Skip to main content
SpringerLink
Log in

Jets and Cavities

  • Chapter
Book cover Fluid Dynamics / Strömungsmechanik

Part of the book series: Encyclopedia of Physics / Handbuch der Physik ((PHYSIK 3,volume 3 / 9))

Abstract

The problems of free streamline theory have long attracted both hydrodynamicists and mathematicians, the former because of the many applications to jet, cavity, and wake phenomena, and the latter because of the unusual and exciting mathematical features of this branch of potential theory. The different interests of these two groups have resulted in a parallel development of the field, emphasizing on the one hand particular solutions and technical applications, and on the other hand general theory and results of a more qualitative nature. These two trends are reflected in the following exposition in that Chap. II and V are concerned with special flows and numerical methods, and Chap. III and IV with the general theory. While this is not an altogether natural division from the physical point of view, we have adopted it as a convenient means of presenting the various methods and of tracing the development of the ideas. In devoting a separate chapter to qualitative features (Chap. III), we hope to direct attention to an elegant part of the general theory which should be useful to those with theoretical and applied interests alike.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

General references

  1. G. Birkhoff and E. Zarantonello.: Jets, wakes and cavities. New York.: Academic Press 1957.

    MATH  Google Scholar 

  2. U. Cisotti.: Idromeccanica Piana. Milan Tamburini 1921.

    Google Scholar 

  3. L. M. Milne-Thomson.: Theoretical Hydrodynamics, 3rd ed. New York.: Macmillan 1956.

    Google Scholar 

  4. H. Villat.: Apercus théoriques sur la résistance des fluides. Collection Scientia. Paris.: Gauthier-Villars 1920.

    Google Scholar 

Bibliography

  • Ablow, C., and W. Hayes.: Perturbation of free surface flows. Tech. Rep. No. 1 (1951), Grad. Div. Appl. Math., Brown Univ.; 11.

    Google Scholar 

  • Ackeret, J.: Experimentelle und theoretische Untersuchungen über Hohlraumbildung (Kavitation im Wasser). Techn. Mech. Thermodyn. 1 (1930); 2.

    Google Scholar 

  • Acosta, A.: A note on partial cavitation of flat plate hydrofoils. Hydrodynamics Lab., Cal. Inst. Tech., Rep. No. E-19.9 (1955); 21.

    Google Scholar 

  • Arms, R., and L. Gates.: The computation of an axially symmetric free boundary problem on NORC-Part II. U.S. Naval Proving Grounds Rep. No. 1533 (1957); 47.

    Google Scholar 

  • Armstrong, A.: Boundary corrections to cavity dimensions and drag coefficients of a twodimensional plate in a free-jet. Arm. Res. Est. Rep. No. 12/51 (1951); 11.

    Google Scholar 

  • Armstrong, A.: Abrupt and smooth separation in plane and axisymmetric cavity flow. Arm. Res. Est. Memo. 22 /53 (1953); 24.

    Google Scholar 

  • Armstrong, A.: Drag coefficients of wedges and cones in cavity flow. Arm. Res. Est. Rep. No. 21/54 (1954); 22.

    Google Scholar 

  • Armstrong, A., and J. Dunham.: Axisymmetric cavity flow. Arm. Res. Est. Rep. No. 12/53 (1953); 22, 46.

    Google Scholar 

  • Armstrong, A., and K. Tadman.: Wall corrections to cavities in closed and open jet axially symmetric tunnels. Arm. Res. Est. Rep. No. 3 /52 (1952); 11.

    Google Scholar 

  • Armstrong, A., and K. Tadman.: Axisymmetric cavity flow about ellipsoids. Arm. Res. Est. Memo. 5/54 (1954); 22.

    Google Scholar 

  • Armstrong, A., and K. Tadman.: Wall corrections to axially symmetric cavities in circular tunnels and jets. Arm. Res. Est. Rep. No. 7/52 (1952); 11, 22.

    Google Scholar 

  • Arnoff, E.: Re-entrant jet theory and cavity drag for symmetric wedges. Naval Ordnance Test Station NAVORD Rep. 1298 (1951); 7, 8.

    Google Scholar 

  • Bauer, W.: Über das Widerstandsgesetz schnell bewegter Kugeln in Wasser. Ann. d. Phys. 82, 1014–1016 (1927); 22.

    Google Scholar 

  • Bazin, R.: Mem. pres. par div. savants Acad. Sci., Paris (2) 32, 1–63 (1902); 2.

    Google Scholar 

  • Berg, P.: On the existence of Helmholtz flows in a compressible fluid. Diss. New York Univ. 1953; 32.

    Google Scholar 

  • Bergman, S.: On representation of stream functions of subsonic and supersonic flow of compressible fluids. J. Rat. Mech. Analysis 4, 883–905 (1955); 12.

    Google Scholar 

  • Bergman, S.: Mehrdeutige Lösungen bei Potentialströmungen mit freien Grenzen. Z. angew. Math. Mech. 12, 95–121 (1932); 32.

    Google Scholar 

  • Bergman, S., and M. Schiffer.: Kernel functions and elliptic differential equations in mathematical physics. New York.: Academic Press 1953; 30.

    Google Scholar 

  • Bers, L.: Existence and uniqueness of a subsonic flow past a given profile. Comm. Pure Appl. Math. 7, 441–504 (1954); 32.

    Google Scholar 

  • Betz, A.: Einfluß der Kavitation auf die Leistung von Schiffsschrauben. Proc. Third Intern. Congr. Appl. Mech. Stockholm 1930; 7.

    Google Scholar 

  • Betz, A., and E. Petersohn.: Anwendung der Theorie der freien Strahlen. Ing.-Arch. 2, 190–211 (1931); 4.

    Google Scholar 

  • Birkhoff, G.: Hydrodynamics. Princeton, N. J.: Princeton University Press 1950; 4.

    Google Scholar 

  • Birkhoff, G.: Remarks on streamlines of discontinuity. Rev. Ciencias, Lima 50, 105–116 (1948); 7.

    Google Scholar 

  • Birkhoff, G, and D. Carter.: Rising plane bubbles. J. Math. Mech. 6, 769–779 (1957); 15.

    Google Scholar 

  • Birkhoff, G, H. Goldstine and E. Zarantonello.: Calculation of plane cavity flows past curved obstacles. Rend. Seminar. Mat. Univ. Politec, Torino 13, 205–224 (1953/54); 40, 41.

    Google Scholar 

  • Birkhoff, G, M. Plesset and N. Simmons.: Wall effects in cavity flow I, II. Quart. Appl. Math. 8, 161–168 (1950)

    MathSciNet  Google Scholar 

  • Birkhoff, G, M. Plesset and N. Simmons.: Wall effects in cavity flow I, II. Quart. Appl. Math. 9, 413–421 (1952); 8, 11.

    Google Scholar 

  • Birkhoff, G, D. Young and E. Zarantonello.: Numerical methods in conformal mapping. Proc. Symp. Appl. Math. Vol. 4, pp. 117–140, Amer. Math. Soc. 1953; 40.

    Google Scholar 

  • Blasius, H.: Funktionentheoretische Methoden in der Hydrodynamik. Z. Math. Phys. 58, 90–110 (1909); 15.

    Google Scholar 

  • Borda, J.: Mémoire sur l’écoulement des fluides par les orifices des vases. Mem. Acad. Sci. Paris 1766, 519–607; 10.

    Google Scholar 

  • Brillouin, M.: Les surfaces de glissement de HELMHOLTZ et la résistance des fluides. Ann. chim. Phys, 23, 145–230 (1911); 4, 9, 26.

    Google Scholar 

  • Brodetsky, S.: The line of action of the resultant pressure in discontinuous fluid motion. Proc. Roy. Soc. Lond., Ser. A 102, 361–372 (1922); 23.

    Google Scholar 

  • Brodetsky, S.: Discontinuous fluid motion past circular and elliptic cylinders. Proc. Roy. Soc. Lond., Ser. A 102, 542–553 (1923); 40.

    Google Scholar 

  • Brodetsky, S.: Fluid motion past circular barriers. Bibl. Hieros. 1, 1–14 (1923); 40.

    Google Scholar 

  • Chaplygin, S.: On gas jets. Ann. Sci. Imp. Univ., math.-phys. Cl. 1904, 1–121;translated in NACA Tech. Note 1063 (1944); 12.

    Google Scholar 

  • Cisotti, U.: Scie limitate. Ann. Scuola Norm. Sup. Pisa (2) 1, 101–112 (1932); 9.

    Google Scholar 

  • Cohen, H., and R. Gilbert.: Two-dimensional, steady, cavity flow about slender bodies in channels of finite breadth. J. Appl. Mech. 24, 170–176 (1957); 21.

    Google Scholar 

  • Cohen, H., and Y. Tu.: A comparison of wall effects on supercavitating flows past symmetric bodies in solid wall channels and jets. Proc. 9th Intern. Cong. Appl. Mech., Brussels 1956; 11, 21.

    Google Scholar 

  • Cooper, E.: Theory of water entry of missiles with flat noses. Naval Ordnance Test Station NAVORD Rep. No. 1154 (1949); 11, 20.

    Google Scholar 

  • Courant, R., and D. Hilbert.: Methoden der Mathematischen Physik, Vol. 2. Berlin.: Springer 1938; 17.

    Google Scholar 

  • Cox, A., and W. Clayden.: Cavitating flow about a wedge at incidence. J. Fluid Mech. 3, 615–637 (1958); 6.

    Google Scholar 

  • Cox, R., and W. Clayden.: Air entrainment at the rear of a steady cavity. Symp. on Cavitation in Hydrodynamics. Nat. Phys. Lab. Her Majesty’s Stationery Office, 1956; 2.

    Google Scholar 

  • Cox, R., and J. Maccoll.: Recent contributions to basic hydroballistics. Proc. Symp. on Naval Hydrodynamics, pp. 215–232, Nat. Res. Counc. Publ. 515 (1957); 6, 20, 22.

    Google Scholar 

  • Curle, N.: On hydrodynamic stability in unlimited fields of viscous flow. Proc. Roy. Soc. Lond., Ser. A 238, 489–501 (1957); 18.

    Google Scholar 

  • Curle, N.: Unsteady two-dimensional flows with free boundaries. Proc. Roy. Soc. Lond., Ser. A 235, 275–381, 382–395 (1956); 18.

    Google Scholar 

  • Demtchenko, B.: Problèmes mixtes harmoniques en hydrodynamique des fluides parfaits. Paris.: Gauthier-Villars 1933; 5.

    MATH  Google Scholar 

  • Dini, M.: Sull’equazione zu=0. Ann. di Mat. (2) 5, 305–345 (1871); 33.

    Google Scholar 

  • Efros, D.: Hydrodynamical theory of two-dimensional flow with cavitation. Dokl. Akad. Nauk SSSR. 51, 267–270 (1946); 7.

    Google Scholar 

  • Efros, D.: Calculation of the hydrodynamic forces acting on a cavitation contour in plane flow. Dokl. Akad. Nauk SSSR. 60, 29–31 (1948) [in Russian]; 7.

    Google Scholar 

  • Eisenberg, P.: On the mechanism and prevention of cavitation. David Taylor Model Basin Rep. 712 (1950)

    Google Scholar 

  • Eisenberg, P.: Addendum, Rep. 842 (1953)

    Google Scholar 

  • Eisenberg, P.: On the mechanism and prevention of cavitation. David Taylor Model Basin Rep. 712 (1950)

    Google Scholar 

  • Eisenberg, P.: Addendum, Rep. 842 (1953)

    Google Scholar 

  • Eisenberg, P.: same as.: Kavitation. Forsch.-H. Schiffstechnik 4, 155–168 (1953)

    Google Scholar 

  • Eisenberg, P.: Addendum, Rep. 842 (1953)

    Google Scholar 

  • Eisenberg, P.: same as.: Kavitation. Forsch.-H. Schiffstechnik 5, 201–212 (1954); 2.

    Google Scholar 

  • Eisenberg, P., and H. Pond.: Water tunnel investigations of steady state cavities. David Taylor Model Basin Rep. 668 (1948); 2, 45.

    Google Scholar 

  • Eppler, R.: Beiträge zu Theorie und Anwendung der unstetigen Strömungen. J. Rat. Mech. Analysis 3, 591–644 (1954); 4, 11, 26, 40.

    Google Scholar 

  • Fage, A., and F. Johansen.: On the flow of air behind an inclined flat plate of infinite space. Proc. Roy. Soc. Lond., Ser. A 116, 170–197 (1920); 2.

    Google Scholar 

  • Finn, R.: Some theorems on discontinuous plane fluid motions. J. d’Analyse Math. 4, 246 to 291 (1956)

    Google Scholar 

  • Finn, R.: Some theorems on discontinuous plane fluid motions. J. d’Analyse Math. 25, 26, 32, 38, 39.

    Google Scholar 

  • Fisher, J.: Discontinuous fluid flow with cavity formation. Underwater Ballistics Res. Comm. Rep. No. 34 (1945); 22.

    Google Scholar 

  • Forchheimer, P.: Hydraulik, 3rd ed. Leipzig.: Teubner 1930; 2, 10.

    Google Scholar 

  • Fox, J., and G. Morgan.: On the stability of some flows of an ideal fluid with free surfaces. Quart. Appl. Math. 11, 439–456 (1954); 18.

    Google Scholar 

  • Friedrichs, K.: Über ein Minimumproblem für Potentialströmungen mit freiem Rande. Math. Ann. 109, 60–82 (1933/34); 30, 32, 38.

    Google Scholar 

  • Garabedian, P.: Oblique water entry of a wedge. Comm. Pure Appl. Math. 6, 957–167 (1953); 20.

    Google Scholar 

  • Garabedian, P.: An example of axially symmetric flow with a free surface. Studies in Mathematics and Mechanics presented to Richard von Mises, pp. 149–159. New York.: Academic Press 1954; 17.

    Google Scholar 

  • Garabedian, P.: The mathematical theory of three-dimensional cavities and jets. Bull. Amer. Math. Soc. 62, 219–235 (1956); 2, 30, 45.

    Google Scholar 

  • Garabedian, P.: Calculation of axially symmetric cavities and jets. Pacific J. Math. 6, 611–684 (1956)

    MATH  MathSciNet  Google Scholar 

  • Garabedian, P.: Calculation of axially symmetric cavities and jets. Pacific J. Math. 8, 28, 30, 42, 45.

    Google Scholar 

  • Garabedian, P.: On steady-state bubbles generated by Taylor instability. Proc. Roy. Soc. Lond., Ser. A 241, 423–431 (1957); 15.

    Google Scholar 

  • Garabedian, P., H. Lewy and M. Schiffer.: Axially symmetric cavitational flow. Ann. of Math. 56, 560–602 (1952); 17, 32, 35.

    Google Scholar 

  • Garabedian, P., E. Mcleod and M. Vitousek.: Recent advances at Stanford in the application of conformal mapping to hydrodynamics. Amer. Math. Monthly 61, No. 7, Part II, 8–10 (1954); 15, 16.

    Google Scholar 

  • Garabedian, P.,and H. Royden.: A remark on cavitational flow. Proc. Nat. Acad. Sci. U.S.A. 38, 57–61 (1952); 32, 35.

    Google Scholar 

  • Garabedian, P.,and M. Schiffer.: Convexity of domain functionals. J. d’Analyse Math. 2, 281–368 (1953); 30.

    Google Scholar 

  • Garabedian, P.,and D. C. Spencer.: Extremal methods in cavitational flow. J. Rat. Mech. Analysis 1, 359–409 (1952); 30, 31, 32, 35.

    Google Scholar 

  • Gategno, G., and A. Ostrowski.: Représentation conforme à la frontière; domaines particulières. Mem. Sci. Math. No. 110; 33.

    Google Scholar 

  • Gerber, R.: Sur l’existence des écoulements irrotationels, plans, periodiques, d’un liquide pesant incompressible. C.R. Acad. Sci., Paris 233, 1560–1562 (1951),; 15.

    Google Scholar 

  • Gerber, R.: Sur les solutions exacts des équations du mouvement avec surface libre d’un liquide pesant. J. Math. pures appl. (9) 34, 185–299 (1955); 32.

    Google Scholar 

  • Geurst, J., and R. Timman.: Linearized theory of two-dimensional cavitational flow around a wing section. Proc. 9th Intern. Cong. Appl. Mech., Brussels 1956; 21.

    Google Scholar 

  • Gilbarg, D.: Unsteady flow with free boundaries. Z. angew. Math. Phys. 3, 34–42 (1952); 18.

    Google Scholar 

  • Gilbarg, D.: Uniqueness of axially symmetric flows with free boundaries. J. Rat. Mech. Analysis 1, 309–320 (1952); 26, 37.

    Google Scholar 

  • Gilbarg, D.: Comparison methods in the theory of subsonic flows. J. Rat. Mech. Analysis 2, 233–251 (1953); 26, 27, 37.

    Google Scholar 

  • Gilbarg, D.: Free streamline theory and steady state cavitation. Proc. Symp. on Naval Hydrodynamics, pp. 281–295, Nat. Res. Counc. Publ. 515 (1957); 4.

    Google Scholar 

  • Gilbarg, D., and R. Anderson.: Influence of atmospheric pressure on the phenomena accompanying the entry of spheres into water. J. Appl. Phys. 19, 127–139 (1948); 2.

    Google Scholar 

  • Gilbarg, D., and D. Rock.: On two theories of plane potential flows with finite cavities. Naval Ord. Lab. Memo. 8718 (1946); 7, 8.

    Google Scholar 

  • Gilbarg, D., and J. Serrin.: Free boundaries and jets in the theory of cavitation. J. Math. Phys. 29, 1–12 (1950); 7, 23.

    MathSciNet  Google Scholar 

  • Gilbarg, D., and J. Serrin.: Uniqueness of axially symmetric subsonic flow past a finite body. J. Rat. Mech. Analysis 4, 169–175 (1955); 37.

    Google Scholar 

  • Gilbarg, D., and M. Shiffman.: On bodies achieving extreme values of the critical Mach number, I. J. Rat. Mech. Analysis 3, 209–230 (1954); 26, 31.

    Google Scholar 

  • Goldstein, S. (ed.).: Modern developments in fluid dynamics, Vol. 2. Oxford 1938; 2, 41

    Google Scholar 

  • Green, A. E.: The gliding of a plate on a stream of finite depth, I, II. Proc. Cambridge Phil. Soc. 31, 589 (1935)

    Article  ADS  MATH  Google Scholar 

  • Green, A. E.: The gliding of a plate on a stream of finite depth, I, II. Proc. Cambridge Phil. Soc. 3, 67–85 (1956); 11.

    Google Scholar 

  • Green, A. E.: Note on the gliding of a plate on the surface of a stream. Proc. Cambridge Phil. Soc. 32, 248–252 (1936); 11.

    Google Scholar 

  • Greenhill, G.: Theory of a streamline past a plane barrier. British Aero. Res. Counc. Reps, and Memos. 19 (1910)

    Google Scholar 

  • Greenhill, G.: Theory of a streamline past a plane barrier. British Aero. Res. Counc. Reps, and Memos. Appendix (1916); 5, 23.

    Google Scholar 

  • Gurevich, M.: Some remarks on stationary schemes for cavitational flow about a flat plate. Izv. Akad. Nauk. SSSR. OTN 1947, 143–150

    Google Scholar 

  • Gurevich, M.: Some remarks on stationary schemes for cavitational flow about a flat plate. David Taylor Model Basin Transi. 224 (1948); 7, 8.

    Google Scholar 

  • Gurevich, M.: Flow past an axisymmetric semi-body of finite drag. Prikl. Mat. Mekh. 11, 97–104 (1947) [in Russian with English summary]; 25.

    MATH  MathSciNet  Google Scholar 

  • Hamel, G.: Ein hydrodynamischer Unitätssatz. Proc. 2nd Int. Congr. Appl. Mech., Zurich 1926, p. 489; 32, 38.

    Google Scholar 

  • Hardy, G., J. Littlewood and G. POLYA.: Inequalities. Cambridge; Cambridge University Press 1934; 34.

    Google Scholar 

  • Helliwell, J., and A. Mackie.: Two-dimensional subsonic and sonic flow past thin bodies. J. Fluid Mech. 3, 93–109 (1957); 12.

    Google Scholar 

  • Helmholtz, H.: Luber diskontinuierliche Flüssigkeitsbewegungen. Mber. Akad. Wiss. Berlin 1868, 215–228; Wiss. Abh. 1, 154; 4, 10.

    Google Scholar 

  • Hopf, E.: A remark on linear elliptic differential equations of the second order. Proc. Amer. Math. Soc. 3, 791–793 (1952); 27.

    Google Scholar 

  • Howarth, L. (ed.).: Modern developments in fluid dynamics. High-speed flow. Oxford 1953; 12.

    Google Scholar 

  • Hsu, E., and B. Perry.: Water tunnel experiments on spheres in cavity flow. Hydrodynamics Lab., Cal. Inst. Tech. Rep. E-24.9 (1954); 41.

    Google Scholar 

  • Huron, R.: Sur l’unicité des solutions du problème de représentation conforme de HELMHOLTZ. C.R. Acad. Sci., Paris 228, 290, 357 (1949); 32.

    Google Scholar 

  • Imai, I.: Discontinuous potential flows as the limiting form of the viscous flow for vanishing viscosity. J. Phys. Soc. Japan 8, 399–402 (1953); 41.

    Google Scholar 

  • Jacob, C.: Sur la détermination des fonctions harmoniques par certaines conditions aux limites. Mathematica 11, 149–175 (1935); 34.

    Google Scholar 

  • Jacob, C.: la méthode approchée de M. LAMLA en dynamique des fluides compressibles. Acad. Roum. Bull. Sect. Sci. 28, 637–641 (1946); 12.

    Google Scholar 

  • Jaffe, G.: Unstetige und mehrdeutige Lösungen der hydrodynamischen Gleichungen. Z. angew. Math. Mech. 1, 398–410 (1920); 36.

    Google Scholar 

  • Jaffe, G.: Über mehrdeutige Lösungen der hydrodynamischen Gleichungen. Phys. Z. 23, 129–133 (1922); 6, 36.

    Google Scholar 

  • Jahnke, E., and F. Emde.: Tables of functions, 3rd ed. Leipzig.: Teubner 1938; reprinted New York.: Dover Publ. 1943; 8.

    Google Scholar 

  • John, F.: An example of a transient three-dimensional flow with a free boundary. Rev. Gen. Hydraul. 18, No. 71, 230–232 (1952); 18.

    Google Scholar 

  • John, F.: Two-dimensional potential flows with a free boundary. Comm. Pure Appl. Math. 6, 497–503 (1953); 15, 18.

    Google Scholar 

  • Joukowsky, N.: A modification of KIRCHHOFF’S method of determining two-dimensional motions of a fluid given constant velocity along an unknown streamline. Coll. Works 2,No. 3; also.: Rec. Math. 25 (1890);4.

    Google Scholar 

  • Karman, T. voN.: Accelerated flow of an incompressible fluid with wake formation. Ann. Mat. pura appl. (4) 29, 247–249 (1949); 19.

    Google Scholar 

  • Karman, T. voN.: The impact on seaplane floats during landing. NACA Tech. Note 321 (1929); 20.

    Google Scholar 

  • Kawaguti, M.: Discontinuous flow past a circular cylinder. J. Phys. Soc. Japan 8, 403–406 (1953),; 41.

    Google Scholar 

  • Keller, J., and I. Kolodner.: Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25, 918–921 (1954); 4.

    Google Scholar 

  • Kempf, G., u. E. Foerster (ed.).: Hydromechanische Probleme des Schiffsantriebs. Hamburg 1932; 2, 4, 8, 41.

    Google Scholar 

  • King, H. W.: Handbook of hydraulics, 3rd ed. New York-Toronto-London.: McGraw-Hill 1939; 2, 10.

    Google Scholar 

  • Kirchhoff, G.: Zur Theorie freier Flüssigkeitsstrahlen. J. reine angew. Math. 70, 289–298 (1869)

    Google Scholar 

  • Kirchhoff, G.: Zur Theorie freier Flüssigkeitsstrahlen. J. reine angew. Math. Ges. Abh. 416; 4, 5, 6, 10.

    Google Scholar 

  • Knapp, R.: Recent investigations of the mechanics of cavitation and cavitation damage. Trans. Amer. Soc. Mech. Engrs. 77, 1045–1054 (1955); 2.

    Google Scholar 

  • Kötter, F.: tYber die Contractio Venae bei spaltförmigen und kreisförmigen Öffnungen. Arch. für Math. Phys. (2) 5, 392–417 (1887); 10.

    Google Scholar 

  • Kolscher, M.: Unstetige Strömungen mit endlichen Totwasser. Luftf.-Forschg. 17, 154 to 160 (1940); 9.

    Google Scholar 

  • Konstantinov, V. A.: Influence of Reynolds number on cavitational flow. Izv. Akad. Nauk. SSSR., OTN 1946, 1355–1373

    Google Scholar 

  • Konstantinov, V. A.: Influence of Reynolds number on cavitational flow. David Taylor Model Basin Transl. 233 (1950); 2, 41.

    Google Scholar 

  • Korn, A.: -Ober Minimalflächen, deren Randkurven wenig von ebenen Kurven abweichen. Abh. Kgl.-Preuss. Akad. Wiss., Berlin 1909, Anhang II; 33.

    Google Scholar 

  • Kravtchenko, J.: Sur l’existence des solutions du problème de représentation conforme de HELMHOLTZ. Ann. Sci. Ec. Norm. Sup. 62, 233–268 (1946)

    Google Scholar 

  • Kravtchenko, J.: Sur l’existence des solutions du problème de représentation conforme de HELMHOLTZ. Ann. Sci. Ec. Norm. Sup. 63, 161–184 (1947); 32.

    Google Scholar 

  • Kravtchenko, J.: Sur le problème de représentation conforme de HELMHOLTZ. J. Math. pures appl. 20, 35–239 (1941); 32.

    Google Scholar 

  • Kreisel, G.: Cavitation with finite cavitation numbers. Admiralty Res. Lab. Rep. No. R 1/H/36 (1946); 7.

    Google Scholar 

  • Kreps, R.: Experimental investigation of impact in landing on water. CAHI Rep. No. 438 (1939)

    Google Scholar 

  • Kreps, R.: Experimental investigation of impact in landing on water. CAHI Rep. translated in NACA Tech. Memo. 1046 (1943); 20.

    Google Scholar 

  • Lamb, H.: Hydrodynamics, 6th ed. Cambridge.: Cambridge University Press 1932; 10, 20, 35.

    Google Scholar 

  • Landweber, L.: The axially symmetric potential flow about elongated bodies of revolution. David Taylor Model Basin Rep. No. 761 (1951); 22.

    Google Scholar 

  • Lansford, W.: Discharge coefficients for pipe orifices. Civ. Engng., Lond. 4, 245–247 (1934); 2.

    Google Scholar 

  • Lauck, A.: Der Überfall über ein Wehr. Z. angew. Math. Mech. 5, 1–16 (1925); 46.

    Google Scholar 

  • Lavrentieff, M.: Sur certaines propriétés des fonctions univalentes et leurs applications 6.1a théorie des sillages. Mat. Sbornik 46, 391–458 (1938)

    Google Scholar 

  • Lavrentieff, M.: Sur certaines propriétés des fonctions univalentes et leurs applications 6.1a théorie des sillages. Mat. Sbornik [Russian with French summary]; 26, 28, 29, 32, 37.

    Google Scholar 

  • Lavrentieff, M M. Keldysh, A. Markuschevitch, L. Sedoff and A. Lotoff.: Collected reports on the problem of impact against a water surface. CAHI Rep. No. 152 (1935); 20.

    Google Scholar 

  • Leray, J.: Les problèmes de représentation conforme de HELMuOLTZ; théorie des sillages et des proues, I, II. Comment Math. Rely. 8, 149–180, 250–263 (1935)

    Google Scholar 

  • Leray, J.: Les problèmes de représentation conforme de HELMuOLTZ; théorie des sillages et des proues, I, II. Comment Math. Rely. 24, 32, 33, 34, 37, 39.

    Google Scholar 

  • Leray, J.: Sur la validité des solutions du problème de la proue. Volume de jubilé de M. BRILLOUIN, pp. 246–257. Paris.: Gauthier-Villars 1935; 4, 24, 32, 36.

    Google Scholar 

  • Leray, J., et J. Schauder.: Topologie et équations fonctionnelles. Ann. Sci. Ec. Norm. Sup. 51, 45–78 (1934); 34, 39.

    MathSciNet  Google Scholar 

  • Leray, J., et A. Weinstein.: Sur un problème de représentation conforme pose par la théorie de HELMuOLTZ. C. R. Acad. Sci., Paris 198, 430 (1934); 32, 38, 39.

    Google Scholar 

  • Levi-Civita, T.: Scie e leggi de resistenza. Rend. Circ. Mat. Palermo 18, 1–37 (1907); 23

    Google Scholar 

  • Levinson, N.: On the asymptotic shape of the cavity behind an axially symmetric nose moving through an ideal fluid. Ann. of Math. 47, 704–730 (1946); 25.

    Google Scholar 

  • Lewy, H.: On steady free surface flow in a gravity field. Comm. Pure Appl. Math. 5, 413–414 (1952); 15.

    Google Scholar 

  • Lewy, H.: A note on harmonic functions and a hydrodynamical application. Proc. Amer. Math. Soc. 3, 11–113(1952); 15.

    Google Scholar 

  • Lighthill, M.: A note on cusped cavities. Aeronaut. Res. Council Rep. and Memo. 2328 (1945); 9.

    Google Scholar 

  • Malavard, M.: Recent developments in the method of rheoelectric analogy applied to aerodynamics. J. Aeronaut. Sci. 24, 321–331 (1957); 47.

    Google Scholar 

  • Marchet, P., and M. Malavard.: Determination des lignes de jet dans les mouvements plans et de revolution. Direction Aerodynamique, Laboratoire d’Analogies Electriques, Centre Nat. Rech. Sci., Paris 1949; 47.

    Google Scholar 

  • Martyrer, E.: Kraftmessungen an Widerstandkörpern und Flügelprofilen im Wasserstrom bei Kavitation. Hydromechanische Probleme des Schiffsantriebs, Hamburg, 1932, ed. G. KEMPF and E. FOERSTER; 2, 41.

    Google Scholar 

  • Mcleod, E.: The explicit solution of a free boundary problem involving surface tension. J. Rat. Mech. Analysis 4, 557–567 (1955); 16.

    Google Scholar 

  • Medaugh, F., and G. Johnson.: Investigation of the discharge and coefficients of small circular orifices. Civ. Engng., Lond. 10, 422–424 (1940).

    Google Scholar 

  • Michell, J.: On the theory of free streamlines. Phil. Trans. Roy. Soc. Lond., Ser. A 181, 389–431 (1890); 5.

    Google Scholar 

  • Mises, R. Von.: Berechnung von Ausfluß und Überfallzahlen. Z. VDI 61, 447–452, 469–473, 493–498 (1917); 10.

    Google Scholar 

  • Münzner, H., and H. Reichardt.: Rotationally symmetrical source-sink bodies with predominately constant pressure distribution. Arm. Res. Est. Transl. No. 1/50 (1950)—German original UM 6616 (1944); 2, 22.

    Google Scholar 

  • Nehari, Z.: Conformal mapping. New York-Toronto-London.: McGraw-Hill 1952; 5.

    MATH  Google Scholar 

  • Nekrasoff, N.A.: Sur la mouvement discontinu à deux dimensions de fluide autour d’un obstacle en forme d’arc de cercle. Publ. Inst. Polytech. Ivanovo-Voszniesiensk 1922; 32, 40.

    Google Scholar 

  • Oudart, A.: L’étude des jets et la mécanique théorique des fluides. Publ. Sci. Tech. Min. de l’air 234, Paris 1949; 3, 12.

    Google Scholar 

  • Oudart, A.: Sur le schema de HELMHOLTZ-KIRCHHOFF. J. Math. pures appl. 22, 245–320 (1943)

    Google Scholar 

  • Oudart, A.: Sur le schema de HELMHOLTZ-KIRCHHOFF. J. Math. pures appl. 23, 1–36 (1944); 32.

    Google Scholar 

  • Pai, S. I.: Fluid dynamics of jets. New York.: Van Nostrand 1954; 2, 12.

    Google Scholar 

  • Parkin, B.: Experiments on circular-arc and flat-plate hydrofoils. J. Ship Res. 1, 34–56 (1958); 2.

    Google Scholar 

  • Parkin, B.: Fully cavitating hydrofoils in nonsteady motion. Hydrodynamics Lab., Cal. Inst. Tech. Rep. 85–2 (1957); 18.

    Google Scholar 

  • Perry, B.: Methods for calculating the effect of gravity on two-dimensional free surface flows. Diss. Stanford U. 1957; 15.

    Google Scholar 

  • Pierson, J.: Stevens Inst. Tech. Rep. No. 381 (1950); 20.

    Google Scholar 

  • Planck, M.: Zur Theorie der Flüssigkeitsstrahlen. Wied. Ann. (2) 21, 499–509 (1884); 5.

    Google Scholar 

  • Plesset, M., et B. Perry.: On application of free streamline theory to cavity flows. Mémoires sur la mécanique des fluides offerts a M. DIMITRI RIABOUCHINSKY, pp. 251–261, Publ. Sci. Tech. Min. de l’Air, Paris 1954; 2.

    Google Scholar 

  • Plesset, M., and P. Shaffer.: Cavity drag in two and three dimensions. J. Appl. Phys. 19, 934–939 (1948); 8, 22.

    Google Scholar 

  • Plesset, M., and P. Shaffer.: Drag in cavitating flow. Rev. Mod. Phys. 20, 228–231 (1948); 8, 22.

    Google Scholar 

  • Polya, G., and G. Szego.: Isoperimetric inequalities of mathematical physics. Princeton 1951; 35.

    Google Scholar 

  • Privaloff, J.: Sur les fonctions conjuguées. Bull. Soc. Math. France 44, 100–103 (1916); 33.

    Google Scholar 

  • Pykhteev, G.: Solution of the inverse problem of a plane cavitational flow along an arc of a curve. Prikl. Mat. Mekh. 20, 378–381 (1956); 23.

    Google Scholar 

  • Lord Rayleigh.: On the resistance of fluids. Phil. Mag., Dec. 1876; Papers 1, 287; 4.

    Google Scholar 

  • Lord Rayleigh.: Theory of sound. New York.: Dover Publications 1945; 2, 4.

    Google Scholar 

  • Reichardt, H.: The laws of cavitation bubbles at axially symmetric bodies in a flow. Min. Aircraft Prod. Rep. and Transl. 766 (1946)

    Google Scholar 

  • Reichardt, H.: German original Göttingen 1945; 2, 22.

    Google Scholar 

  • Riabouchinsky, D.: On steady fluid motion with free surface. Proc. Lond. Math. Soc. (2) 19, 206–215 (1920); 8.

    Google Scholar 

  • Riabouchinsky, D.: On some cases of two-dimensional fluid motions. Proc. Lond. Math. Soc. (2) 25, 185-194 (1926); 8.

    Google Scholar 

  • Riabouchinsky, D.: Sur un problème de variation. C. R. Acad. Sci., Paris 185, 840–841 (1927); 30.

    Google Scholar 

  • Richardson, A.: Stationary waves in water. Phil. Mag. (6) 40, 97–110 (1920); 15.

    Google Scholar 

  • Rosaxo, A.: A new hodograph for free streamline theory. NACA TN 3168 (1954); 4, 11, 41.

    Google Scholar 

  • Rouse, H., and A. Abul-Fetouh.: Characteristics of irrotational flow through axially symmetric orifices. J. Appl. Mech. 17, 421–426 (1950); 47.

    Google Scholar 

  • Sakurai, T.: The flow past a flat plate accompanied with an unsymmetric dead air at Mach number 1. J. Phys. Soc. Japan 11, 710–715 (1956); 12.

    Google Scholar 

  • Sautreaux, C.: Question d’hydrodynamique. Ann. Sci. Ec. Norm. Sup. (2) 10 Suppl., 95–182 (1893); 15.

    Google Scholar 

  • Sautreaux, C.: Mouvement d’un liquide parfait soumis à la pesanteur. Determination des lignes de courant. J. de Math. (5) 7, 125–159 (1901); 15.

    Google Scholar 

  • Schach, W.: Umlenkung eines kreisförmigen Flüssigkeitsstrahles an einer ebenen Platte senkrecht zur Strömungsrichtung. Ing.-Arch. 6, 51–59 (1935); 46.

    Google Scholar 

  • Scheid, F.: On the asymptotic shape of the cavity behind an axially symmetric nose moving through an ideal fluid. Amer. J. Math. 72, 485–501 (1950); 25.

    Google Scholar 

  • Schiffer, M.: Analytical theory of subsonic and supersonic flows. Encyclopedia of Physics, Vol. IX; 12.

    Google Scholar 

  • Schmieden, C.: Die unstetige Strömung um einen Kreiszylinder. Ing.-Arch. 1, 104–109 (1929); 40.

    Google Scholar 

  • Schmieden, C.: Über die Eindeutigkeit der Lösungen in der Theorie der unstetigen Strömungen. Ing.Arch. 3, 356 - 370 (1932); 6, 40.

    Google Scholar 

  • Schmieden, C.: Über die Eindeutigkeit der Lösungen der unstetigen Strömungen. Ing.-Arch. 5, 373–375 (1934); 40.

    Google Scholar 

  • Schmieden, C.: Über die Hohlraumbildung in der Flüssigkeit. Ann. d. Phys. (5) 2, 350–356 (1929); 41.

    Google Scholar 

  • Schmieden, C.: Der Aufschlag von Rotationskörpern auf eine Wasseroberfläche. Z. angew. Math. Mech. 33, 147–151 (1953); 20.

    Google Scholar 

  • Schmieden, C.: Über den LandestoB von Flugzeugschwimmern. Ing.-Arch. 10, 1–13 (1939); 20.

    Google Scholar 

  • Sedov, L.: Der Stoß eines starren Körpers der auf Oberfläche einer inkompressiblen Flüssigkeit schwimmt. CAHI Rep. No. 187 (1934); 20.

    Google Scholar 

  • Self, M., and J. Ripken.: Steady-state cavity studies in a free-jet water tunnel. St. Anthony Falls Hydraulic Lab., Univ. of Minn. Rep. No. 47, 1955; 2.

    Google Scholar 

  • Serrin, J.: Comparison theorems for subsonic flows. J. Math. Phys. 33, 27–45 (1954); 26, 37.

    MathSciNet  Google Scholar 

  • Serrin, J.: Existence and uniqueness of the flows solving four free boundary problems. Thesis, Indiana University 1951, Appendix A.; 26.

    Google Scholar 

  • Serrin, J.: Existence theorems for some hydrodynamical free boundary problems. J. Rat. Mech. Analysis 1, 1–48 (1952); 26, 32, 33, 34.

    Google Scholar 

  • Serrin, J.: Uniqueness theorems for two free boundary problems. Amer. J. Math. 74, 492–506 (1952); 26, 37.

    Google Scholar 

  • Serrin, J.: Two hydrodynamic comparison theorems. J. Rat. Mech. Analysis 1, 563–572 (1952); 26.

    Google Scholar 

  • Serrin, J.: On plane and axially symmetric free boundary problems. J. Rat. Mech. Analysis 2, 563–575 (1953); 26, 28, 29, 32.

    Google Scholar 

  • Shiffman, M.: On free boundaries of an ideal fluid. I, II. Comm. Pure Appl. Math. 1, 89–99 (1948)

    Google Scholar 

  • Shiffman, M.: On free boundaries of an ideal fluid. I, II. Comm. Pure Appl. Math. 2, 1–11 (1949); 3, 7, 13.

    MathSciNet  Google Scholar 

  • Shiffman, M., and D. SPENCER.: The flow of an ideal incompressible fluid about a lens. Quart. Appl. Math. 5, 270–288 (1947); 20.

    Google Scholar 

  • Shiffman, M., and D. SPENCER.: The force of impact on a cone striking a water surface. Comm. Pure Appl. Math. 4, 379–417 (1951); 20.

    Google Scholar 

  • Smith, H.: Hydraulics. London-New York.: John Wiley 1886; 2.

    Google Scholar 

  • Southwell, R.: Relaxation methods in theoretical physics. Oxford 1946; 47.

    Google Scholar 

  • Southwell, R., and G. Vaisey.: Fluid motions characterized by “free” streamlines. Phil. Trans. Roy. Soc. Lond., Ser. A 240, 117–161 (1948)

    Article  ADS  MathSciNet  Google Scholar 

  • Southwell, R., and G. Vaisey.: Fluid motions characterized by “free” streamlines. Phil. Trans. Roy. Soc. Lond., Ser. 10, 11, 15, 47.

    Google Scholar 

  • Squire, H. B.: On the laminar flow of a viscous fluid with vanishing viscosity. Phil. Mag. 7 (17), 1150- 1160 (1934); 41.

    Google Scholar 

  • Tan, H. S.: A unique law for ideal incompressible flow with preserved pattern of finite separation. Quart. Appl. Math. 12, 78–80 (1954); 19.

    Google Scholar 

  • Theron, P.: Sur un théorème d’existence des mouvements des fluides plans avec sillage. C. R. Acad. Sci., Paris 228, 1922 (1949); 32.

    Google Scholar 

  • Trevftz, E.: liber die Kontraktion kreisförmiger Flüssigkeitsstrahlen. Z. Math. Phys. 64, 34–61 (1916); 46.

    Google Scholar 

  • Trilling, L.: The impact of a body on a water surface at an arbitrary angle. J. Appl. Phys. 21, 161–170 (1950); 20.

    Google Scholar 

  • Tsien, S.: Two-dimensional subsonic flow of compressible fluids. J. Aeronaut. Sci. 6, 399 to 407 (1939); 12.

    Google Scholar 

  • Tulin, M.: Steady two-dimensional cavity flows about slender bodies. David Taylor Model Basin Rep. 834 (1953); 21.

    Google Scholar 

  • Tulin, M.: Supercavitating flow past foils and struts. Symposium on Cavitation in Hydrodynamics, National Phys. Lab., Her Majesty’s Stationery Office, 1956; 21.

    Google Scholar 

  • Vandrey, F.: A direct iteration method for the calculation of the velocity distribution of bodies of revolution and symmetrical profiles. Aeronaut. Res. Counc. FM 1665 (1951); 22.

    Google Scholar 

  • Villat, H.: Sur le changement d’orientation d’un obstacle dans un courant de fluide. Ann. Fac. Sci. Toulouse (3) 5, 375–404 (1913); 9.

    Google Scholar 

  • Villat, H.: Sur la résistance des fluides. Ann. Sci. Ec. Norm. Sup. 28, 203–240 (1911); 33.

    Google Scholar 

  • Villat, H.: Sur la validité des solutions de certains problèmes d’hydrodynamique. J. de Math. (6) 10, 231–290 (1914); 24.

    Google Scholar 

  • Villat, H.: L’écoulement des fluides pesants. Ann. Sci. Ec. Norm. Sup. (3) 32, 177–214 (1915); 15

    Google Scholar 

  • Vitousek, M.: Some flows in a gravity field satisfying the exact free surface condition. Tech. Rep. No. 25 (1954), Appl. Math. Stat. Lab., Stanford Univ.; 15.

    Google Scholar 

  • Wagner, H.: Über Stoß-und Gleitvorgänge an den Oberflächen von Flüssigkeiten. Z. angew. Math. Mech. 12, 193–215 (1932); 11, 20.

    Google Scholar 

  • Waid, R.: Water tunnel investigations of two-dimensional cavities, Hydrodynamics Lab., Cal. Inst. Tech. Rep. E-73.6 (195 7); 41.

    Google Scholar 

  • Watanabe, S.: Resistance of impact on water surface, Parts I, II, IV, V, VI. Inst. Phys. Chem. Res. Tokyo (Sci. Papers), I-cone.: 12, 251–267 (1930)

    Google Scholar 

  • Watanabe, S.: Resistance of impact on water surface, Parts I, II, IV, V, VI. Inst. Phys. Chem. Res. Tokyo (Sci. Papers), II-cone.: 14, 153–168 (1930)

    Google Scholar 

  • Watanabe, S.: Resistance of impact on water surface, Parts I, II, IV, V, VI. Inst. Phys. Chem. Res. Tokyo (Sci. Papers), IV-circular plane.: 23, 118–135 (1933)

    Google Scholar 

  • Watanabe, S.: Resistance of impact on water surface, Parts I, II, IV, V, VI. Inst. Phys. Chem. Res. Tokyo (Sci. Papers), V-sphere.: 23, 202–208 (1934)

    Google Scholar 

  • Watanabe, S.: Resistance of impact on water surface, Parts I, II, IV, V, VI. Inst. Phys. Chem. Res. Tokyo (Sci. Papers), VI-cylinder.: 23, 249–255 (1934); 20.

    Google Scholar 

  • Wayland, H.: Scale factors in water entry. Naval Ord. Test Station, NAVORD Rep. 978 (1947); 2.

    Google Scholar 

  • Wayland, H., and J. White.: Boundary layer effects on spinning spheres. Heat Transfer and Fluid Mechanics Institute. Amer. Soc. Mech. Eng. 1949, 51–64; 2.

    Google Scholar 

  • Weible, A.: The penetration resistance of bodies with axial head forms at perpendicular impact on water. German Aviation Res. Rep. No. 4541; Naval Res. Lab. Transi. No. 286 (1952); 20.

    Google Scholar 

  • Weinig, F.: Die Ausdehnung des Kavitationsgebietes. Hydromechanische Probleme des Schiffsantriebs, ed. by G. Kempf and E. Foerster. Hamburg 1932; 8.

    Google Scholar 

  • Weinstein, A.: Ein Hydrodynamischer Unitätssatz. Math. Z. 19, 265–274 (1924); 32,38.

    Google Scholar 

  • Weinstein, A.: Generalized axially symmetric potential theory. Bull. Amer. Math. Soc. 59, 20–38 (1953); 42.

    Google Scholar 

  • Weinstein, A.: Non-linear problems in the theory of fluid motions with free boundaries. Proc. Symposia Appl. Math., Vol. 1, pp. 1–18, Amer. Math. Soc. 1949; 32, 38.

    Google Scholar 

  • Weinstein, A.: Zur Theorie der Flüssigkeitsstrahlen. Math. Z. 31, 424–433 (1929); 32, 38, 39.

    Google Scholar 

  • Weyl, H.: Strahlbildung nach der Kontinuitätsmethode behandelt. Nachr. Ges. Wiss. Göttingen 1927, 227–237; 32, 38.

    Google Scholar 

  • Woods, L.: Compressible subsonic flow in two-dimensional channels with mixed boundary conditions. Quart. J. Math. Mech. 7, 263–282 (1954); 13.

    Google Scholar 

  • Woods, L.: Unsteady cavitating flow past curved obstacles. Aeron. Res. Coun. Current Paper No. 149 (1954) 18.

    Google Scholar 

  • Woods, L.: Two-dimensional flow of a compressible fluid past given curved obstacles with infinite wakes. Proc. Roy. Soc. Lond., Ser. A 227, 367–386 (1955); 13.

    Google Scholar 

  • Woods, L.: Unsteady plane flow past curved obstacles with infinite wakes. Proc. Roy. Soc. Lond., Ser. A 229, 152–180 (1955); 18.

    Google Scholar 

  • Worthington, A.: A study of splashes. New York.: Longmans Green 1908; 2.

    Google Scholar 

  • Wu, T.: A note on the linear and non-linear theories for fully cavitated hydrofoils. Hydrodynamics Lab., Cal. Inst. Tech. Rep. 21–22 (1956); 21.

    Google Scholar 

  • Wu, T.: A free streamline theory for two-dimensional fully cavitated hydrofoils. J. Math. Phys. 35, 236–265 (1956); 2, 7, 8, 11.

    Google Scholar 

  • Wu, T.: A linearized theory for nonsteady cavity flows. Hydrodynamics Lab., Cal. Inst. Tech. Rep. 85–6 (1957); 18.

    Google Scholar 

  • Wu, T.: A simple method for calculating the drag in the linear theory of cavity flows. Hydrodynamic Lab., Cal. Inst. Tech. Rep. 85–5 (1957); 21.

    Google Scholar 

  • Young, D., L. Gates, R. Arms and D. Eliezer.: The computation of an axially symmetric free boundary problem on NORC. U.S. Naval Proving Ground Rep. No. 1413 (1955); 47.

    Google Scholar 

  • Zarantonello, E.: A constructive theory for the equations of flows with free boundaries. Collectanea Mathematica 5, 175–225 (1952); 40.

    Google Scholar 

  • Zarantonello, E.: Parallel cavity flows past a plate. J. Math. pures appl. (9) 33, 29–80 (1954); 9.

    Google Scholar 

  • Zoller, K.: Widerstand einer ebenen Platte mit Totwassergebiet. Dtsch. Luftf.-Forschg. UM 4518 (1943); 7, 8.

    Google Scholar 

Download references

Authors
  1. David Gilbarg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

C. Truesdell

Rights and permissions

Reprints and permissions

Copyright information

© 1960 Springer-Verlag OHG. Berlin · Heidelberg

About this chapter

Cite this chapter

Gilbarg, D. (1960). Jets and Cavities. In: Truesdell, C. (eds) Fluid Dynamics / Strömungsmechanik. Encyclopedia of Physics / Handbuch der Physik, vol 3 / 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45944-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45944-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45946-7

  • Online ISBN: 978-3-642-45944-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation