Vízügyi Közlemények, 1957 (39. évfolyam)
4. füzet - VI. Kisebb közlemények
(7) According to Crump the Chézy formula may be retained for the framework of calculations based on theoretical relationships if coefficient с is calculated by the formula с = — \WTg log In the above formula q is the gravity acceleration (m/s 2), v the kinematical viscosity (m 2/s) characterizing the inner friction of the fluid, e the equivalent sphere diameter according to Nikuradse, characterizing channel roughness (m). Cramp's formula is directly applicable to closed conduits, since the e-values are also known for the major part of conventional pipe materials according to Lamont [10] and others. To extend the practical application of the solution of general validity to the case of open channels a correlation has been established between the roughness numbers n after Kutler and Ganguillet, most generally used in hydraulic engineering, and the yardstick e of theoretical research. The solution of the problem was supported principally by the results of classical tests executed about 100 years ago by Darcy and Bazin [4]. Accessorily some data of the works of Strickler [17] and Lindquist [14] and some measurements of the Hungarian Hydrographie Service were made use of. The results of 110 measurements contained in Table I. are summed up in Fig. 11. and formula 1 915 - = 19,8 log (31) П £ (Value of e had to be substituted in cm.) From data of the individual measurements the values of e were determined with the aid of Fig. 7. which solves graphically the basic equation of Colebrook and White (24). In the diagram the locations of the points corresponding to the different data of Table I. were determined by the Reynolds number calculated by formula (9) and by the friction factor Л. By interpolation between the isometric lilies of the field of the diagram the relative roughnesses e/R characterizing the individual measurements were found, and afterwards the diameter e of the equivalent sphere of Nikuradse. Coefficients n after Kutter - Ganguillet were read off from Fig. 10. giving solution of the Manning formula, on the basis of values of R and с taken from columns 5. and 12. of Table 1. Fig. 11. gives correlated values of e and n. Since for the determination of the Reynolds number the knowledge of the kinematical viscosity v was necessary, which is a function of temperature, the lacking temperature data were supplemented on the basis of Fig. 9., the time of measurement taken account of. For the construction of the aids for calculation it is expedient to separate the pure quadratic zone indicating full turbulence. Fig. 12. includes the values of Re and e/R corresponding to points M,, M 2 ... of the boundary line originating from II. Rouse marked in Fig. 7. From Fig. 13., drawn on the basis of calculations executed by formula (33) on the strength of values summed up in Table 11., read off Fig. 11. and 12., it is ascertainable that in the case of a roughness coefficient of e > 1 cm (or n > 0,017) conditions of flow practically always fall into the zone of full turbulence. Since in the purely quadratical zone there is a univocal relation between velocity coefficient с and relative roughness e/R, a simple three-variable correlation chart can be drawn for the determination of coefficient с (Fig. 14.). In the transitional zone and in the zone oj hydraulically smooth pipes the value of coefficient с is affected according to formula (27) by the viscosity of the fluid and by the hydraulic gradient. The weights of the different factors are represented in Fig. 17. in connection with numerical examples characterizing conditions of the transitional zone. To facilitate calculations on the basis of formulas (1), (27) and (31) coaxial graphs, in scale and execution fit for practical use, are contained in a special publication of the Research Institute for Water Resources. Fig. 14., 1С., 18., 10. and 20. present the graphs in reduced size. 0,0676 — R 0,222 v R 1 fa J H (27)
