Experimental determination of time lag due to phase shift on a flexible pipe conveying fluid

A finite element model of a flexible tube conveying fluid is developed in MATLAB© based on the principle of virtual work, using a three-node isoparametric beam element. Finite element equations are formulated by applying Galerkin technique on the coupled equations of pipe conveying fluid. The present element developed is capable to model three-dimensional flexible tubes by including curved geometry, effects of damping, velocity and gyroscopic effects. The external excitation applied at the middle of the tube in the lateral direction produced a time lag between the lateral responses, which were measured at two equidistant points from the excitation point. This is due to the Coriolis effect, and the same is simulated using the developed code. An experiment, supported with a robust error analysis, is also conducted on a straight polyurethane tube conveying water, subjected to a sinusoidal excitation at the center between the clamped supports. The measured time responses are compared with the numerical values predicted by the code. The time lags for both cases are obtained from the temporal shift along the time axis, between the zero crossing points of the time-response curves. The results obtained agreed well. The code can be used to predict the time lag, which is correlated to the mass flow rate. The proposed method will help to design Coriolis mass flow meters for existing pipelines, without altering the system.