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Concise equations for the tangential, radial, and axial velocities as well as the water‐surface profile of air‐core vortices at hydraulic intakes have been derived. The equations were developed by modifying the equation for tangential velocity originally proposed by Rosenhead in 1930. Laboratory experiments were conducted on strong air‐core vortices near a water intake. The results indicate the equations agree with experimental measurements and are applicable to vortex motion in general. The equations for radial and axial vortex velocities contain an eddy‐viscosity term, which should be proportional to vortex circulation. Dimensionless parameters describing the circulation and intake Froude numbers and the intake submergence are also used in the analysis. Using these equations, the depth and three velocity components of an air‐core vortex at certain hydraulic intakes can be predicted. This information may be helpful to the practicing engineer in determining the submergence required to avoid air‐entraining vortices at intakes.
Hite et al. (Tue,) studied this question.