The objective of this work is to propose a new approach to the calculation of the linear dimension of a rectangular channel at critical flow, whose internal walls are characterized by the relative roughness . The calculation takes into account the effect of kinematic viscosity of flowing liquid, through the Reynolds number R. This approach is based on one hand on the universally accepted relations of Darcy-Weisbach (1854) and Colebrook-White (1939). ), and on the application of the critical flow relation on the other hand. Explicit relationships are inferred and the results can be considered as accurate. They apply in the whole range of the relative roughness and for any value of Reynolds number Re> 2300. The theoretical development shows that the equation governing the linear dimension of the channel in critical flow regime is of third order whose resolution is made possible by trigonometric functions.


channel flow, relative-roughness, viscosity, regime, critical flow, rectangular, design.

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