An analytic approximation of the drag coefficient for the viscous flow past a sphere

We give an analytic solution at the 10th order of approximation for the ste ady-state laminar viscous flows past a sphere in a uniform stream governed by the exact, fully non-linear Navier-Stokes equations. A new kind of analy tic technique, namely the homotopy analysis method, is applied, by means of which Whitehead's paradox can be easily avoided and reasonably explained. Different from all previous perturbation approximations, our analytic appro ximations are valid in the whole field of flow, because we use the same app roximations to express the flows near and far from the sphere. Our drag coe fficient formula at the 10th order of approximation agrees better with expe rimental data in a region of Reynolds number R-d < 30, which is considerabl y larger than that (R-d < 5) of all previous theoretical ones. (C) 2001 Els evier Science Ltd. All rights reserved.