Equivalent diameter for non-circular pipes

For pipes of non-circular cross section, the inside diameter d, in equations 2.13 and 2.22 can be replaced by an equivalent diameter de defined as four times the cross-sectional flow area 5 divided by the appropriate flow perimeter. 

Consider a pipe of circular cross section with an inside and an outside diameter of d, and d0 respectively. Let this pipe be placed symmetrically inside a larger pipe having an inside diameter of D, and let a fluid flow through the annulus. Since the shear stress resisting the flow of fluid acts on both walls of the annulus, the appropriate flow perimeter required to calculate the equivalent diameter of the annulus de is (TrD,+nd0). Therefore 

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