Consider a parallel-plate channel with wall spacing 2H. If the logarithmic velocity profile given by Eq. (10.5-16) is assumed to apply throughout the channel and if Re is based on the hydraulic diameter, show that the expression for the friction factor is nearly identical to Eq. (10.5-26). This illustrates how the near-universality of the law of the wall underlies the success of the hydraulicdiameter approach for calculating f for turbulent flow in noncircular channels.

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v (y) = 2.5 Iny+ +5.5. (10.5-16)