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Bernoulli's Theorem

Bernoulli's theorem is implied by the conservation of mass and energy in fluid flow. Consider a nonviscous, incompressible fluid flowing through a pipe with cross-sectional area and pressure , such that an element is moved a distance . The theorem states that the sum of the pressure, the potential, and kinetic energy per unit volume is equal to a fixed constant at any point of a fluid.

Note: This page has interactive demonstrations activated with Wolfram CDF player - a free viewing software tool for CDF files. To take full advantage of the educational content below download the Wolfram CDF player.

In symbols , where is the pressure, is the density (of water, in this case), is gravitational acceleration, is the height, and is the velocity. In the graphic, the subscript 1 denotes quantities on the left and right sides of the pipe.

The arrow that represents is drawn at one-tenth its real size because it grows too much compared to .

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