Hydraulics play an important role in many oil field operations. Currently available hydraulic models do not allow a prediction of the hydraulics behavior of a well during drilling operations adequately. They are either too simple or too sophisticated in terms of computing power required. Boundary conditions show a probabilistic behavior, e.g. exact hole geometry, down hole mud pump properties are not exactly known. In the first part of this work two different hydraulics modelling packages are presented and with these two programs the hydraulic pressure drop is calculated for eleven scenarios. These calculated values are compared with the actual values of the measured real-time pump pressure. The results of this comparison are very unreliable: the average error spreads from under 1% up to 53%. The second part of the thesis presents a new data driven approach using neural networks. These networks are based on the neural elements of the human brain, which means that these artificial neural networks are able to recognize patterns and generalize the patterns of the past into actions of the future. Some examples are presented in which a neural network is trained with data from Well A. These trained network is then used to simulate the pressure drop of a second Well B accurately. The necessary steps and the problems arising are described in detail.