Using Maximum Entropy To Develop Explicit Formulae For Friction Factor Calculation In Pipe Flow
Free (open access)
251 - 261
V. E. M. G. Diniz, P. A. Souza & A. G. Moraes
This paper uses the maximum entropy model to develop explicit formulae to calculate the friction factor for three flow regimes present in the Moody Diagram without iterations for four different problems. The developed formulae calculate the friction factors for the critical point flows, for the smooth turbulent flows and for the laminar flows. The development of the friction factor formulae is based on the maximum entropy model. This development can be regarded as a conceptual model, but not completely, because of the relationship between the Reynolds number (Re) and the entropy parameter (M) determined by curve fittings accomplished with accurate experimental data. The developed friction factors formulae can be used to calculate the discharges, head losses and diameters of pipes for the steady state and for the extended period simulation. It is concluded that the developed formulae to calculate the discharges, the head losses and the diameters are correct and have the potential to be also used in real hydraulic networks. It is also concluded that the developed formulae made easier the calculation of the friction factor for the three flow regimes. Keywords: maximum entropy, friction factor calculation, four different problems, steady state, pipe flow, moody diagram.
maximum entropy, friction factor calculation, four different problems, steady state, pipe flow, moody diagram