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ALL ABOUT AIR series White Paper #28 Down the Tube © Tom Kreher
Someone said, “When your only tool is a hammer every problem looks like a nail.” You might throw up your hands and say, “Here he comes again with that same darn formula.” If you don’t, you may need to be more critical and less accepting in your thinking. An instruction about the amount of flow that would produce a 10% pressure drop of compressed air in 100 feet of schedule 40 pipe stated a common equation based on based on the Darcy or Harris formula. The next statement tripped the BS-amometer. In essence it said that for 200 feet double the pressure calculated for 100 feet. It follows that starting with 100 PSIG and the flow that would cause a 10 PSIG pressure drop in 100 feet that in 1,000 feet the pressure drop would be 100%. If the reader interpreted this statement of double the pressure drop for an additional 100 feet of pipe would the pressure drop double at 200 feet and again at 300 feet and again at 400 feet for an 80 PSI drop at 400 feet? The best way to illustrate the problem here is use a monetary example to compare simple interest to compound interest. Some equations taught and used in error for pneumatic calculations based on a linear or additive approach. In the real world these changes are compounded. Resistance to compressed air flow in plumbing causes a pressure drop. With lower pressure the loss is aggravated. The loss in two feet is not the same as the loss in one foot times two. Back to our old friend the decay formula or die away curve, P1 = P0 (e^-KL). The constant of pressure loss, K would be found by experiments and L represents the length. This concept and utilization of Newton’s law of cooling formula is treated respectfully by Silvanus P. Thompson in his book, “Calculus made easy” and as stated, “Is very important in physical science.” The formulas we have proposed for flow and pressure decay are also somewhat simplistic. At some point we must deal with the change in resistance to flow when the velocity of the compressed air drops below 1200 feet per minute and the flow become laminar. The sonic choke at pressure ratios of 53% or less is another factor to consider. For starters, the formulas for die away and organic growth are technically correct and significantly more accurate than linear, additive techniques. For tubing it is simple to start with 100 feet of tubing and record the time required to vacate a known volume. Then cut the tubing progressively shorter. We have only tested ¼ “ OD Nylon. We used 100’, 75’, 50’, 25’, 20’, 15’, 10’, 5’, 4’, 3’, 2’, 1’, 6”, 4”, 2”, and 1”. The number of test points may be reduced if a consistent pattern emerges when testing other tube sizes. The entrance factor is significant in addition to the friction resistance. From the time in seconds to decay the volume to 37% of the initial pressure we established the flow with each length of tubing. By using the top 63% of the pressure we are operating in sonic, turbulent flow. These results are consistent for the most common usage of flow through tubing above the laminar threshold. With minor discrepancy, possibly from the entrance factor the flow or resistance to flow for this tubing follows the die away curve. I’m off for Alaska. If the bear wins you are on your own.