Boundary Flow Along a Circular Cylinder

The Karman-Prandtl mixing-length theory for fluid flow over a flat surface with a laminar sublayer near the boundary is adapted to the flow along an infinite circular cylinder on the supposition that, in the nature of the radial inward convection of momentum towards the boundary, there is no accumulation of the momentum within any arbitrary finite volume of fluid. Experimental results for smooth and rough pipe flows are invoked in order to develop the nature of the boundary flow over a range of conditions from the quasi-smooth to the fully turbulent regimes. The drag coefficient for tangential friction is evaluated as a function of Reynolds number and surface roughness and is shown to lie within the limits 0.002 and 0.02, depending on roughness, for diameter Reynolds numbers greater than 103. Theoretical indications compare favorably with results from towing tests of stranded cables.