An Expansion Formula for the Drag on a Circular Cylinder Moving Through a Viscous Fluid at Small Reynolds Numbers

In the present paper an expansion formula is derived for the drag experienced by a circular cylinder moving through a viscous fluid at small Reynolds numbers, by starting from the general expression for the drag on the cylinder obtained by us previously. Our expansion formula is expressed in a power series of the Reynolds number of the undisturbed flow and includes Lamb's well-known formula as its first approximation. The range of values of the Reynolds number for which our expansion formula is applicable is estimated. We find that our expansion formula correct to the fourth power of the Reynolds number can be used with sufficient accuracy, provided that the Reynolds number is numerically less than 4.