Entry Flow In A Duct

• 
  Growth of boundary layer has a remarkable influence on flow through a constant area duct or pipe.
  Consider a flow entering a pipe with uniform velocity.
  1. The boundary layer starts growing on the wall at the entrance of the pipe.
  2. Gradually it becomes thicker in the downstream.
  3. The flow becomes fully developed when the boundary layers from the wall meet at the axis of the pipe. 
• The velocity profile is nearly rectangular at the entrance and it gradually changes to a parabolic profile at the fully developed region. 
• Before the boundary layers from the periphery meet at the axis, there prevails a core region which is uninfluenced by viscosity. 
• Since the volume-flow must be same for every section and the boundary-layer thickness increases in the flow direction, the inviscid core accelerates, and there is a corresponding fall in pressure. 
• Entrance length : It can be shown that for laminar incompressible flows, the velocity profile approaches the parabolic profile through a distance L_e from the entry of the pipe. This is known as entrance length and  is given by

For a Reynolds number of 2000, this distance,  the entrance length is about 100 pipe-diameters. For turbulent flows, the entrance region is shorter, since the turbulent boundary layer grows faster.

• At the entrance region,

1. The velocity gradient is steeper at the wall, causing a higher value of shear stress as compared to a developed flow.
2. Momentum flux across any section  is higher than that typically at the inlet due to the change in shape of the velocity profile. 
3. Arising out of these, an additional pressure drop is brought about at the entrance region as compared to the pressure drop in the fully developed region.

Fig. 31.1 Development of boundary layer in the entrance region of a duct