Pipe Network Analysis 12’’- 1500’ 10’’- 3500’ 8’’- 1000’ 6’’- 1000’ 12’’- 3000’ 3.34 cfs 1.11 cfs 4.45 cfs Junction 3 Junction 4 Junction 2 Junction Figure 1: A Small Pipe Network

12’’- 1500’ 10’’- 3500’ 8’’- 1000’ 6’’- 1000’ 12’’- 3000’ 3.34 cfs 1.11 cfs 4.45 cfs Junction 3 Junction 4 Junction 2 Junction Figure 1: A Small Pipe Network F1F2F3F4F1F2F3F4

10’’- 3500’ 12’’- 1500’ 8’’- 1000’ 6’’- 1000’ 12’’- 3000’ 3.34 cfs 1.11 cfs 4.45 cfs Junction 3 Junction 4 Junction 2 Junction Figure 2: A Small Pipe Network Loops Loop 1 Loop 2

Dimensional coefficients D (pipe diameter)L (pipe length)C K (dimensional constant) Feet 4.73 InchesFeet8.56 X 10 5 Meters Some typical values of roughness coefficient C HW MaterialC HW PVC150 Very Smooth Pipe140 Cement-Lined Ductile Iron140 New Cast Iron or Welded Steel130 Wood, Concrete120 Clay or New Riveted Steel110 Old Cast Iron, Brick100 Badly Corroded Cast Iron80

10’’- 3500’ 12’’- 1500’ 8’’- 1000’ 6’’- 1000’ 12’’- 3000’ 3.34 cfs 1.11 cfs 4.45 cfs Junction 3 Junction 4 Junction 2 Junction Loop 1 Loop 2

10’’- 3500’ 12’’- 1500’ 8’’- 1000’ 6’’- 1000’ 12’’- 3000’ 3.34 cfs 1.11 cfs 4.45 cfs Junction 3 Junction 4 Junction 2 Junction Loop 1 Loop 2

Root sought 0xnxn x y Newton’s Method 1.Guess a first approximation to a root of the equation 2.Use the first approximation to get a second, the second to get a third, and so on, using the formula

F1F1 F2F2 F3F3 F4F4 F5F5

First Iteration MathCAD

Second Iteration MathCAD

Third Iteration MathCAD

Fourth Iteration MathCAD

Fifth Iteration MathCAD

Sixth Iteration MathCAD

Seventh Iteration MathCAD