Bernoulli's Formula principle

Bernoulli's principle is a fundamental principle in fluid mechanics that describes the relationship between the speed of a fluid and the pressure it exerts. It is named after the Swiss mathematician and physicist Daniel Bernoulli, who first articulated the principle in the 18th century.

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The principle states that as the speed of a fluid increases, the pressure it exerts decreases, and vice versa. This can be seen in the flow of a fluid through a pipe or over an object, such as an airplane wing or a sailboat.

According to Bernoulli's principle, the faster-moving fluid has lower pressure than the slower-moving fluid. This can be demonstrated using the equation:

P + 1/2 ρv^2 + ρgh = constant

where P is the pressure of the fluid, ρ is its density, v is its velocity, h is its height above a reference point, and g is the acceleration due to gravity.

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This equation shows that if the velocity of the fluid increases, the pressure must decrease in order to keep the total constant. Bernoulli's principle is important in many applications, including the design of airplane wings, the flow of blood through arteries, and the operation of fluid pumps and turbines.