BL growth in closed conduit

Concept of boundary layer

The boundary layer is the thin layer next to a solid surface in which the fluid velocity changes from zero (at the wall, no-slip) to nearly the free-stream value. Viscous effects are confined to this layer; outside it the flow is inviscid.

Growth in a closed conduit (pipe flow)

 inlet            entrance length Le          fully developed
  ---------------------------------------------------------
   U0 ->  boundary layers grow     core meets   parabolic /
   uniform    from wall inward ->  at centre    turbulent profile
  ---------------------------------------------------------

1. At the pipe entrance the velocity is nearly uniform, $U_0$. A boundary layer begins to grow from the wall at the entrance.
2. The layer thickens along the pipe, slowing the fluid near the wall. By continuity the core fluid, outside the layer, accelerates, and the pressure drops faster than in fully developed flow.
3. At a distance called the entrance (inlet) length $L_e$, the layers from the opposite walls meet at the centre. After this the velocity profile no longer changes with $x$, and the flow is fully developed.
4. Entrance length: laminar flow $L_e \approx 0.05\,Re\,D$; turbulent flow $L_e \approx 4.4\,Re^{1/6}D$ (about 25 to 40 diameters).

Three examples of use of the boundary layer concept

1. Calculation of skin friction drag on ships, aircraft wings and plates.
2. Explaining separation and stall on aerofoils, and the design of streamlined bodies to reduce form drag.
3. Design of wind tunnels, diffusers and ducts (allowing for displacement thickness), and prediction of the heat transfer from surfaces.