Accurate estimation of frictional pressure loss in an annulus is crucial for selecting appropriate pump systems, determining horsepower requirements, and controlling hole cleaning.Generally, when calculating the friction factor, the temperature of the fluid and the rotation of the inner pipe are not considered, which can lead to errors in estimating the pressure difference in the annulus.To ensure accurate pressure drop calculations, the effects of temperature and inner pipe rotation, along with other parameters, were included.An extensive exptl. study was conducted at Izmir Katip Celebi University's Flow Loop using 2 CM-cellulose (CMC) solutions, across various fluid velocities, fluid temperatures, diameter ratios, and inner pipe rotation speeds.A dimensional anal. was performed to identify the parameters that affect friction factors in the annulus.Finally, friction factor equations were developed based on the exptl. data using optimization algorithms such as interior point (fmincon), genetic, minimax, and simulated annealing.The predictions from all the algorithms tested in the study closely matched the exptl. results; however, the interior point algorithm (fmincon) provided the best performance, with an average absolute percentage error of 9.4%.