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

768

6

As mentioned above, the transition Reynolds number ReT2 and the coefficient B depend on both the diameter of the pipeline and the roughness of the pipe surface. Therefore, we will check the correctness of the selection of the value of the Reynolds number ReT2, which divides the scope of application of formulas (5) and (6), first for a pipe with an outer diameter of 377 mm. The obtained results are shown in Figure 2a. As shown in Figure 2a, for a pipeline with an outer diameter of 377 mm, the value of the Reynolds number, for which the results of the calculations of the coefficient of hydraulic resistance according to formulas (5) and (6) practically coincide, also does not need to be specified and is Re T2 = 28000, as provided by VNTP 2-86. a b

Fig. 2. Comparison of the results of calculating the coefficient of hydraulic resistance according to formulas (5) and (6) (a) – for a pipeline with a diameter of 377 mm; (b) – for a pipeline with a diameter of 159 mm. Similar studies were conducted for other standard pipe diameters. Studies have proven the need to adjust the values of Reynolds numbers Re T2 , given in VNTP 2-86. Table 2 contains the adjusted Reynolds number values Re T2 , for pipe diameters greater than 219 mm.

Table 2. Adjusted values transition Reynolds Re T2 , numbers. Outer diameter, mm 1220 1020 820

720

530

426

377

325

273

Value Re T2

126000

120000

107000

100000

71000

56000

28000

16500

15000

For the adjusted values of the transient Reynolds numbers Re T2 given in Table 2, the difference in the results of calculating the coefficient of hydraulic resistance according to formulas (5) and (6) does not exceed 0.0004. It was established that for the smallest pipe diameters of 159 mm and 219 mm, the values of the transitional Reynolds numbers Re T2 given in VNTP 2-86 do not provide the same results for determining the coefficient of hydraulic resistance according to formulas (5) and (6) for any Reynolds number Re T2 . An example of the obtained graphical dependencies for a pipeline with a diameter of 159 mm is shown in Figure 1b. For these pipelines, as the calculations showed, in the case of applying formulas (5) and (6), when the friction zone of the turbulent regime is changed, there will be a jump-like change in the value of the coefficient of hydraulic resistance by 0.001 for a diameter of 219 mm and by 0.002 for a diameter of 159 mm. The method of hydrodynamic calculation of the pipeline given in VNTP 2-86 (1987) provides for the transition from the use of formula (5) to formula (6) for the coefficient of hydraulic resistance at a certain transitional Reynolds number Re T2 , which should separate the zone of hydraulic smooth pipes and the zone of mixed friction turbulent regime of fluid motion. It should be noted that there is no unanimity among domestic and foreign scientists regarding the determination of the reliable value of the specified transitional Reynolds number. Table 3 shows the equations from various sources for determining the Reynolds number Re T2 , which separates the zone of hydraulic smooth pipes and the zone of mixed friction of the turbulent regime, and the calculation results at k e =0,1 mm for a pipeline with an internal diameter of 361 mm. The results of the calculation differ significantly, which makes it doubtful to use the method of hydrodynamic calculation of pipelines given in VNTP 2-86 (1987) without making changes.