Computing the Trajectory of Free Jets

Abstract

In recent years, design floods have increased beyond spillway capacity at numerous large dams. When additional spillway capacity is difficult or expensive to develop, designers may consider allowing the overtopping of a dam during extreme events. For concrete arch dams, this often raises issues of potential erosion and scour downstream from the dam, where the free jet initiating at the dam crest impacts the abutments and the downstream river channel. A recent review has shown that a commonly cited equation for predicting the trajectory of free jets is flawed, producing jet trajectories that are much too flat in this application. This could lead analysts to underestimate the amount of scour that could occur near a dam foundation, or conversely to overestimate the extent of scour protection required. This technical note presents the correct and incorrect jet trajectory equations, quantifies the errors associated with the flawed equation, and summarizes practical information needed to model the trajectory of free jets overtopping dam crests.

Estimating Flow Characteristics of Different Weir Types and Optimum Dimensions of Downstream Receiving Pool

“…Scimemi profile, Creager profile). (Davis et al, 1999;Dey, 2002;Wahl et al, 2008). Therefore, present study data are compared with Scimemi and Creager profiles (Fig.…”

Investigating the bottom free surface nappe (ogee profile) across a sharp-crested weir caused by the flow in an asymmetrical approach channel

“…Research on the projectile movement of a free-falling jet of water revealed that the shape of the lower nappe of a jet of water flowing over a ventilated sharp-crested weir resembled the shape of an ogee spillway (Chow 1959;Hager 1987;Knapp et al 1970;Melsheimer & Murphy 1970;Ministry of Science and Technology 2007;Murphy 1973;USACE (a) 1987;USACE (b) 1987;USBR 1987;Wahl et al 2008). However, both the numerical relationships for the flow over a sharp-crested weir and the principle for the projectile movement of a free-falling jet of water describing this shape only consider the two-dimensional characteristics of the flow, namely the available energy (i.e.…”

Shape of the Nappe During Free Overfall from a Rectangular Channel with Zero Bed Slope

“…In the area of description of the trajectory and shape of a free overfall nappe, they cannot be used generally. The trajectory of a free overfall nappe was discussed in White et al (1943), Markland (1965), Marchi (1993), Davis et al (1999), Wahl et al (2008), Hong et al (2010) and others. Particularly a confined and fully aerated nappe is described to a distance before it is compact.…”

“…During the flow of water in a channel near the end section when the curvature of streamlines can be neglected, the hydraulic calculation of the shape of the compact part of a nappe (without air entrainment) is relatively well explained (Kolář et al, 1983;Wahl et al, 2008), but less explained with self aeration (Falvey, 1980). This concerns cases with a supercritical regime when the assumption of the non-curvature of streamlines is fulfilled and, at the same time, the flow is without air entraimnment.…”