A Unified Theory for the Pressure Change of Sudden Expansions and Contractions Based on the Momentum Balance

Abstract

In this paper a unified approach based on the momentum balance is presented, capable of predicting the pressure change of sudden contractions and sudden expansions. The use of empirically determined correction coefficients is not necessary. Therefore, the momentum balance is derived similarly for both applications but with different control volumes. The control volume takes into account the specific geometry of the hydraulic structure. With a properly chosen control volume, the unified approach requires coefficients that account for the velocity as well as pressure distributions on the boundaries of the control volume. These coefficients can be obtained by parameterizing the results of numerical simulations by simple analytical functions. The numerical model itself is validated by checking the simulated pressure change against calculated or measured pressure changes. It is found that the formulation of the momentum balance for the sudden expansion is more complex compared with the sudden contraction. The prediction of the pressure change of flows through sudden expansions can be improved by applying the momentum balance non-idealized. Most of the correction coefficients originate from an inappropriate application of Bernoulli’s energy conservation principle. Consequently, this leads to a gap between theory and experimental results. The proposed unified approach solely contains physical coefficients that are used to substitute integrals by averaged expressions.