Verification Of Bernoulli Equation.docx

The flow of a fluid has to conform with a number of scientific principles in particular the conservation of mass and the conservation of energy. The first of these when applied to a liquid flowing through a conduit requires that for steady flow the velocity will be inversely proportional to the flow area. The second requires that if the velocity increases then the pressure must decrease.

The Bernoulli principle is an approximate relation between pressure, velocity, and elevation and is valid in regions of steady, incompressible flow where net frictional forces are negligible. Both Bernoulli’s equation and the continuity equation are essential analytical tools required for the analysis of most problems in the subject of mechanics of fluid. The Bernoulli’s equation was first stated in words by the Swiss mathematician Daniel Bernouilli. It states that The sum of the kinetic, potential and flow energies of a fluid particle is constant along a streamline during steady flow when the compressibility and frictional effects are negligible. In equation 𝑃 𝑉2 + + 𝑧 = ℎ = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝜌𝑔 2𝑔 Bernoulli’s equation between any two points along the streamline can be written as 𝑃1 𝜌𝑔

+

𝑉12 2𝑔

+ 𝑧1 =

𝑃2 𝜌𝑔

+

𝑉22 2𝑔

+ 𝑧2 + ℎ𝑓

In the above equation hf represents the energy loss due to fluid friction. If the fluid is not inviscid then there will be a small loss of head due to friction within the fluid and between the fluid and the walls of the passage. The terms on the left hand side of the above equation represent the pressure head, velocity head and elevation head, respectively. According to the Bernoulli’s theorem of fluid flow through a pipe, the total head at any cross section is constant. In real flow, due to friction and other imperfections, as well as measurement uncertainties, the result will deviate from the theoretical ones.

Practical application

Bernoulli’s equation can be applied for the construction of flow measuring devices such as venturimeter, flow nozzle, orifice meter, and Pitot tube. Furthermore, it can be applied to the problems of flow under sluice gate, free liquid jet, radial flow and free vortex motion.

Bernoulli‟s principle tells us that windows tend to explode rather than implode when

hurricanes. During the hurricanes, a very high speed of air outside the window leading to lowair pressure compare to inside, which the air is still. The differences of forces causing thewindows push outward and explode. That it is why to better open all windows during thehurricane

Assumptions: 1. It assumes viscous (friction) effects are negligible; 2. It assumes the flow is steady; 21 3. The equation applies along a streamline; 4. It assumes the fluid to be incompressible; and 5. It assumes no energy is added to or removed from the fluid along the streamline.