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The purpose of this paper is to present a new friction factor equation for practical use, including fluid temperature, pipe diameter ratio and inner pipe rotation effects.

A friction factor relationship is developed by applying Buckingham’s Theorem of dimensional analysis. Then, the formula is calibrated using experimental data conducted at Izmir Katip Celebi University flow loop. Moreover, the effects of fluid temperature, inner pipe rotation and pipe diameter ratio on friction factor are investigated experimentally.

Satisfactory agreements are obtained between proposed formula and experiments. The experimental results indicate that major variable parameters affecting friction factor is Reynolds number. Pipe rotation has negligible effect on friction factor at high Reynolds number. Prandtl number is one of the important parameters affecting the friction factor. Moreover, as the pipe diameter ratio is decreased, friction factor increases.

Determining fluid behavior of fluids under high temperature is especially important for deep wells during drilling. Temperature drastically changes fluid properties and flow characteristics in wells. These changes have a remarkable effect on pressure losses. However, since the temperature is considered constant in the calculation of the pressure loss, problems can be encountered in most systems. Friction factor is one of the important parameters for determining pressure loss in closed conduits. The originality of this work is to propose a new friction factor equation for practical use, including fluid temperature, pipe diameter ratio and inner pipe rotation effects.

The purpose of this paper is to solve Navier–Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms.

A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one.

The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop.

The originality of this work is that Navier–Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.