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Jets from two-dimensional symmetric nozzles of arbitrary shape

Published online by Cambridge University Press:  29 March 2006

Bruce E. Larock
Affiliation:
University of California, Davis

Abstract

A unified approach to the problem of jet efflux from symmetrical channels of finite width and possessing a general curvilinear nozzle shape is presented. The nozzle may be composed of polygonal and/or curved-arc segments. Precise nozzle shapes cannot be initially prescribed, however. The solution is based on the combined use of conformal mapping and the Riemann-Hilbert solution to a mixed boundary-value problem. The selection of an appropriate curvature function is described; examples show possible applications.

Type
Research Article
Copyright
© 1969 Cambridge University Press

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References

Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. New York: Academic Press.
Churchill, R. V. 1960 Complex Variables and Applications, 2nd ed. New York: McGraw-Hill.
Cisotti, V. 1908 Esempio di efflusso da un recipients a serzione non rettilinea. R.C. mat. Palermo, 26, 378382.Google Scholar
Gilbarg, D. 1960 Jets and cavities. Handb. Phys. 9, 311445.Google Scholar
Helmholtz, H. 1868 On the discontinuous motion of fluids. Trans. Phil. Mag. (4) 36, 337345.Google Scholar
Henderson, F. M. 1966 Open Channel Flow. New York: MacmillanM.
Keldysh, M. V. & Sedov, L. I. 1937 Effective solution of some problems for harmonic functions. Dokl. Akad. Nauk, SSSR, 16, 1.Google Scholar
Larock, B. E. 1969 Gravity-affected flow from planar sluice gates. J. Hydraulics Division, Proc. Am. Soc. Civil Eng. (to appear).Google Scholar
Larock, B. E. & Street, R. L. 1965 A Riemann-Hilbert problem for nonlinear, fully eavitating flow. J. Ship. Res. 9, 170178.Google Scholar
Larock, B. E. & Street, R. L. 1968 Cambered bodies in cavitating flow—a nonlinear analysis and design procedure, J. Ship. Res. 12, 113.Google Scholar
Levi-Civita, T. 1907 Scie e leggi di resistenza. R. C. mat. Palermo, 23, 137.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th ed. New York: Macmillan.
Robertson, J. M. 1965 Hydrodynamics in Theory and Application Englewood Cliffs, N.J.: Prentice-Hall.
Sedov, L. I. 1965 Two-dimensional Problems in Hydrodynamics and Aerodynamics. New York: Wiley.
Song, C. S. 1963 A quasi-linear and linear theory for non-separated and separated two-dimensional, incompressible, irrotational flow about lifting bodies. University of Minnesota, Minneapolis SAF Hydraulic Lab. Tech. Paper, B 43.Google Scholar
Villat, H. 1911 Sur la résistance des fluids. Ann sci. ec. norm. sup. Paris, 28, 203240.Google Scholar