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The Expansion of the Bernoulli Equation to Finite Flow Cross Sections at One Level

Author(s): Ulf Teschke

Linked Author(s): Ulf Teschke

Keywords: Bernoulli equation; Correction coefficients; Potential flow; Energy flux; Flow profile;

Abstract: The Bernoulli Equation is one of the most important equations in fluid mechanics. It states that for incompressible fluids at a static height, the sum of geodetic height, pressure and velocity remains constant along one flow line. In engineering practice, however, statements along spatial coordinates are required for the pressure and velocity, depending on the geodetic height in finite flow cross sections. As an approximation of this, the Bernoulli Equation is also often used despite it only applying exactly along one streamline. In order to minimise the emergence of errors, the velocity head is multiplied by a correction coefficient. In the literature appear different approaches for the coefficients with different results. In this paper an approach that confirms the applicability of two different approaches is presented. The coefficients must be based on the three-dimensional velocity vector rather than merely on the normal components of velocity. In addition, when observing energy flow, the median pressure has to be replaced by the median energy flow pressure. These two median pressures are generally different. If the changes listed above are taken into account, these results in a Bernoulli Equation extended to finite cross sections and an energy flow equation associated with this. Both equations are precise and deliver the same results in relation to the description of flow processes in a finite flow cross section with asymmetric pressure and velocity distribution. The considerations presented here are verified using potential flow. When observing pulse currents, the balance of forces is thus checked.

DOI: https://doi.org/10.3850/38WC092019-0724

Year: 2019

Source: Proceedings of the 38th IAHR World Congress (Panama)

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