Electronic Thesis and Dissertation Repository

Thesis Format



Master of Engineering Science


Mechanical and Materials Engineering


Khayat, Roger E.


When a laminar inclined circular jet impinges on a horizontal surface, it forms a non-circular hydraulic jump governed by a non-axisymmetric flow. In this thesis, we use the boundary-layer and thin-film approaches in the three dimensions to theoretically analyse such flow and the hydraulic jumps produced in such cases. We particularly explore the interplay among inertia, gravity, and the effective inclination angle on the non-axisymmetric flow.

The boundary-layer height is found to show an azimuthal dependence at strong gravity level only; however, the thin film thickness as well as the hydraulic jump profile showed a strong non-axisymmetric behaviour at all gravity levels. Interestingly, at the free surface, radial and azimuthal velocity components are found prior to the jump location. The presence of an azimuthal velocity component is unique to non-circular jumps. Finally, a comparison between the current work and the existing literature is presented.

Summary for Lay Audience

When a vertical liquid column impacts a solid horizontal surface, a thin film of the liquid spreads on the surface in a symmetric manner with respect to the liquid column. At a certain distance from the point of impact on the horizontal surface, the thickness of this film rises abruptly, this is known as a “hydraulic jump”. It is also referred as a “circular hydraulic jump” due to the circular form it takes with respect to the point of liquid impact on the surface. Circular hydraulic jumps are commonly found in kitchen sinks when water discharges from the tap. On the other hand, when the liquid column is tilted by a certain angle, different geometries, other than the circular one, are expected to be produced, such as an ellipse. The underlying fluid flow dynamics that caused a shift in the hydraulic jump shape has been a challenge for scientists and engineers to theoretically explain, due to the complexity of the flow in this case.

In many engineering applications, jet impingement is used for cooling hot surfaces, where a jet of fluid impacts a hot surface to cool it. It was noticed that the occurrence of hydraulic jumps in such applications negatively affects the performance of cooling. Although circular hydraulic jumps have been extensively studied in the literature, non-circular jumps produced due to inclined jets is have not been given enough attention.

In this thesis, we develop the mathematical and physical formulations needed to analyse the phenomenon of the “non-circular” hydraulic jumps. We study the effect of several parameters on the shape of the formed hydraulic jumps, such as the gravity effect and the inclination degree of the liquid column as it impacts the solid surface. At the edge of the thin film, surface velocities with different directions are observed. Also, it has been found that the thickness of the thin film shows a different behaviour as perceived from different angles with respect to the point of fluid impact on the surface. These observations are found to characterise the flow of liquid in cases where non-circular hydraulic jump occurs.