Bernoulli's Equation

Bernoulli’s equation is a restatement of the conservation of energy in terms of the jargon of fluid dynamics.  Consider a certain tube of flow (like a pipe) within a liquid, a section of which is shown in the figure below.

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Let the density of the liquid be r.  Consider two points within the tube of flow, points 1 and 2.  Let the pressure, height (above some reference  position – sound familiar?), and speed of the liquid at these two points be denoted p1, y1, v1, and p2, y2, and v2.  Bernoulli’s restatement of the  conservation of energy then states that

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(You should recognize the second term as a kinetic energy term, and the third term as a potential energy term!).  In other words, the quantity p +  (½)rv2 + rgy is a constant throughout a given tube of flow.  Unless heights are given or obviously play an important role, we shall make the approximation that the change in height, Dy = y2 – y1, contributes a negligible amount of energy to the equation above, so that the “potential  energy” terms cancel out on the two sides of the equation. Therefore, unless height information is explicitly given, we shall usually apply Bernoulli’s equation in the approximate form

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You should understand this equation enough to see that it tells us that, as the speed of an airflow increases, the corresponding pressure exerted by that airflow decreases.  This concept explains such things as the flight of planes and roofs being removed by tornadoes. 

    Click HERE to see an application of Benoulli’s principle to a robot being able to move across a wall or ceiling.