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Daniel Bernoulli

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Daniel Bernoulli (Groningen, 8 February 1700 – Basel, 8 March 1782) was aDutch-Swiss mathematician and was one of the many prominent mathematicians in theBernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability andstatistics. Bernoulli's work is still studied at length by many schools of science throughout the world.
In Physics :-
He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law.[2]
He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation.[9] Bernoulli's principle is of critical use inaerodynamics.[4]

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By multiplying with the fluid density ρ, equation (A) can be rewritten as:

or:

where: is dynamic pressure, is the piezometric head or hydraulic head (the sum of the elevation z and the pressure head)[8][9] and is the total pressure (the sum of the static pressure p and dynamic pressure q).[10]
The constant in the Bernoulli equation can be normalised. A common approach is in terms of total head or energy head H:

The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached. In liquids – when the pressure becomes too low – cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid

Simplified form
In many applications of Bernoulli's equation, the change in the ρ g z term along the streamline is so small compared with the other terms it can be ignored. For example, in the case of aircraft in flight, the change in height z along a streamline is so small the ρ g z term can be omitted. This allows the above equation to be presented in the following simplified form:

where p0

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