8 A Collection of Handy Hydraulic Formulas: Based on an Industry-Standard Reference for Pressure Drop Calculations, Incompressible Fluid Flow in Piping and Ducts—Crane Technical Paper No. 410
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Crane Technical Paper No. 410 is the reference most used by facility and utility design engineers, plant engineers, and piping/HVAC consultants for mechanical (pressure) piping systems analysis.
Commercial software for PCs is available for performing the number-crunching for most parts of the Crane reference. I wrote my own program back in the early 1980s, combining the Crane differential pressure — liquid flowrate relationships and fitting loss data, Bernoulli's equation for solving system curve analysis, Colebrook's equation for calculating friction factor f, and miscellaneous adjunct utilities. I mention this because part of this topic includes a formula derivation made by myself, and it references “LIQUIDFLOW,” which is the name I gave my program. I no longer make that program available to others since it runs under an MS-DOS shell only, which few people understand any longer. Modern commercial software, such as commercially available applications of the Crane manual, is written for MS-Windows.
I believe strongly that it is dangerous and unprofessional to use engineering software without having the ability to check its output via hand calculations. To that end, in this topic I have summarized some of the most useful relationships from Crane Technical Paper No. 410, plus the additional one derived by myself (equivalent loss coefficient for flow across parallel pipe branches.) These are noted or illustrated where helpful.