The objective of this Recommended Practice (RP) is to provide a basic understanding of and guidance about drilling fluid rheology and hydraulics@ and their application to drilling operations.The target audience for this RP covers both the office and wellsite engineer. The complexity of the equations used is such that a competent engineer can use a simple spreadsheet program to conduct the analyses. Given that the equations used herein are constrained by the spreadsheet limitation@ more advanced numerical solutions containing multiple subroutines and macros are not offered. This limitation does not mean that only the results given by the spreadsheet methods are valid engineering solutions.Rheology is the study of the deformation and flow of matter. Drilling fluid hydraulics pertains to both laminar and turbulent flow regimes. The methods for the calculations used herein take into account the effects of temperature and pressure on the rheology and density of the drilling fluid.For this RP@ rheology is the study of flow characteristics of a drilling fluid and how these characteristics affect movement of the fluid. Specific measurements are made on a fluid to determine rheological parameters under a variety of conditions. From this information the circulating system can be designed or evaluated regarding how it will accomplish certain desired objectives.The purpose for updating the existing Recommended Practice@ last published in May 2003@ is to make the work more applicable to the complex wells that are now commonly drilled. These include: High-Temperature/High-Pressure (HTHP)@ Extended-Reach Drilling (ERD)@ and High-Angle Wells (HAW). Drilling fluid rheology is important in the following determinations:a) calculating frictional pressure losses in pipes and annulib) determining equivalent circulating density of the drilling fluid under downhole conditionsc) determining flow regimes in the annulusd) estimating hole-cleaning efficiencye) estimating swab/surge pressuresf) optimizing the drilling fluid circulating system for improved drilling efficiencyThe discussion of rheology in this RP is limited to single-phase liquid flow. Some commonly used concepts pertinent to rheology and flow are presented. Mathematical models relating shear stress to shear rate and formulas for estimating pressure losses@ equivalent circulating densities and hole cleaning are included.The conventional U.S. Customary (USC) unit system is used in this Recommended Practice.Conversion factors and examples are included for all calculations so that USC units can be readily converted to SI units. Where units are not specified@ as in the development of equations@ any consistent system of units may be used.The concepts of viscosity@ shear stress@ and shear rate are very important in understanding the flow characteristics of a fluid. The measurement of these properties allows a mathematical description of circulating fluid flow. The rheological properties of a drilling fluid directly affect its flow characteristics and all hydraulic calculations. They must be controlled for the fluid to perform its various functions.This revised document includes some example calculations to illustrate how the equations contained within the document can be used to model a hypothetical well. Due to space constraints@ it has not been possible to include a stepby- step procedure for every case. However@ the final results should serve as a benchmark if the user wishes to replicate the given cases.