Considering the non-uniformity of the flow velocity distribution in fluid-conveying pipes caused by the viscosity of real fluids, the centrifugal force term in the equation of motion of the pipe is modified for laminar and turbulent flow profiles. The flow-profile-modification factors are found to be 1.333, 1.015-1.040 and 1.035-1.055 for laminar flow in circular pipes, turbulent flow in smooth-wall circular pipes and turbulent flow in rough-wall circular pipes, respectively. The critical flow velocities for divergence in the above-mentioned th...