Head‐Discharge Relation for Vortex Shaft

Abstract

Hydraulic flow characteristics for vortex shafts are investigated for subcritical approach conditions. The analysis is based on Pica's approach by simplifying considerably his procedure. Using appropriate scalings the head-discharge relation may be expressed as a unique function. Using the stability condition that the air core along the shaft axis is not below a certain minimum, explicit expressions for the maximum upstream flow depth and the maximum discharge in terms of the shaft radius, the upstream channel width and the distance of the channel axis from the shaft center are derived. These relations permit a simple and rapid determination of the vortex shaft capacity. Analytical results are compared with observations on model and prototype evaluations. Agreement is favorable in the complete range of the respective parameters. Also, no scale effects could be detected. The present approach, therefore, can be regarded as a universal head-discharge relation for arbitrary, subcritical inflow conditions. Moreover, a graphical evaluation of the relation in question enables a simple and rapid application to cases in practice.