Bernoulli's Theorem

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA



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 .

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.