Inzynieria Chemiczna i Procesowa, Vol.15, No.1, 83-100, 1994
FLOW RESISTANCE OF DILUTE MACRO-MOLECULAR POLYMER-SOLUTIONS
The critical review of some chosen formulas determining the now resistance coefficient in smooth and rough pipes has been presented. The disadvantage of these formulas lies in the necessity of determining empirical coefficients dependent on various parameters. The experimental results have been compared with the resistance curves calculated from the formulas derived by different authors. The formula worked out by the author of this paper and presented in the form of equations (14)-(20) allows us to calculate the resistance coefficient basing on assigned geometrical parameters of the pipe: D, It, mean now velocity U, and the material constants of the solution: K', n', p, c, hi. It follows from the comparison of determined resistance curves with the experimental data that in the range of Reynolds numbers Rc* = 3.10(3)-1.10(5) the mean square deviation of the measuring points from obtained curves does not exceed 5% (Figs. 3, 5, 6). In Fig. 3 it has been shown that for the now of the solution of low concentration (0.001%) through the pipe of high roughness (k/D=0.032) the drag reduction does not occur, whereas at higher solution concentration (0.05%) the drag reduction in a rough pipe is greater than in a smooth one (Fig. 4). The diameter effect has been demonstrated in Fig. 7. It appears from the shape of resistance curves that in coordinates lambda, vs Re* the resistance curves determined for pipes of various diameters are close to each other. In Fig. 8 the maximum drag reduction effect has been presented. The measuring points obtained for 0.005% and 0.01% DP-9 solutions are dose to determined resistance curves. In Fig. 9 the experimental results obtained by the author have been compared with the resistance curves determined from the equation of VIRK (Tab. 1, [15]) KOZLOV (Tab. 1, [30]), SHAVER and MERRILL (Tab. 1, [22]) It can be seen that the equations derived by Virk and Kozlov describe approximately the resistance coefficient lambda, under conditions of maximum drag reduction, whereas the curves calculated from equation of Shaver and Merrill do not agree with the results of the author. Figure 10 shows that in the modified Prandtl-Karman coordinates the resistance curves are linear, which stands for the constancy of coefficients A and B for each curve. It should be mentioned that the difficulty level of determining parameters alpha*, alpha(e), u(*kr), A(0), ($) over bar A(0) is similar to that for coefficients A and B.,
Keywords:DRAG REDUCTION