A well-known cornerstone in fluid mechanics is the equations that relate the friction factor to the Reynolds number obtained from the measurements in cylindrical cross-sectional tubes. The extension of these equations...A well-known cornerstone in fluid mechanics is the equations that relate the friction factor to the Reynolds number obtained from the measurements in cylindrical cross-sectional tubes. The extension of these equations to different geometries failed to give reliable results. The introduction of the Hydraulic Diameter has fixed this issue particularly for the square ducts. However, for non-symmetric flows, as in concentric annuli, the discrepancies were unacceptable. Several attempts have been made to fix these problems with finally the introduction of a new concept like, “Laminar Equivalent Hydraulic Diameter” or “Efficient Hydraulic Diameter” provided satisfactory results. This approach seems to have fixed the problem and hence has been widely accepted. Nevertheless, it is based on a non-robust theoretical argument. In the present paper, it has been demonstrated that the solely use of the “Hydraulic Diameter” concept is insufficient to describe non-symmetric flows as in concentric annuli. It appears the need to use the Z axis component of the skew driving force for the laminar flow and the parameter <span style="white-space:nowrap;">λ</span> for the turbulent one. At the same time, instead, it has been shown that in the case of flow in square and rectangular ducts, the “Hydraulic Diameter” is sufficient to describe it. In this case, the flow is practically symmetric. Moreover, several new straightforward equations are provided, which simplify a lot dealing with non-cylindrical cross-sectional conduits. In doing so, the concept of “Eigenvectors-Eigenvalues” has been implemented. This theoretical approach could help to simplify other non-symmetric cases in fluid dynamics. To mention, “Flow past immersed non-symmetric bodies”, “Flow in curved conduits” etc.展开更多
文摘A well-known cornerstone in fluid mechanics is the equations that relate the friction factor to the Reynolds number obtained from the measurements in cylindrical cross-sectional tubes. The extension of these equations to different geometries failed to give reliable results. The introduction of the Hydraulic Diameter has fixed this issue particularly for the square ducts. However, for non-symmetric flows, as in concentric annuli, the discrepancies were unacceptable. Several attempts have been made to fix these problems with finally the introduction of a new concept like, “Laminar Equivalent Hydraulic Diameter” or “Efficient Hydraulic Diameter” provided satisfactory results. This approach seems to have fixed the problem and hence has been widely accepted. Nevertheless, it is based on a non-robust theoretical argument. In the present paper, it has been demonstrated that the solely use of the “Hydraulic Diameter” concept is insufficient to describe non-symmetric flows as in concentric annuli. It appears the need to use the Z axis component of the skew driving force for the laminar flow and the parameter <span style="white-space:nowrap;">λ</span> for the turbulent one. At the same time, instead, it has been shown that in the case of flow in square and rectangular ducts, the “Hydraulic Diameter” is sufficient to describe it. In this case, the flow is practically symmetric. Moreover, several new straightforward equations are provided, which simplify a lot dealing with non-cylindrical cross-sectional conduits. In doing so, the concept of “Eigenvectors-Eigenvalues” has been implemented. This theoretical approach could help to simplify other non-symmetric cases in fluid dynamics. To mention, “Flow past immersed non-symmetric bodies”, “Flow in curved conduits” etc.
