Head‐Discharge Relation for Vortex Shaft
Publication: Journal of Hydraulic Engineering
Volume 111, Issue 6
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.
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References
1.
Drioli, C., “Esperienze su installazioni con pozzo di scarico a vortice,” (Observations on vertical vortex shafts), L'Energia Electtrica, Vol. 46, 1969, Nr. 6, pp. 399–409.
2.
Kleinschroth, A., “Stroemungsvorgaenge in Wirbelfallschaechten” Mittl. Inst. Hydraulik und Gewaesserkunde, TU Muenchen, Heft 8, Muenchen, 1972.
3.
Pica, M., “Scaricatori a vortice” (Vortex shafts), L'Energia Elettrica, Vol. 47, 1970, Nr. 4, pp. 217–234.
4.
Viparelli, M., “Su un particolare tipo di imbocco e sull' efflusso con vortice” (On a particular inlet type and its discharge characteristics for vortex flow), L'Energia Elettrica, Vol. 27, 1950, Nr. 10, pp. 610–621.
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Copyright © 1985 ASCE.
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Published online: Jun 1, 1985
Published in print: Jun 1985
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