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# Relation between velocity and and pressure for fluids

Sir,
I see fumes going up in the     atmostphere , fumes flow become turbulent i.e its velocity is increasing  and as we go up in the atmostphere .. atmostpheric pressure decreases .. so is there any inverse relation between velocity and and pressure for fluids.. ? (Aditya asked)
There is a relation between pressure and velocity of flow in fluids.
Bernoullis Theorem
Bernoulli’s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.
Bernoulli’s principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy. (Courtesy: Wikipedia http://en.wikipedia.org/wiki/Bernoulli%27s_principle)
Smoke rising in a straight path from a cigarette is undergoing laminar flow. After rising a small distance, the smoke usually changes to turbulent flow, as it eddies and swirls from its regular path.
Ref: http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html

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