This paper presents an analytical solution for the turbulent boundary-layer flow in the entrance region of a pipe. The equations yield the relative momentum thickness at any station within ten diameters of the entrance, and from this the pressure drop and head loss are calculated. The ratio of these quantities to the corresponding values for fully developed pipe flow are found to be practically independent of Reynolds number. Comparison of the theoretical expressions with the few data that are available shows good agreement, confirming the formulas for design applications.

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