© 1954 by Oxford University Press
THE SKIN FRICTION ON INFINITE CYLINDERS MOVING PARALLEL TO THEIR LENGTH
( Trinity College Cambridge )
The frictional force on a cylinder moving steadily parallel to its length through a viscous liquid which is initially at rest is determined with reasonable accuracy over the whole range of values of the duration of the motion and for a wide variety of shapes of the cylinder cross-section. When the time t is small, the first approximation gives a force per unit area which is the same as that for a flat plate of infinite width. The second approximation takes the shape of the cylinder into account and the force on unit length of cylinder is determined in terms of the number of corners, and their angles, in the cylinder cross-section; if there are no corners, the force on unit length of the cylinder is the same, to this approximation, as that on a circular cylinder of the same perimeter. For large values of t the determination of the frictional force is reducible to that of a potential problem, the solution of which is known for a number of different shapes. The approximations for small and large values of t for any one cylinder do not overlap but can be joined without much ambiguity. For no value of t do the forces on cylinders of different shape (excluding those whose curvature is not everywhere inwards) differ by more than about 25 per cent.