The Bernoulli principle is the state-of-the-art method for practical calculations in hydraulics, like the pressure difference of flows through hydraulic structures. Therefore, the energy of a specific fluid particle must be considered at different times. It means that the Bernoulli principle is only valid when applied to a single streamline (and when additional restrictions are considered). However, almost every hydraulic textbook applies the Bernoulli principle to the whole cross-section for simple applicability, disregarding the restrictions. This strong simplification is accompanied by a significant deviation of the calculated result from the empirical result. To bridge the gap between calculation and measurement, correction coefficients are introduced that are specifically determined for every hydraulic structure. In the end, erroneously applying the Bernoulli principle and introducing a proper correction coefficient yields a result that is acceptably close to the measurement. This is the common approach to calculations in hydraulics. However, there are approaches capable of correctly predicting the empirical results without artificial correction coefficients, like the state-of-the-art method employed for numerical simulations. In fluid dynamics, the momentum-based Navier-Stokes equations are solved (among others) for any kind of flow and yield results with a very high agreement to measurements. Momentum-based approaches for analytical calculations are already reported by the literature but the theories are often presented as ideal solutions, not detailed up to applicability or blended with the Bernoulli principle. Based on Newton’s fundamental laws of motion, a straightforward momentum-based and applicable alternative to the established method is presented. The presented approach is aided by numerical simulations accounting for physical coefficients that occur due to the substitution of integral by averaged expressions. In this case, the coefficients are physically well-defined but not for the correction of a faultily applied approach. The derived integral momentum balance requires knowledge of the pressure and velocity distributions which can be obtained by numerical simulations. With the subsequent parametrizations of the coefficients, the approach can be applied by simple analytical formulas. The momentum-based approach is applied to the sudden contraction, the sudden expansion, and the metering orifice as a combination of a contraction and an expansion. Due to the application of the same approach, similarities in the flow behavior of the hydraulic structures are identified. As a result, parametrizations of some coefficients are also valid for additional structures than they were defined for. The numerical simulations are performed with ANSYS based on the finite volume method and solving the Reynolds-Averaged Navier Stokes equations. The k!-SST turbulence model is employed, which shows the best performance for all investigated hydraulic structures compared with literature numbers and own experiments. The evaluation of the numerical simulations and the comparison with the theory and the reference data is performed with MATLAB. The results obtained with the proposed approach show a very high correlation between the experimental data and the literature numbers. The derived momentum-based formulas in combination with the numerically obtained coefficients also confirm empirical parametrizations. In addition, the flow rate through a metering orifice can be predicted with the momentum-based approach as precisely as by applying the Bernoulli principle with the empirical correction coefficient. Consequentially, the proposed approach is applicable to various hydraulic structures and does not require extensive empirical investigations but yields a very high agreement to the measurements.     «

The Bernoulli principle is the state-of-the-art method for practical calculations in hydraulics, like the pressure difference of flows through hydraulic structures. Therefore, the energy of a specific fluid particle must be considered at different times. It means that the Bernoulli principle is only valid when applied to a single streamline (and when additional restrictions are considered). However, almost every hydraulic textbook applies the Bernoulli principle to the whole cross-section for si...     »