Conservation laws and conserved quantities for laminar radial jets with swirl (Q636115)

Summary: Conserved quantities play a central role in the solution of jet flow problems. A systematic way of deriving conserved quantities for radial jets with swirl is presented. The multiplier approach is used to derive the conservation laws for the system of three boundary layer equations for the velocity components and for the system of two partial differential equations for the stream function. When the swirl is zero or at a large distance form the orifice (at infinity), the boundary layer equations for the radial jets with swirl reduce to those of the purely radial jets. The conserved quantities for the radial liquid, free and wall jets with swirl are derived by integrating the conservation laws across the jets.