This paper provides detailed information in three different areas of flow equation usage. First, a step by step development of the fundamental flow equation is included. factor equations and their relation to the Moody Diagram. This includes the diameter dependent, Reynold's Number dependent and the recently developed explicit friction factor equations. considerations of using the Fundamental Flowequation. ranges, sensitivity, and efficiency factor usage are included.

I. Introduction

As Computers became more prevalent in the workplace, many of us lost touch with the origins of various formulas or software packages. Because of the flow equation's implicit nature, variations were developed. flow situations, and were incorporated into the computer world. Too often, a program is used without knowing which flow formula variation is inccrporated into the program, or what assumptions are contained within a particular formula. For this reason, a review of the General Flow equation is considered desirable. These variations were used as approximations for differing The myriad of flow formulas are all related to the General Flow equation. technology. For example, as higher yield strength pipe was manufactured, system operated at higher pressures and flows. This changed the commonly used friction factor relationships, thereby requiring a new adaptation of the General Flow equation. A number of the equations were developed when computers were not available, these equations were great time savers because a slide rule could be used, rather than using tables. The original assumptions and subtleties of these early variations are not commonly known among those of the computer age. Most were developed to fit the existing pipe or computational The Moody diagram, as derived by using Colebi~ok's implicit friction factor equation, is considered the industry standard for determining friction factors. Today's desktop computers have the capability of handling the iterative solutions required by Colebrook's equation. Therefore, pipe system models should use the General Flow equation with a Colebrook Friction factor. To reduce computing time or cost, some explicit approximations of the Colebrook equation provide a good correlation over the entire range of the Moody diagram. These equations include Chen's, Shacham's and others docmented later easier.

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