Machine Learning for Dynamic Pressure Coefficient Prediction in Vertical Water Jets

Vertical water jets present significant challenges for hydraulic structures due to their potential to cause erosion and structural damage. This study aimed to predict the dimensionless pressure coefficient (Cp) of vertical water jets by examining the relationships between experimental parameters, such as Froude number, slope, and the ratio of waterfall height over the product of the Froude number and diameter, referred to as alpha, using machine learning models. Two hundred forty controlled experiments were conducted, with pressure data collected. To address the problem's non-linearity, six machine learning models were tested: linear regression, K-nearest neighbors, decision tree, support vector regression, random forest, and XGBoost. The XGBoost model outperformed others, achieving an R-squared of 0.953 and a Root Mean Squared Error (RMSE) of 0.191. Residual analysis validated its better performance, demonstrating that it delivered the most accurate predictions with minimal bias. Feature importance analysis revealed the Froude number was the most significant predictor, followed by slope and diameter. This study emphasizes the importance of the Froude number in predicting jet behavior and shows the efficacy of advanced machine learning models in capturing complex fluid dynamics, providing valuable insights for optimizing engineering applications such as water jet cutting and cooling systems.