The radial basis function neural network (RBFNN) simulation has been designed to simulate and predict the mean velocity of capillary flow in transition from laminar to turbulent flow and the root-mean-square vorticity as a function of wall-normal position at different values of Reynolds number. The system was trained on the available data of the two cases. Therefore, we designed the system to work in automatic way for finding the best network that has the ability to have the best test and prediction. The proposed system shows an excellent agreement with that of an experimental data in these cases. The technique has been also designed to simulate the other distributions not presented in the training set and predicted them with effective matching.