Buoyant Jets of Elliptic Shape: Approximation for Duckbill Valves

The intrusion of seawater into a pipeline servicing an ocean outfall can significantly reduce its operational efficiency. Duckbill valves are sometimes installed on sewage outlet ports to help prevent such intrusions. While there is growing literature associated with the hydraulics of duckbill valves, there appears to be little published information on the trajectory and dilution achieved by the buoyant jets when the outlet ports are fitted with duckbill valves. Further, no models presently exist that incorporate the effects on the rise and dilution of buoyant jets discharged through orifices fitted with duckbill valves for which the size and shape of the opening varies with the effluent flow. Solutions to the asymptotic equations for jets and plumes are generated for ports fitted with duckbill valves by assuming that the shape of the duckbill is elliptical. This allows asymptotic expressions to be generated for the trajectory and dilution of the jet/plume. In the limiting case when the ellipse becomes circular, these expressions reduce to those for discharges from round outlets and are consistent with expressions for round ports found in literature.