The Reynolds-averaged Bernoulli equation and its application to internal flows

The Reynolds-averaged form of the Bernoulli equation is derived and applied to internal flows. Previous researchers have attempted with limited success to relate the turbulent kinetic energy in screens and nozzles to internal flow loss coefficients. The turbulent Bernoulli equation confirms that turbulent kinetic energy and dissipation in internal flows are related to the loss coefficient. The loss coefficient can be viewed as a simple empirical turbulence model. Further, the turbulent Bernoulli equation confirms the hypothesis of several researchers that the failure of previous screen turbulence theories is partly due to the neglect of dissipation. However, including both dissipation and turbulent kinetic energy may not be sufficient, as there are many other turbulent terms which require accounting as well. As an example of the practical application of the turbulent Bernoulli equation, the turbulent kinetic energy at the outlet of a nozzle, e.g., for an atomizer, is estimating by modeling the unclosed terms.