Study of shear stress in laminar pipe flow using entropy concept

In fluid mechanics, the shear stress is calculated from the frictional force caused by viscosity and fluctuating velocity. Shear stress equations are used widely because of their simplicity. On the other hand, they have a critical limitation of requiring an energy gradient, which is generally difficult to estimate in practice. In particular, measuring the shear stress and velocity gradient on the boundary layer is difficult. The point velocity throughout the entire cross section is needed to calculate the velocity gradient. This study proposes the shear stress distribution equations for laminar flow based on entropy theory using the mean velocity and entropy coefficient. The proposed equations were compared with the measured shear stress distribution using Nikuradse’s data. The results revealed a correlation coefficient of approximately 0.99, indicating that the proposed method fits the Nikuradse’s data. Therefore, the shear stress distribution can be estimated easily and accurately using the proposed equations, which can be used in future for the management and design of a water pipeline.