An analytical approximation to the entire centerline trajectory of inclined round dense jets in dimensionless form is proposed, in terms of a fourth degree polynomial. The coefficients of the polynomial for a certain inclination angle can be easily obtained if the position of the maximum height and the return point are known. Experimental data of the authors are used to determine these coefficients for six inclination angles between 35° and 75°. The resulting trajectories are then compared to data of other investigators and found to be in good agreement. The variation of the polynomial coefficients with inclination angle is also studied. The proposed analytical expression allows for a straightforward computation of the trajectory length for any inclination angle in the range studied. It is found that the longest trajectory occurs for the 60° angle. The relation between the computed length and the measured minimum (centerline) dilutions at the location of maximum height and at the return point is examined. Finally, the laws governing the variation of the minimum dilution with the axial distance from the source are explored and similarities with the laws of simple jets and plumes are discussed.

In this paper, five computational approaches are used to model bulk flow parameters of inclined round negatively buoyant jets. More specifically, an integral model employing Gaussian distributions for velocity and apparent acceleration of gravity, proposed in earlier study, is implemented with two different entrainment formulae. The remaining three computational approaches include an integral model known as EMA, which takes into consideration the fluid detachment occurring in the inner side of the flow near the terminal height, the widely known commercial model Corjet and analytical solutions that were proposed in a previous study. Predictions are provided for the maximum centerline height and its horizontal position, the terminal height of the upper jet boundary, the horizontal distance to the points where the jet centerline and the upper jet boundary return to the source level, the centerline dilution at the maximum height and the centerline dilution at the return point. Detailed comparisons are made in dimensionless form between the estimations provided by the models and a wide range of experimental data for discharge angles between 15° and 90°. Conclusions are drawn regarding the performance of the five computational approaches.