In drilling processes, the rheological properties pointed to the nature of the run-off and the composition of the drilling mud. Drilling mud performance can be assessed for solving the problems of the hole cleaning, fluid management, and hydraulics controls. The rheology factors are typically termed through the following parameters: Yield Point (Yp) and Plastic Viscosity (μp). The relation of (YP/ μp) is used for measuring of levelling for flow. High YP/ μp percentages are responsible for well cuttings transportation through laminar flow. The adequate values of (YP/ μp) are between 0 to 1 for the rheological models which used in drilling. This is what appeared in most of the models that were used in this study. The pressure loss is a gathering of numerous issues for example rheology of mud), flow regime and the well geometry. An artificial neural network (ANN) that used in this effort is an accurate or computational model stimulated by using JMP software. The aim of this study is to find out the effect of rheological models on the hydraulic system and to use the artificial neural network to simulate the parameters that were used as emotional parameters and then find an equation containing the parameters μp, Yp and P Yp/ μp to calculate the pressure losses in a hydraulic system. Data for 7 intermediate casing wells with 12.25" hole size and 95/8" intermediate casing size are taken from the southern Iraq field used for the above purpose. Then compare the result with common equations used to calculate pressure losses in a hydraulic system. Also, we calculate the optimum flow by the maximum impact force method and then offset in Equation obtained by (Joint Marketing Program) JMP software. Finally, the equation that was found to calculate pressure losses instead of using common hydraulic equations with long calculations gave very close results with less calculation.