
end that is able to slide up and down, in and out like a
piston. If the volume is slowly decreased, the corpuscles
are more crowded in the progressively smaller space and the
number of collisions per second with the walls would be
larger (i.e., the pressure should become greater, as
observed). Bernoulli even calculated the magnitude of this
expected increase and found that it corresponded to Boyle?s
At the time of Bernoulli?s discovery, his work was
generally ignored. The lack of general attention was due to
the unclear knowledge of gases. Yet more than a century
later, his work simultaneously clarified the main problems
of the nature of gases, heat and chemistry. For Bernoulli,
in effect, had made two enormous leaps in his thinking for
which most scientists were not ready to take. First, he
illucidates, the direct equivalence of heat and internal
molecular motion, ignoring any interactions between the two.
Second, he confirmed the idea that a well-defined numerical
relationship, such as Boyle?s simple law, could be deduced
from a chaotic picture of randomly moving particles.
Bernoulli?s principle was centerd around the notion
that we suppose a small portion of liquid flow from one
point to another point, and that change of position is
affected without incurring any waste of energy. From the
principle of conservation of energy, it may be asserted that
the total energy is not changed during the displacement.
This statement is known as Bernoulli?s theorem and is often
P + 1/2 pv2 + pgy = constant
Bernoulli?s equation states that the sum of the pressure
(P), the kinetic energy per volume (1/2 pv2), and the
potential energy per unit volume (pgy) have the same value
at all points along a streamline. Using Bernoulli?s law,
because there is no waste of energy during the passage of
the liquid, the total energies at each three places are
equal. If the fluid is incompressible then the internal
energy is the same, which proves, in turn, that Bernoulli?s
equation holds true along any streamline.
Bernoulli?s foregoing principle explains a number of
phenomena about the behavior of liquids which, at first,
seem strange. Suppose two ships are steaming side by side
in still water: The relative motion of the ships with
respect to the water will remain unchanged if the ships are
imagined to be stationary and the water imagined to flow
with the same velocity in the opposite direction. the water
entrapped between the ships will speed up because of the
narrow space. As a consequence, the pressure in the water
between the ships will be reduced and will become less than
the water pressure on the far sides of the ships. The
excess pressure will cause the ships to become closer in
Bernoulli?s theorem, when applied to gasses instead of
liquids, explains such effects as the curved flight of a
tennis ball that is spinning when served, the action of an
atomizer in dividing a jet of liquid into a fine spray, the
reduction of gas pressure in a container by using an
aspirator connected to a water faucet and the propulsion of
a ship by wind power using cylindrical rotors instead of
Bernoulli?s theorem provides a means for measuring the
flow of a liquid through a pipe. A section of pipe
containing a constriction or throat is inserted in the pipe
line and the pressures are measured both at the throat and
in the pipe by pressure gauges or their equivalent. The
rise of liquid in small tubes, called manometers, indicate
the pressure. The pipe beyond the throat flares out slowly
so that the velocity of the liquid can be reduced without
disturbing the streamline flow.
Since the velocity of the liquid is greater at the
throat than in the pipe, the pressure at the throat will be
less than that in the pipe, as prescribed by Bernoulli?s
equation, and consequently, the liquid in the throat
manometer elevations, together with a knowledge of the
cross-sections of pipe and throat, permit the liquid flow to
be measured. This device is known as a Venturi meter.
Bernoulli?s theorem is not only applicable for liquids,
but also for gasses. In this case, the mathematical
treatment is complicated by the fact that gases are highly
compressible, but the general effect is the same as
previously described; namely, that when a flowing stream of
gas speeds up, its pressure decreases, and vice versa.
The lift on an aircraft wing can be explained by this
effect. Airplane wings are designed so that the air speed
above the wing is greater than that below the wing. As a
result, the air pressure above the wing is less than the
pressure below, and there is a net upward force on the wing
called the ?lift?.
In conclusion, Bernoulli contributed much to the world
and to the realm of physics. Daniel Bernoulli derived a
fundamental expression that relates pressure to fluid speed
and elevation. Bernoulli?s equation is not a freestanding
law of physics, but instead a consequence of energy
conservation as applied to the ideal fluid.
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