Entrance effects for flow in tubes

The previous diseussion on flow in pipes has been restricted to fully-developed flow where the velocity at any position in the cross-section is independent of distance along the pipe. In the entrance and exit sections of the pipe this will no longer be true. Since exit effects are much less significant than entrance effects, only the latter are dealt with in detail here. 

Applying the mechanical energy balance between points T and 3 , noting zi = Z3 and Vi V3, and substituting for pEF from equations (3.97) and (3.98)  

Noting (l/2)pV3 = w// and that / = 16/Rcms in laminar region, it is customary to re-arrange equation (3.100) as  

There is little information on either the entrance length or the additional pressiue drop for fully developed turbulent flow. Dodge and Metzner [1959] indicated that both the entrance length and the extra pressure loss for inelastic fluids were similar to those for Newtonian fluids. 

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