1. CEE 410 Hydraulic Engineering - Lecture 15 -Unsteady Flow and Surge in Piping Networks Mark Oleinik, P.E.

2. Unsteady Flow and Surge in Piping Networks Today Takeaway(s), ◦ What is Unsteady Flow and Surge ◦ What Causes Unsteady Flow and Surge ◦ How is it calculated. ◦ What can be done about it.

3. Unsteady Flow and Surge in Piping Networks “Andrew – attached are files containing main break and pressure recordings in our system. They believe that since the new wtp came on line they are getting more main breaks. We would like your help in diagnosing the problem. The one email has a spreadsheet of all main breaks and another spreadsheet of the ones they suspect are related to high peak pressures. See if you can map out the high pressure main breaks to give us a better idea of where they are occurring.” What is Unsteady Flow and Surge

4. Unsteady Flow and Surge in Piping Networks What is Unsteady Flow and Surge “I have located all the main break locations that they gave us which they said were caused by high pressures. See attached maps for locations. In the Southern pdf, I’ve circled a few areas that look to me to have a higher concentration of main breaks that may be worth investigating further in the model and for ground elevations. ”

5. Unsteady Flow and Surge in Piping Networks What is Unsteady Flow and Surge This is Unsteady Flow and Surge

6. Unsteady Flow and Surge in Piping Networks Today Takeaway(s), ◦ What is Unsteady Flow and Surge ◦ What Causes Unsteady Flow and Surge ◦ How is it calculated. ◦ What can be done about it.

7. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge? Eastland Elevated Tank Woodlake Reservoir and Pumping Station Q = 22,000 gpm --------------- 25 miles – 42 inch main ------------------------ Eastland Elevated Tank

8. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge? Eastland Elevated Tank Woodlake Reservoir and Pumping Station Q = 22,000 gpm --------------- 25 miles – 42 inch main --------------- Recall: Conservation of Energy -- Bernoulli’s Equation Conservation of Mass -- Control Volume

9. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge? Let’s look at the pipeline with the elevated tank shutoff valve as a control volume. Q in = Q out = 22,000 gpm = 31.7 mgd = 49 cfs V 42 = 5.1 fps Pump

10. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge Pump Elevated Tank 2 Bernoulli's Equation: V + P + Z = hgl 2g γ (What’s Missing?) _________________________________________________________ hgl _____

11. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge Pump Elevated Tank Now – CLOSE THE VALVE! What Happens Upstream of the Valve? _________________________________________________________ hgl What else do we need to know?

12. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge Pump What else do we need to know? When. Does all flow stop everywhere in the pipe at the same time?

13. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge The flow does not stop simultaneously all along the pipe. The water at the valve must stop. The remainder of the water, all 40,000 tons, continues to flow at 5.1 fps. Flow incrementally and progressively stops, working back to the pump. t = 0

14. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge In each time period t, an increment of the flow compresses. t = 1

15. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge t = 2 In each time period t, an increment of the flow compresses. In each time period, the pipe walls stretch.

16. Unsteady Flow and Surge in Piping Networks What Causes Unsteady Flow and Surge t = 3 In each time period t, an increment of the flow compresses. In each time period, the pipe walls stretch. The compression wave travels at the speed of sound, a, of the liquid.

17. Unsteady Flow and Surge in Piping Networks t = 4 In each time period t, an increment of the flow compresses. In each time period, the pipe walls stretch. The compression wave travels at the speed of sound, a, of the liquid. a can be calculated knowing the liquid and pipe material. a Unsteady Flow and Surge is caused by rapid changes in fluid velocity. What Causes Unsteady Flow and Surge?

18. Unsteady Flow and Surge in Piping Networks Today Takeaway(s), ◦ What is Unsteady Flow and Surge ◦ What Causes Unsteady Flow and Surge ◦ How is it calculated. ◦ What can be done about it.

19. Unsteady Flow and Surge in Piping Networks How is it calculated? Rigid Column Theory – The fluid is incompressible and the pipe walls rigid. Limited application but calculation possible without Computers. Elastic Theory – Fluid compressibility and flexure of pipe walls taken into account. Difficult or impossible to calculate without Computers. We will focus on Elastic Theory.

20. Unsteady Flow and Surge in Piping Networks How is it calculated? Elastic Theory – How to determine a, velocity of the pressure wave. a = E v ρ ____________________________ 1 + E v D ψ E e

21. Unsteady Flow and Surge in Piping Networks How is it calculated? Elastic Theory – How to determine a, velocity of the pressure wave. E v ρ ____________________________ 1 + E v D ψ E e a = a = characteristic wave celerity of the liquid E v = bulk modulus of elasticity of the liquid E e = Young’s modulus of elasticity for pipe material ρ = liquid density D = Inside pipe diameter ψ = 1 – u² for pipe anchored along entire length u = Poissions Ratio

22. Unsteady Flow and Surge in Piping Networks How is it calculated? Elastic Theory – How to determine a, velocity of the pressure wave in Lexington. E v ρ ____________________________ 1 + E v D ψ E e a = E v = bulk modulus of elasticity of water (20 ⁰ C) = 45.7 x 10 ⁶ lb/in² E e = Young’s modulus of elasticity for ductile iron = 3.59 x 10 ⁹ lb/in² ρ = density of water (20 ⁰ C) = 1.94 slugs/ft ³ D = Inside pipe diameter = 3.5 ft ψ = 1 – u² for pipe anchored along entire length u = Poissions Ratio for ductile iron pipe = 0.28 a = 3300 fps

23. Unsteady Flow and Surge in Piping Networks How is it calculated? Elastic Theory – Typical Wave Speeds in Ductile Iron and PVC Pipe-

24. Unsteady Flow and Surge in Piping Networks How is it calculated? Elastic Theory – Joukowski Equation 1898 - The pressure increases approximately 100 ft per fps of velocity change. So – In Lexington, V = 5.1 fps Joukowski: P surge = 100 ft x 5.1 fps = 510 ft, 240 psi !! This is a conservative calculation.

25. Unsteady Flow and Surge in Piping Networks How is it calculated? Elastic Theory – Method of Characteristics Solved via computer analyzed using commercial software. Hammer - haestad Methods Surge - KYPipe AFT (Applied Flow Technology) Flowmaster HYTRAN 2.7 (Shareware) Surge Control Equipment Vendors Be Careful!

26. Unsteady Flow and Surge in Piping Networks How is it calculated What do we know? Water mains breaks have increased in frequency since the new WTP has gone on- line. Field monitoring has detected significant pressure spikes, both + and -. Joukowski equation results in a maximum potential surge pressure of 240 psi. The speed of the pressure wave is about 3300 fps. Rapid changes in fluid velocity can cause significant pressure spikes. But, what is Rapid?

27. Unsteady Flow and Surge in Piping Networks All systems have a characteristic distance, L, and characteristic time T. L is the longest path from the source of the surge to a point of wave reflection. In this case it is the elevated tank. T is the time is takes a pressure wave to travel from the source of the surge, to the point of reflection and back to the source. T = 2 L/a How is it calculated

28. Unsteady Flow and Surge in Piping Networks We used the closed valve example to demonstrate the phenomena. No valve slammed shut here. What could have happened here that could have initiated a pressure wave? Eastland Elevated Tank Woodlake Reservoir and Pumping Station Q = 22,000 gpm --------------- 25 miles – 42 inch main --------------- How is it calculated

29. Unsteady Flow and Surge in Piping Networks Correct! Starting and stopping the pump. Starting the pump causes the flow velocity to change from 0 up to 5.1 fps. Obviously this doesn’t happen instantly, like closing a valve. How long does it take? The operator reports the pump is started by a variable frequency drive (VFD). It takes a very long time, 45 seconds, to get up to full speed, so this cannot be the problem, Right? How is it calculated

30. Unsteady Flow and Surge in Piping Networks The characteristic time for this system is: ◦ T = 2L/a = 2*(25 m)*5280/3300 fps = 80 seconds ◦ So, the 45 second pump start time is too short to effectively control pressure surge. ◦ So, how to we keep this water system from coming apart every time the pump is started? How is it calculated

31. Unsteady Flow and Surge in Piping Networks Discharge - GPM Head - Ft Pump Affinity Laws Q varies with speed H varies with speed ² P varies with speed ³ What part of the 45 second ramp time is effective? How is it calculated?

32. Unsteady Flow and Surge in Piping Networks Pump Elevated Tank _________________________________________________________ _____ Correct! 10 Seconds, pressure wave will travel 3300 fps x 10 s = 33,000 ft How is it calculated?

33. Unsteady Flow and Surge in Piping Networks Pump Elevated Tank _____ Correct! 10 Seconds, pressure wave will travel 3300 fps x 10 s = 33,000 ft T = 10 seconds How is it calculated?

34. Unsteady Flow and Surge in Piping Networks Pump Elevated Tank _____ Correct! 10 Seconds, pressure wave will travel 3300 fps x 10 s = 33,000 ft T = 10 + t seconds How is it calculated?

35. Unsteady Flow and Surge in Piping Networks Max hgl = + surge t = 80 seconds = L/a Pump Elevated Tank Static hgl Pressure wave reaches the tank Friction attenuates the surge Elevated tank relieves the pressure surge (why?) Entire line is at maximum surge pressure Elevated tank reflects the pressure wave (why?) How is it calculated?

36. Unsteady Flow and Surge in Piping Networks Max hgl = + surge Pump Elevated Tank Static hgl Min hgl = - surge -t-t t A negative pressure wave then reflects back to the source of the wave. -2t How is it calculated.

37. Unsteady Flow and Surge in Piping Networks Pump Elevated Tank Min hgl = - surge t = 160 seconds = 2L/a=T Pressure wave reaches point of origination Entire line is at its minimum surge pressure Now what happens? How is it calculated?

38. Unsteady Flow and Surge in Piping Networks Max hgl = + surge Pump Elevated Tank Static hgl Steady –state pumping hgl Min hgl = - surge Correct! – Wave continues to bounce back and forth in system until friction dampens it out and system reaches equilibrium at pumping hgl. How is it calculated?

39. Unsteady Flow and Surge in Piping Networks Now – do we see any of these phenomena in our pressure trace? Pump Start? Upsurge? Static P should be about 132 psi? 416 Glenwood = 865 ft msl Pump Stop? Downsurge? Eastland Tank of = 1170 ft msl How is it calculated?

40. Unsteady Flow and Surge in Piping Networks Does field data match theory? How is it calculated?

41. Unsteady Flow and Surge in Piping Networks Theory vs Field Observations. Distribution System Multiple pipe sizes Multiple pipe materials Multiple connections Pipe unknowns Valve and position unknowns Pipe material is not uniform – Gaskets are compressible. Air entrained in water Multiple elevated tanks and wave reflection points. How is it calculated?

42. Unsteady Flow and Surge in Piping Networks Theory vs Field Observations. How is it calculated? New Reports from the Front. Q?

43. Unsteady Flow and Surge in Piping Networks Theory vs Field Observations. How is it calculated? New Reports from the Front. Δ Q = 5 mgd! So ∆ V = 0.8 fps ∆ H = 80 ft, 35 psi

44. Unsteady Flow and Surge in Piping Networks Today Takeaway(s), ◦ What is Unsteady Flow and Surge ◦ What Causes Unsteady Flow and Surge ◦ How is it calculated. ◦ What can be done about it.

45. Unsteady Flow and Surge in Piping Networks ◦ Velocity Control ◦ Pipe Material ◦ Pressure Relief Valves ◦ Surge Tanks ◦ Air-Vacuum Valves ◦ Surge Anticipation Valves What can be done about it.

46. Unsteady Flow and Surge in Piping Networks ◦ Velocity Control  Larger Diameter Pipe  Variable Speed Drives  Motor Controlled Discharge Valves Control Measures- Interior booster pumps. What can be done about it.

47. Unsteady Flow and Surge in Piping Networks ◦ Pipe Material – Use less rigid pipe. What can be done about it.

48. Unsteady Flow and Surge in Piping Networks ◦ Pressure Relief Valves What can be done about it.

49. Unsteady Flow and Surge in Piping Networks Surge Tanks What’s wrong with this picture? What can be done about it.

50. Unsteady Flow and Surge in Piping Networks Pump Elevated Tank Revised Pipeline Profile hgl As hgl drops below pipe profile, P goes negative- Pipe can collapse, If P < -14 psi a vapor cavity can form When hgl recovers vapor cavity can collapse, causing a pressure surge- What can be done about it.

51. Unsteady Flow and Surge in Piping Networks Pump Elevated Tank Air Vacuum Valve at high point opens, allows air in, avoids vapor cavity and potential pipe collapse. Revised Pipeline Profile hgl What can be done about it.

52. Unsteady Flow and Surge in Piping Networks ◦ Surge Anticipation Valves Opens prior to arrival of pressure wave and releases it as it arrives. What can be done about it. ELECTRO-HYDRAULIC SERIES 118Electrical power connection to pumping system for opening on loss or power or on a pressure switch low pressure signal. Valve closes after (adjustable) predetermined time on power failure or low pressure opening. Hydraulic, pilot operated, high pressure relief opening. Available with Surge Commander electronics package (Model 118-4). OCV

53. Unsteady Flow and Surge in Piping Networks Today Takeaway(s), ◦ What is Unsteady Flow and Surge ◦ What Causes Unsteady Flow and Surge ◦ How is it calculated. ◦ What can be done about it. Remember This - Surge Happens! You don’t have to do precise calculations – Understand the potential causes of surge and water hammer and incorporate flexibility into your design to prevent it and, if that system fails, relieve it. Ask “old guys” for help and support. Sleep at night rule -

54. Pump Elevated Tank

55. Pump Elevated Tank

57. Unsteady Flow and Surge in Piping Networks