Intelligent Flow Friction Estimation

Table 2

Maximal relative error produced by the ANN compared with the seven most accurate explicit approximations of Colebrook equation; the Reynolds number (Re) is used as the base.

Maximal relative error (%)
Reynolds number (Re)	(a)	(b)	(c)	(d)	(e)	(f)	(g)	(h)
10^4	0.00141	0.00074	0.00569	0.12272	0.13563	0.13453	0.13301	0.13313
5 ⋅ 10^4	0.00247	0.00219	0.00574	0.14112	0.13784	0.11047	0.13736	0.13736
10^5	0.00384	0.00246	0.00698	0.14467	0.13812	0.10281	0.13793	0.13793
5 ⋅ 10^5	0.00287	0.00250	0.00802	0.14712	0.13841	0.08915	0.13839	0.13839
10^6	0.00440	0.00235	0.00816	0.14727	0.13846	0.08426	0.13845	0.13845
5 ⋅ 10^6	0.00672	0.00167	0.00826	0.14725	0.13850	0.07315	0.13850	0.13850
10^7	0.00527	0.00122	0.00828	0.14722	0.13851	0.06754	0.13850	0.13850
5 ⋅ 10^7	0.01946	0.00022	0.00829	0.14718	0.13851	0.04876	0.13851	0.13851
10^8	0.06060	0.00005	0.00829	0.14718	0.13851	0.04841	0.13851	0.13851

(a)-Artificial Neural Network (ANN).
(b)-Ćojbašić and Brkić [37]-Improved Serghides [42]; (A.7).
(c)-Ćojbašić and Brkić [37]-Improved Romeo et al. [43]; (A.6).
(d)-Vatankhah and Kouchakzadeh [44]; (A.2).
(e)-Buzzelli [45]; (A.1).
(f)-Romeo et al. [43]; (A.3).
(g)-Serghides [42]; (A.4).
(h)-Zigrang and Sylvester [46]; (A.5).