Supporting Calculations
The following calculations are state-of-the-art calculations and are way beyond the scope of this Op Ed. However, these calculations are provided as technical proof of statements in this Op Ed.
Based on decades of experience, and invented water hammer theory, the water hammer event at the Shaw's Creek water plant was a combined slug flow and trapped air water hammer. Based on experience, my engineering judgement is that water hammer pressure calculations are within 10 to 15 percent.
Slug flow and air pocket water hammer effects
The slug flow is described by the classic Joukowski equation ("Fluid Mechanics, Water Hammer, Dynamic Stresses, and Piping Design", click here). During normal operations, the present variable frequency drive pump startup times of 45 seconds are woefully inadequate to prevent slug flow water hammers, which explain many ongoing water hammer water main breaks in the 455 miles of water mains in Aiken, following power outages during subsequent pump restarts. For a Savannah River Site piping system, the ramp-up time for a 910-feet-long piping systems was required to be 3 minutes to control water hammer pressures near 1000 ponds per square inch.
When the valves near the plant were opened, trapped air was forced to the high point in the system, and a slug flow then impacted that trapped air. Ductile iron, Class 51, was assumed since FOIA requested information was withheld from Aiken. Runout conditions were assumed from the pump curves shown in Figure 3, where the pump curves - that were falsely claimed to be unavailable in response to an FOIA request - were included within a different FOIA requested report. As published in earlier research, assuming runout conditions is appropriate near a pump for slug flow water hammers ("Water Hammer in an Open End Pipe", click here).
Water hammer calculation results
Calculation results are presented in Figure 4, where definitions are provided in references. Note that Aiken refused to provide appropriate data that was requested in FOIA requests for the 'Brown Water Fiasco' and water hammer pressure estimates were limited by such refusals. There are three different sets of calculations.
The first set of calculation estimated the maximum possible water hammer pressures that occur due to frequent Aiken power outages - perhaps as often as monthly - and subsequent pump restarts. Note that Dominion Electric refused to provide appropriate power outage data. These pressures explain routine water main breaks found after power outages.
The second set of calculations estimated the maximum possible pressure if all three pumps had been restarted during the 'Brown Water Fiasco' Note that water hammer piping stresses could have cracked water mains near Shaw's Creek, since the ultimate tensile strength could have been exceeded. Results using a DLF = 2 is presented, where the DLF could have been as low as 1, but such a low DLF was improbable. In other words, if three pumps were used by Aiken during restart, cracks in the water main near Shaw's Creek are a reasonable possibility.
Again, Aiken refused to provide confirmatory information, which was requested under authority of the FOIA. If multiple pumps were used to restart the system to cause the 'Brown Water Fiasco', and water mains lie below Highway 1, leak inspections may be prudent, since under-road leaks have been known to create sink holes to collapse roads.
The third set of calculations estimated the maximum possible water hammer pressure for restarting the system with only the largest 600 horsepower pump in service, which was possible. Stresses would have been near yield and above the fatigue limit, where permanent fatigue damage would have occurred. Once again, Aiken refused to provide confirmatory information, which was requested under authority of the FOIA.
Proven fact: Water hammer findings = Water hammers break mains
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