Numerical and Theoretical Investigation to Estimate Darcy Friction Factor in Water Network Problem Based on Modified Chun-Hui He’s Algorithm and Applications

Table 2

The water problem (Figure 2) displaying the first iteration of technique NM ([32]). It is not necessary to follow Kirchhoff’s law in NM.

Pipes	Loops	Diameter (m)	Length (m)		Sign (q)	, equation (1)	NM,
1		0.457	120	0.125	1	3.48	0.0892094	−0.0357906
9	I	0.406	160	0.05	1	1.34	0.0352368	−0.0147632
13		0.355	120	−0.025	−1	−0.49	0.112488	0.087488
7		0.304	120	−0.175	−1	−52.34	0.210791	0.035791
8		0.304	280	0.175	1	122.12	0.139209	−0.035791
	Loop					74.11		0.0369342
2		0.457	150	0.075	1	1.57	0.0539726	−0.0210274
10	II	0.406	160	0.04	1	0.86	0.017803	−0.022197
11		0.406	150	−0.015	−1	−0.11	0.0877249	0.0727249
9		0.406	160	−0.05	−1	−1.34	0.0352368	−0.0147632
	Loop					0.97		0.0147373
3		0.457	150	0.035	1	0.34	0.0361696	0.0011696
4	III	0.406	160	−0.025	−1	−0.34	0.0238304	−0.0011696
12		0.406	150	0.015	1	0.11	−0.0355278	−0.0505278
10		0.406	160	−0.04	−1	−0.86	0.017803	−0.022197
	Loop					−0.74		−0.0727248
5		0.457	120	−0.09	−1	−1.80	0.0383025	−0.0516975
6	IV	0.609	300	−0.15	−1	−2.98	0.0983025	−0.0516975
13		0.355	120	0.025	1	0.49	0.112488	0.087488
11		0.406	150	0.015	1	0.11	0.0877249	0.0727249
12		0.406	150	−0.015	−1	−0.11	−0.0355278	−0.0505278
						−4.29		0.0062901

All bold values are based on multidimension.