Velocity Distribution in the 90-degree Bend based on the Probability and Entropy Concept

Document Type: Original Article


1 Ph.D. Student, Department of Water Eng., Faculty of Civil Eng., University of Tabriz

2 Professor, Department of Water Eng., Faculty of Civil Eng., University of Tabriz


Practical concept of velocity distribution of pressure flow in the bends is interesting and hence, the professional engineering design has been investigated in the current study. This paper shows that velocity distribution in the bends can be analyzed in terms of the probability distributions. The concept of entropy based on the probability is an applied and new approach to achieve velocity profiles in bends, presented by the probability distribution and Tsallis entropy maximization under the importing constraints. Due to the lack of a specific equation of velocity distribution in the bends, the particular equation in the various band sections was obtained through the numerical simulation of three dimensional flow in the 90-degree bend (via Fluent). In this simulation, flow regime was laminar and the Reynolds number was in the range of 100 to 2000. Then, for m=2, the velocity distribution function was obtained. Studies showed that the proposed model for the mentioned range of Reynolds numbers is in a good agreement with other study results. The calculated error values indicated a reasonable accuracy. The model can directly calculate the velocity at each point of the spatial position. The calculated values were also compared with the results obtained from the velocity distribution based on the Shannon entropy. The results showed a reliable estimate of the velocity profiles.