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

experimental law.

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

expressed as:

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

proximity.

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

sails.

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.

References

Adiar, Robert. The Great Design: Particles, Fields and

Creation. New York: Oxford University Press, 1987.

Benton, William. ?Bernoulli, Daniel?. Encyclopedia

Britannic. 1969.

Duncan and Starling. A Textbook of Physics. London:

Macmillan and Co. 1948.

Furry, Purcell and Street. Physics. New York: Blankston

Co. 1952.

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