Hydrodynamic Entry Length of Flow Through Circular Annulus

If the gap between the cylinders is small compared to the radii of the cylinders, then you can treat it as flow between parallel plates. Do you have an estimate of the hydrodynamic entry length for flow between parallel plates? If the inner radius is much smaller than the outer radius, then you are essentially dealing with flow in a circular tube. Do you have an estimate of the hydrodynamic entry length for flow in a circular tube?

Chet

 

The entry length for a circular tube is going to be longer than for an annulus if the Re is defined in terms of the outer diameter for both. So, to be conservative, why not just use the value K=20.

In the entrance region, irrespective of whether it's an annulus or just a tube, the boundary layer growth is initially going to be that for the Blasius solution. This is because the inlet velocity profile is flat, and the boundary layer thickness is negligible compared to the radius of curvature. So it's the same as for flow over a flat plate. So I would determine a nominal boundary layer thickness from the Blasius solution, and divide that by the tube radius (or half the gap between the cylinders in the case of an annulus). When that number is about equal to unity, this would give a reasonable approximation to the entry length. I guess this is how they came up with the values of the entry length for a tube or for parallel plates. Try this, and see what you get.

Chet