Entry Length

There is an entrance region where a nearly inviscid upstream flow converges and enters the tube. Viscous boundary layers grow downstream, retarding the axial flow v(x, r) at the wall and thereby accelerating the center-core flow to maintaintain the incompressible continuity requirement

Q = \(\grave{o}\)v dA = constant

At a finite distance from the entrance, the boundary layers merge and the inviscid core disappears. The flow is then entirely viscous, and the axial velocity adjusts slightly further until at x = L_e it no longer changes with x and is said to be fully developed, v = v(r) only. Downstream of x = L_e the veocity profile is constant, the wall shear is constant, and the pressure drops linearly with x, for either laminar or turbulent flow.

\[L_e D = 0.06 Re_D\] for laminar

\[\frac{L_e}{D} = 4.4 Re_D^{\frac{1}{6}}\] Where L_e is the entry length; and
Re_D is the Reynolds number based on Diameter.