Bernoullis Equation

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Bernoulli’s Equation

This illustration is meant to simplify how Bernoulli’s equation can be applied to a tank pipe problem. The assumptions of this problem are that there are no pressure losses in the flow of the fluid, the fluid is oncompressable and the width of the pipe has no pressure difference (fluid inside the pipe has the same pressure throughout any cross section). At the point where the fluid enters the pipe there needs to be a driving force. This driving force is the pressure developed from the top of the vat of fluid. If the vat emptied onto the floor at point one the pressure would be converted entirely into kinetic energy. Because the fluid doesn’t empty at this point the height that the fluid changes needs to be considered. Once the fluid passes point 1 it begins to lose height or potential flow energy. At point two some of the initial pressure and the potential flow energy has been converted to velocity of the fluid. At this point the pipe begins to reduce in diameter. Because the fluid cannot be compressed (incompressible) the same amount of fluid must be flowing through all cross sectional areas (conservation of mass). Therefore, the fluid velocity must increase as the cross sectional area decreases to maintain the same flow rate.