Analysis of frequency-dependent friction in transient pipe-flow using non-integer order derivative models

The design of hydraulic transmission lines for control and actuation requires accurate knowledge of their dynamic response. Some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this paper an efficient procedure is developed for simulating frequency-dependent friction in transient laminar liquid flow. This is investigated by means of a bi-dimensional approach and the laminar flow frequency-dependent friction is modelled using non-integer order derivatives, which may consistently improve the accuracy of the simulated line response in comparison with more traditional newtonian models. The results of the theoretical analysis are compared with experimental data obtained from frequency-response tests, and discussed in detail.