# the textbook has completely confused me while giving derivation about bernaullis principle.can i get a simple short and clear explanation?

105 Points
11 years ago

Dear Prabhav,

Bernoulli's principle can be derived from the principle of conservation of energy. This states that in a steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. If the fluid is flowing out of a reservoir the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit mass (the sum of pressure and gravitational potential ρ g h) is the same everywhere.

${v^2 \over 2}+gz+{p\over\rho}=\text{constant}$

where:

$v\,$ is the fluid flow speed at a point on a streamline,
$g\,$ is the acceleration due to gravity,
$z\,$ is the elevation of the point above a reference plane, with the positive z-direction pointing upward — so in the direction opposite to the gravitational acceleration,
$p\,$ is the pressure at the point, and
$\rho\,$ is the density of the fluid at all points in the fluid.

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