According to similarity theory, any geometrical parameter of the channel can be taken as an independent dimension. However, it is advisable to choose an independent dimension that takes into account the hydrodynamic characteristics of fluid flow. Therefore, as an independent dimension of channels with internal flow, use is made of an equivalent hydraulic diameter DH characterizing the relation between the cross-sectional are and the wetted perimeter P: Dh = 4S/P. DH is chosen such that the ratio of pressure forces, acting on the flow cross section, to friction forces, applied along the channel perimeter of arbitrary shape, corresponds to the ratio of the forces in an equivalent circular pipe with the diameter D = DH Applicability of hydraulic diameter as a universal, independent dimension for channels of various geometrical shapes is limited by the following restrictions.
The thickness of the boundary layer, in which the greater part of the variation of velocity with distance from the wall occurs, should be much less than the diameter of the channel or the radius of curvature of the perimeter.
The thickness of the boundary layer and the wall shear stress should vary only slightly around the channel perimeter.
Using DH makes it possible in some cases, within the restrictions indicated above, to calculate hydraulic characteristics of the flow in channels of various geometrical shapes by the formulas derived for a circular pipe. For free surface flows, the hydraulic radius rH = S/P is commonly used as an independent dimension; for large flow width, this equals the mean depth of the fluid.