Drag Coefficient of a Circular Tube

In the region of stabilized turbulent flow in a smooth circular tube, the drag coefficient can be estimated from the Prandtl-Nikuradze implicit formula [318] 

These formulas are also accurate within 2% [276, 427]. The first line in Eq. (1.6.13) follows from the assumption that the average velocity profile is given by the power law (1.6.9) with n = 7. 

In the transient zone, it is recommended to calculate the drag coefficient by the formula [254] 

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