Pressure Drop for Fully Developed Turbulent Flow in Circular and Noncircular Ducts

The objective of this paper is to furnish the engineer with a simple and convenient means of estimating frictional pressure drop in ducts and the original physical behavior can be clearly reflected. Fully developed turbulent flow frictional pressure drop in noncircular ducts is examined. Simple models are proposed to predict the frictional pressure drop in smooth and rough noncircular channels. Through the selection of a novel characteristic length scale, the square root of the cross-sectional area, the effect of duct shape has been minimized. The proposed models have an accuracy of 6% for most common duct shapes of engineering practice and can be used to predict pressure drop of fully developed turbulent flow in noncircular ducts. It is found that the hydraulic diameter is not the appropriate length scale to use in defining the Reynolds number to ensure similarity between the circular and noncircular ducts. By using the Reynolds number based on the square root of the cross-sectional area, it is demonstrated that the circular tube relations may be applied to noncircular ducts eliminating large errors in estimation of pressure drop. The square root of the cross-sectional area is an appropriate characteristic dimension applicable to most duct geometries. The dimensionless mean wall shear stress is a desirable dimensionless parameter to describe fluid flow physical behavior so that fluid flow problems can be solved in the simple and direct manner. The dimensionless mean wall shear stress is presented graphically and appears more general and reasonable to reflect the fluid flow physical behavior than the traditional Moody diagram.