Vízügyi Közlemények, 1957 (39. évfolyam)

4. füzet - VI. Kisebb közlemények

(6) COMPUTATION OF THE VELOCITY OF FLOW (Work-Helps for Design) K. Szesztay Cand. of Eng. Sc. (Figures and tables on pp. 22—61. of Hungarian text) UDC. 532.54 : 626/628 Hydraulic di mensioning of open channels, serving different purposes, as wel as of closed conduits transporting water or other fluids is the most extensive chapter of hydraulics which looks back on the most varied past. Since physical investigation for the est- hlishment of a formula for flow velocity calculations had not yielded a practicable result up to the last years, engineering practice had to put up with practical formulas derived from measurement results. The formula of Chézy V = с I RJ (1) dates from 1775 (v is mean velocity, R the hydraulic radius of the cross section, J the slope). The difficulty of practical application of the formula manifests itself in the determination of velocity coefficient c. On the basis of laboratory tests and of velocity measurements executed on natural streams Bazin (2), Kutter and Ganf/uillet (3), Manning, Strickler and Lindquist (4), Pavlovsky (5) and many others derived empirical relationships for the computation of coefficient c. In one or another narrow range of practical problems the empirical formulas show good agreement with one another and with the basic data (Fig. 1.). For comparison the relation between roughness coefficients of the different empirical formulas has to be known (Fig. 2.). This relation may be regarded — with practically permissible approximation — as unequivocal, though from more detailed investigations it appears that — depending on the difference in the construction of the formulas — the „scale effect" is always present (Fig. 3.). With the investigation extended on the practically possible range of the hydraulic radius and roughness, differences of several hundred % are found between results given by the different formulas. The different shape of curves of Fig. 4. clearly shows that the buildup of the formulas is also contradictory. From Fig. 4e and 5 it is evident that the formula of Pavlovsky (5) leads with greater radii and rougher channels to absurdity, while in connection with the Bazin formula (2) it is found on the basis of Fig. 6 that there is no physical explanation either for the opposite curvature of the curves or for the value c

ma

i = 87. The buildup of the formulas of Kutter —Ganguillet (3) and Manning (4) does not meet requirements of theoretical research, and they lack a yardstick of roughness based on physical reasoning. The "roughness coefficient" of such empirical formulas levels off the contradictions arising from shortcomings of the buildup of the formulas. The structure of Agroskin's formula (6) satisfies theoretical requirements for the case of natural streams and open channels (in the pure quadratic zone), but with regard to the yardstick of roughness this formula does not yield either a satisfactory solution. In the case of hydraulically smooth pipes and in the transition zone the formula (6) is not applicable. The application of empirical formulas restricted to one group or another of practical problems is cumbersome and liable to errors. Therefore it is an old desire of researchers to elaborate a velocity formula of general validity, physically founded and extending over the entire range of values that can occur. For pioneer work in theoretical research Prandtl and Kármán [16] are to be credited. Experiments of Nikuradse in 1933 opened the way to the physical interpretation of the effect of roughness [15]. Colebrook and White arrived in 1939 at the theoretical basic equation [9 ] including the entire range of turbulent motion wherefrom British researcher E. S. Crump derived in 1956 a velocity formula of general validity [3].