Question

Characteristic length for different geometries

Answer 1

For flow of fluid over a flat plate, the boundary layer grows along the length of the plate which is the characteristic dimension.  For flow in a tube, the boundary grows in the radial direction which is known as the developing length.  In the fully developed region, the boundary layer thickness is equal to the diameter of the tube.  Hence, the diameter of the tube is the characteristic dimension for flow of fluid in the tube.  In Fig.1, the direction in which the boundary layer grows in the fluid flow direction is the characteristic dimension.  The second figure is not clear.  The basic concept of characteristic dimension may be extended to the second figure also.