Pipe Network Analysis

1. Pipe Network Analysis by Marc Pitman (director) and Andrey Korchmar (secretary)

2. 1.11 cfs Junction 2 Junction 1 12’’- 3000’ 1 4.45 cfs 6’’- 1000’ 3 4 8’’- 1000’ 10’’- 3500’ 2 12’’- 1500’ 5 3.34 cfs Junction 4 Junction 3 Figure 1: A Small Pipe Network Pipe Network Analysis

3. 1.11 cfs Junction 2 Junction 1 12’’- 3000’ 1 4.45 cfs 6’’- 1000’ 3 4 8’’- 1000’ 10’’- 3500’ 2 12’’- 1500’ 5 3.34 cfs Junction 4 Junction 3 Figure 1: A Small Pipe Network F1 F2 F3 F4

4. 1.11 cfs Junction 2 Junction 1 12’’- 3000’ 1 4.45 cfs Loop 1 3 6’’- 1000’ 4 8’’- 1000’ 2 Loop 2 10’’- 3500’ 12’’- 1500’ 5 3.34 cfs Junction 4 Junction 3 Figure 2: A Small Pipe Network Loops

6. Junction 2 1.11 cfs Junction 1 12’’- 3000’ 1 4.45 cfs Loop 1 3 6’’- 1000’ 4 8’’- 1000’ 2 Loop 2 10’’- 3500’ 12’’- 1500’ 5 3.34 cfs Junction 4 Junction 3

7. Junction 2 1.11 cfs Junction 1 12’’- 3000’ 1 4.45 cfs Loop 1 3 6’’- 1000’ 4 8’’- 1000’ 2 Loop 2 10’’- 3500’ 12’’- 1500’ 5 3.34 cfs Junction 4 Junction 3

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

12. First Iteration MathCAD

13. Second Iteration MathCAD

14. Third Iteration MathCAD

15. Fourth Iteration MathCAD

16. Fifth Iteration MathCAD

17. Sixth Iteration MathCAD

18. Seventh Iteration MathCAD