# Application of Bernoulli's Theorem

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• Published : March 7, 2013

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Bernoulli’s theorem

Bernoulli’s theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematicianDaniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow and is the basis for many engineering applications. Bernoulli’s theorem implies, therefore, that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity. If the fluid is flowing through a horizontal pipe of varying cross-sectional area, for example, the fluid speeds up in constricted areas so that the pressure the fluid exerts is least where the cross section is smallest. This phenomenon is sometimes called the Venturi effect, after the Italian scientist G.B. Venturi (1746–1822), who first noted the effects of constricted channels on fluid flow.

Application of Bernoulli's Theorem

When we blow air over a strip of paper as shown in the above figure, we find that the paper moves up. This is because, on blowing air, the velocity of air increases, creating low pressure above the paper and high pressure below the paper. This difference in pressure, lifts the paper

The working of spray-gun is based on Bernoulli's theorem

When the rubber bulb is squeezed, air is blown into the tube A, due to which, low pressure and high velocity is created. Since this pressure is less than the atmospheric pressure, the liquid is pushed up. This rising liquid is sprayed out of...