PSI - Issue 59

Mariia Serediuk et al. / Procedia Structural Integrity 59 (2024) 763–770 Mariia Serediuk et al. / Structural Integrity Procedia 00 (2019) 000 – 000

767

5

0.25 0.3164 Re

(5)

,

 

if Re > Re T2

1.7

B   

(6)

,

0.5

Re

where Re cr – is the critical Reynolds number that separates the laminar and transitional modes of fluid motion; Re T1 – is the Reynolds number that separates the transition mode and the zone of hydraulic smooth pipes of the turbulent mode of fluid movement; Re T2 – is the Reynolds number, which separates the zones of hydraulic smooth pipes and mixed friction of the turbulent mode of fluid movement, a function of the diameter of the pipeline and the roughness of the pipe; B – is a coefficient, the values of which depend on the diameter of the pipeline and the accepted values of the roughness of the pipe. It should be noted that the values of the Reynolds number Re T2 and coefficient B given in VNTP 2-86 (1987) correspond to a specific absolute equivalent surface roughness of k e = 0.125 mm for pipes with a diameter of up to 377 mm inclusive and k e = 0.1 mm for pipes with a larger diameter. Next, pressure losses due to friction in the pipeline are calculated using the formula Pτ and the total pressure losses in the pipeline Ptotal are found. Determine the required number of pumping stations (hereafter NS) on the nNS pipeline. Let us investigate how correctly the value of the critical Reynolds number Re кр =2000, which separates the laminar and transitional modes of fluid movement in the pipeline, was chosen in VNTP 2-86 (1987). To do this, we calculate the coefficient of hydraulic resistance according to formulas (3) and (4) in the range of Reynolds numbers bordering on the critical value. According to the results of the calculations, the following graphical dependencies were obtained (Fig. 1a). a b

Fig. 1. Comparison of the results of calculating the coefficient of hydraulic resistance: (a) - according to formulas (3) and (4); (b) - according to formulas (4) and (5). As shown in Fig. 1a, the refined value of the critical Reynolds number, for which the results of calculations according to formulas (3) and (4) practically coincide, is not 2000, but Re ʹ кр =2041. Similarly, let us investigate the correctness of choosing the Reynolds number Re T1 =2800, which separates the transition mode and the zone of hydraulically smooth pipes of the turbulent mode of fluid movement in the pipeline, using formulas (4) and (5). Based on the results of the calculations, we build graphic dependencies (Fig. 1b). The value of the Reynolds number, for which the results of calculations according to formulas (4) and (5) practically coincide, does not need to be clarified and is, as stipulated in VNTP 2-86 – Re T1 = 2800.