Numerical Check

To check the equations, run through examples of each. Solve for head loss in each pipe individually and then combine to see how the head loss in the equivalent pipe compares for series pipes and for parallel, see how the flow compares. Stick with the SI units (i.e., flow in m³/s, D, L and h in m).

Series

Use Q = 1 m3/s and solve for head loss. Pipe 1 is the dominant pipe.

Comparison between the Sum of the Headlosses from the Two Pipes and the Headloss from the Equivalent Pipe

	Pipe 1	Pipe 2	Resulting, solve for D	Resulting, solve for C,n
Length	100	80	180	180
Diameter	1	0.75	0.88	0.75k, 0.855n
C	100	120	100	71
k	0.002	0.0015	0.002	X
n	0.013	0.012	0.013	0.0197
h (Hazen)	0.21	0.49	0.72	0.72
h (Manning)	0.17	0.55	0.72	0.72
h (Darcy)	0.20	0.58	0.77	X

Parallel

Use head loss = 1 m and solve for Q .

Comparison between the Sum of the Flows from the Two Pipes and the Flow from the Equivalent Pipe

	Pipe 1	Pipe 2	Resulting, solve for D	Resulting, solve for C,n
Length	100	80	100	100
Diameter	1	0.75	0.88	1.18n, 1.21k
C	100	120	100	163
k	0.002	0.0015	0.002	X
n	0.013	0.012	0.013	0.0083
Q (Hazen)	2.31	1.47	3.74	3.77
Q (Manning)	2.40	1.35	3.72	3.75
Q (Darcy)	2.26	1.31	3.55	X