3. 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 1 1 2 4 3 5 Figure 1: A Small Pipe Network

4. 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 1 1 2 4 3 5 Figure 1: A Small Pipe Network F1F2F3F4F1F2F3F4

5. 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 1 1 2 4 3 5 Figure 2: A Small Pipe Network Loops Loop 1 Loop 2

6. Dimensional coefficients D (pipe diameter)L (pipe length)C K (dimensional constant) Feet 4.73 InchesFeet8.56 X 10 5 Meters 10.67 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

7. 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 1 1 2 4 3 5 Loop 1 Loop 2

8. 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 1 1 2 4 3 5 Loop 1 Loop 2

9. 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

10. F1F1 F2F2 F3F3 F4F4 F5F5

13. First Iteration MathCAD

14. Second Iteration MathCAD

15. Third Iteration MathCAD

16. Fourth Iteration MathCAD

17. Fifth Iteration MathCAD

18. Sixth Iteration MathCAD

19. Seventh Iteration MathCAD