EFFECTS OF VISCOSITY ON EQUATION OF MOTION AND CRITICAL FLOW VELOCITY OF FLUID-CONVEYING PIPE

Considering the non-uniformity of the flow velocitydistribution in a fluid-conveying pipe caused by the viscosity of real fluid,the centrifugal-force term in the equation of motion of the pipe is modifiedin the cases of laminar flow and two modes of turbulent flow. Themodification factors are found to be 1.333, 1.020 and 1.037\sim1.055 forlaminar flow in circular pipe, turbulent flow in smooth circular pipe andturbulent flow in rough circular pipe, respectively. The critical flowvelocities for divergence in the above-mentioned three cases are found to be13.4\%, 1.0\% and 1.8\%\sim2.6\%, respectively, lower than thosefor ideal fluid flow. The effects of fluid viscosity on the equation of motion and thecritical flow velocity of fluid-conveying pipe are explicitly relatedto the flow mode only. The viscosity coefficient plays an implicit role viaReynolds number, which determines the flow mode.