Određivanje brzine i pritiska za vreme strujanja u krivinama

摘要

U radu Dean je došao do rešenja (20)-(22) za projekcije brzine za vreme nestišljivog strujanja u krivinama, ali rešenje za promenu pritiska (18) odnosno (19) nije našao. Tom prilikom, Dean je eliminisao pritisak iz dinamičkih jednačina povećavajući im red izvoda, što je stvorilo niz teškoća u toku kasnijeg integraljenja i zadovoljenja graničnih uslova. U ovom radu je to izbegnuto na taj način što se najpre, korišćenjem činjenice da izvodi jedne te iste funkcije dve promenljive moraju biti jednaki bez obzira na red diferenciranja, našla promena pritiska pa, zatim, projekcije brzine. Usput je izloženo i niz matematičkih finesa i obavljena je detaljna analiza dobijenih rezultata sa grafičkim prikazom. Razume se, nađena je i promena pritiska za vreme strujanja u krivinama, što u Dean-ovim radovima nije učinjeno.%In paper Dean has given solutions (20)-(22)for velocity projections during the incompressible flow in bends, but the expression (18) i.e. (19) for pressure distribution he has omitted to give. Dean obtained these solutions (20)-(22) by integrating the appropriate system of differential equations, Le. by raising their derivation order in order to eliminate the pressure distribution in them. This procedure seemed to be very complex and that was the reason the solution of the mentioned problem has been treated again in this paper. And really, starting with the fact that the mixed derivations of the very same function are mutually equal no matter of the order the partial differentiation has been done, the solution for pressure distribution has been achieved without any difficulties, and than afterwards the velocity projections were obtained In this paper, the graphic sketch of the obtained results has also been presented, including the analysis and the appropriate conclusions.