Bernoulli's Principle
This is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton's 2nd law will cause an acceleration of the fluid. The fundamental relation,
$\textstyle \parbox{4.5in}{\vspace*{5pt} work done = change in kinetic energy \vspace*{5pt}}$
in this situation can be written as
$\textstyle \parbox{4.5in}{\vspace*{5pt} - (change in pressure) x area x distance = change in kinetic energy, \vspace*{5pt}}$
which furthermore can be expressed as
$\textstyle \parbox{4.5in}{\vspace*{5pt} change in pressure + change in ( kinetic energy / volume ) = 0. \vspace*{5pt}}$
In other words,
\fbox{\parbox{4.5in}{\vspace*{7pt} Pressure + ( kinetic energy / volume ) = constant \vspace*{7pt}}}
which is known as Bernoulli's principle. This is very similar to the statement we encountered before for a freely falling object, where the gravitational potential energy plus the kinetic energy was constant (i. e., was conserved).
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