Date of Award
Doctor of Philosophy (PhD)
This work is an experimental study of the Stokes drag on a right circular cylinder moving with constant velocity through a Newtonian viscous fluid. The cylinder velocity is parallel to its longitudinal axis, and the fluid is bounded on the outside by a fixed coaxial cylindrical tube of circular cross section. The length to diameter ratio of the moving cylinder ranges from 1.0 to 390, the ratio of the width of the annular gap to the cylinder length ranges from 0.0077 to 0.86, and the ratio $\alpha$ of the cylinder diameter to the tube diameter ranges from 0.022 to 0.91. Experimental values of the drag are compared with a theoretical expression which assumes a flow that is entirely axial in the annular region and a drag that is due entirely to the viscous stress on the cylinder side plus the effect of the dynamic pressure difference on the ends of the cylinder. An end correction term is obtained which is found to be proportional to the annular gap width and to the square root of $\alpha$. This term is found to be consistent with previous numerical studies of the narrow gap case and with experimental studies of the wide gap case. Drag values are also presented for the situation in which the bottom of the tube is open to a larger fluid reservoir. A second problem is considered in which a thin circular disk moves broadside through a viscous fluid toward a plane wall that is parallel to the disk. An expression for the Stokes drag is obtained which agrees with the experiment and reduces to known theoretical results at extremes of large and small distances from the disk to the plane.
Wehbeh, Elias George, "Boundary Effects on the Drag of a Cylinder in Axial Motion at Low Reynolds Number." (1987). LSU Historical Dissertations and Theses. 4430.