Field measurements carried out in recent years have revealed that the pressure drop over a borehole during drilling of a slim oil well can depend significantly on the rotational speed of the drill pipe. This paper seeks to explain this phenomenon through experimental, analytical and numerical studies of the laminar flow of a Newtonian liquid in the radial, tangential and axial directions between two eccentric cylinders, the innter one of which is rotating. Special attention is paid to the inertial forces in the liquid caused by the rotation and the eccentricity of the inner cylinder. After reviewing the results of small-scale experiments that confirm the phenomenon's dependence on both the rotation and the eccentricity of the inner cylinder, a perturbation calculation is carried out in which, in the zeroth-order approximation, the inertial forces are neglected. Then first- and second-order corrections due to the effect of inertia are derived. In first-order approximation there is no correction for the axial pressure drop, because of the symmetry of the flow field. However, in second-order approximation a correction for the pressure drop exists, which depends on the eccentricity, the width of the gap between the inner- and the outer cylinder and the rotational speed. The results of the calculation are of limited validity; for larger values of the inertial forces still higher-order perturbation terms may no longer be neglected. However, the calculation of higher-order terms is very complicated. Therefore, also numerical calculations based on the full flow equations have been carried out. The results have been compared with some of the results of the perturbation calculation; a good agreement was found. The numerical simulations confirm, that for large values of the inertial forces the axial pressure drop can depend significantly on the rotational speed of the inner cylinder.
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