Intelligent Flow Friction Estimation

Table 1

Relative error of friction factor produced by the shown ANN over the practical domain of the relative roughness () and the Reynolds number (Re).

Relative error (%)	Relative roughness ()
Reynolds number (Re)	10^−6	5 ⋅ 10^−6	10^−5	5 ⋅ 10^−5	10^−4	5 ⋅ 10^−4	10^−3	5 ⋅ 10^−3	10^−2	5 ⋅ 10^−2
10^4	0.00134	0.00088	0.00031	0.00017	0.00123	0.00141	0.00041	0.00099	0.00096	0.00069
5 ⋅ 10^4	0.00102	0.00174	0.00080	0.00096	0.00220	0.00163	0.00247	0.00063	0.00224	0.00124
10^5	0.00114	0.00145	0.00125	0.00356	0.00099	0.00384	0.00097	0.00117	0.00104	0.00076
5 ⋅ 10^5	0.00181	0.00032	0.00287	0.00084	0.00047	0.00090	0.00028	0.00011	0.00055	0.00064
10^6	0.00163	0.00246	0.00126	0.00073	0.00419	0.00440	0.00176	0.00190	0.00023	0.00053
5 ⋅ 10^6	0.00449	0.00672	0.00207	0.00377	0.00012	0.00077	0.00071	0.00031	0.00038	0.00074
10^7	0.00126	0.00054	0.00417	0.00527	0.00005	0.00089	0.00015	0.00033	0.00063	0.00186
5 ⋅ 10^7	0.01946	0.00382	0.00490	0.00835	0.00260	0.00174	0.00011	0.00071	0.00038	0.00022
10^8	0.06060	0.05266	0.03614	0.02413	0.01682	0.00410	0.00165	0.00544	0.00579	0.00068