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

Table 5

Start node	End node	Pipe index	Hardy Cross method ()	Newton method ()	Modified NM ()
A	B	1	0.0860912	0.0860912	0.0860912
B	C	2	0.057979	0.057979	0.057979
C	D	3	0.0380804	0.0380804	0.0380804
D	G	4	^(a) −0.0219196	0.0219196	0.0219196
G	J	5	−0.0854642	0.0854642	0.0854642
J	I	6	−0.145464	0.145464	0.145464
I	H	7	−0.213909	0.213909	0.213909
H	A	8	0.136091	0.136091	0.136091
B	E	9	0.0281122	0.0281122	0.0281122
C	F	10	−0.0198986	0.0198986	0.0198986
E	F	11	0.0365569	Hoboken	0.0365569
F	G	12	−0.0135446	0.0135446	0.0135446
E	I	13	0.0684447	0.0684447	0.0684447

^(a)The stream is moving in the opposite direction of the original flow, as indicated by the negative signs. The final water flow of HCM, NM, and MNM is explained in columns 7–9.