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Abstract
The Moody Diagram is widely used to determine the friction factor for fluid flow in pipes. The diagram combines the effects of Reynolds number and relative roughness to determine the friction factor. The relationship is highly non-linear and appears to have a complex interaction between viscous and boundary roughness effects. The Moody Diagram is based on predictions from an equation developed by Colebrook in 1939. The relationship requires an iteration process to make predictions. While empirical relationships have been developed that provide good predictions without an iteration process, no one has fully explained the cause for the observed results. The objective of this paper is to present a logical development for prediction of the friction factor. An equation has been developed that models the summed effect of both the laminar sublayer and the boundary roughness on the fluid profile and the resulting friction factor for pipes. The new equation does not require an iteration procedure to obtain values for the friction factor. Predicted results match well with values generated from Colebrook’s work that is expressed in the Moody Diagram. Predictions are within one percent of Colebrook values and generally less than 0.3 percent error from his values. The development provides insight to how processes operating at the boundary cause the friction factor to change.
Highlights
Many people have contributed to understanding and describing fluid flow
The diagram combines the effects of Reynolds number and relative roughness to determine the friction factor
The objective of this paper is to present a logical development for prediction of the friction factor
Summary
Many people have contributed to understanding and describing fluid flow. The association of velocity, V, diameter, d, density, ρ, and viscosity, μ, to form the dimensionless term, Vdρ/μ, known as the Reynolds number was a major contribution in relating friction to fluid properties, especially for laminar flow [1]. A subsequent major development was the concept of a mixing length for tur-. A. McEnery 220 bulent flow by Prandtl (1926) [2]. McEnery 220 bulent flow by Prandtl (1926) [2] Building on this concept, an equation to describe the velocity distribution in turbulent flow can be developed
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