The drag coefficient of a sphere in unconfined flow is given in most fluid mechanics texts, for example, Massey (1979).

The drag coefficient, CD, is determined by measuring the force exerted on the sphere by the fluid when the relative velocity between the sphere And the oncoming fluid is known. Fluid flow over a sphere located inside a tapered tube has been studied because of application to flowmeter design (Blevins, 1984). … The purpose of this note is to present the drag coefficient of a sphere in a square channel at low Reynolds number (Re < 1800). For smooth spheres, the drag coefficient depends on Re and the ratio d/W. This information is lacking in the literature.