Hidrológiai Közlöny 1960 (40. évfolyam)
5. szám - Ivicsics L.: Hidromechanikai feladatok megoldása rétegkisminták segítségével
374 Hidrológiai Közlöny 1960. 5. Sz. Ivicsics L.: Hidromechanikai feladatok megoldása réteg kismintákkal PEUIEHHE rHflPOMEXAHHMECKHX 3A^AM C 110MOmbK) mEHEBblX MO^EJlEft Jl. Meutui KaHA- TexH. HayK npw pemeHHH rHflpoMexaHHiecKHx 3aAan BO MHOTHX ciiyiaHx MO>KHO n0Jib30BaTbCH c noHHTneM aHajiorHMeCKHX HBJIGHHH. AHa/lOZUHeCKUMU R6A£HUHMU CHUmüwmcH tpu3unecKue neAenun. pa3nozo xapaKmepa, npoqecc Komopbix xapaKmepu3yemcn ypaenenuHMU, npueodiiMbiMU na oöufee MameMammecKoe ebipa>KeHue, HO eeAunuHu, coomeemcmeywiifue dpye dpyey u xapaKmepu3ywufue omdeAbHbie neAemiH, Hsjwwmcsi orrmacmu, UAU noAHoembw pa3AU1HblMU. MacTO pemaioTCH 3aflaHH no (jHijibTpannH c ncnojib30BaHHeM 0CH0BH0r0 coo6pa>KeHHH, no KOTopoMy (})HJibTpaúHOHHoe flBHMceHiie BOflbi n pacTnpocTpaHeHne 3JieKTpnMecKoro TOKa B sjieKTpojinTe, HJIH B /ipyroM npoBOAHiiKe HBJIHIOTCH aHajiornnecKHMH HBJieHHHMH. 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BBHfly Toro, hto aHajioraMH cMHTaioTCH He TOJibKO 3BA YKA3AHHBIE JIBNEHHH, HO U mypöyAenmHoe u AÜMUHapnoe űeunceHUH, ufeAeeue MOÖCAU MOWHO npwvieHHTb He TOJibKO npH pemeHHH tpuAbmpaquoHHbix 3adan, HO U E HeKomopux CAyianx npu peuienuu 3adan, C8H3üHHbix c dpyeuMü neAenuHMü. To 06CT0HTE.NBCTB0, MTO jiaivuiHapHoe H TypöyjieHTHoe ABIDKCHHH ÍIBJIHIOTCH aHaJiorHHecKHMH HBJTeHHHMH MO>KHO FLOKA3ATB nyTeM COnOCTaBJieHHH (J)H3HHECKHX CBOHCTB FLBYX HBJIEHHH, ^AJIEE CpaBHeHHeM ypaBHeHHH HaBnep—CTOKca n PefíHOJiffca, T. e. ypaBHeHHH 19—21 H 23—25, Tat<>Ke II ypaBHeHHií HenpepbiBHOCTH 22,26 B cjiyiae jiaMHHapHoro N TypöyneHTHoro «BHweHHÜ, Aanee conocTaBneHneivi ypaBHeHiifí MOJieKyjinpHbix KacaTeJibHbix HANPH>KEHHH H MHHMOTO KacaTejibHoro HaiipflweHHH no BycHHecKy. Solutioii oí Hydromechanical Troblems by the Aid oí Layer Scale Models By L. Ivicsics Candidate of Technical Sciences Analogous phenomena are frequently used with success for the solution of hydromechanical problems. Physical phenomena, although differring in character but described by equations that can be reduced to a common form regardless of the fact that the corresponding quantities characterizing individual phenomena are in part, or entirely different, are considered analogous. Problems relating to seepage are frequently solved by recurring to the basic principle, that percolating water movement and the propagation of electric current in an electrolyte, or any other conductor, constitute analogous phenomena. Percolating water movement can be brought into analogy with several other, e. g. thermal, magnetic and structural phenomena as weil. As can be demonstrated, the phenomenon of a viscous fluid moving at low velocity in a thin layer between two parallel planes can alsó be considered analogous to seepage, provided certain criteria are satisfied. In fact, the two components (u, v) of velocity of movement can be described in both cases by equations of identical form [Eqs. (3) and (4), respectively (6) and (7)], however the permeability coefficient (fc and k v) is defined differently in the case of seepage [Eqs. (1) and (2)] than in the case of movement between parallel planes [Eq. (5)] and physically the two phenomena are essentially different. Demonstration is based on the Navier-Stokes equation, in the form as expressed in a Cartesian coordinate system. With certain simplifying assumptions the velocity components can be expressed therefrom [Eqs. (ti) and (7)]. As one of the simplifications it was assumed, that the inertia forces alsó equal zero, however, this assumption is not valid for every kind of laminar movement. Scale models constructed on the basis of the analogy existing between percolating water movement and movement in a thin layer between parallel planes are termed „layer scale models" (of which a schematical drawing is shown in Fig. 2). Inasmuch as besides the two lastmentioned phenomena turbulent and laminar movement are alsó analogous phenomena, layer scale models can be applied in certain cases alsó to the solution of problems related to other phenomena in addition to seepage. The circumstance, that laminar and turbulent movement are analogous phenomena can be demonstrated by comparing the Navier-Stokes equation and the Reynolds equation [Eqs. (19) to (21) and Eqs. (23) to (25)], as weil as the continuity equations for the cases of laminar and turbulent movement [Eqs. (22) and (26)], further the definitions of molecular shearing stress and of the apparent shearing stress by Boussinesque [Eqs. (15) and (16)], and finally the physical characteristics of the two phenomena.
