End effects for the falling cylinder viscometer

Experimental results are presented for the Stokes velocity of a circular cylinder of radius a and length L moving axially through a viscous fluid contained within a coaxial closed cylindrical tube of radius b and length H. The results cover the intermediate range 0.21 ≤a/b≤0.70 and are found to be consistent with theoretical results for the narrow gap case (a≂b) and with previous experimental results for the wide gap case (a≪b). The fractional difference between the observed drag and the theoretical drag is represented well by 1.67x−0.017, where x=(b−a)(a/b)1/2/L. The negative term is interpreted as representing an effective cylinder length of 0.983L, and the 1.67x term is interpreted qualitatively as a measure of the degree to which the fluid is displaced radially by the falling cylinder. The limitations of our expression for end effects are explored experimentally. Additional experimental results are presented for two cases in which the ends of the cylindrical tube are not closed.