The viscous drag on cylinders falling symmetrically between parallel walls

Abstract

An analogue technique for the approximate solution of the biharmonic equation is used to determine the viscous drag at Reynolds number approaching zero for cylinders falling symmetrically in a liquid between parallel walls. Results obtained show good agreement with numerical solutions, with results by direct experiment and with the work of other authors. Streamlines are obtained with a maximum error of 2% and vorticities and viscous drag forces with a maximum error of approximately 10%. Symbols viscosity kinematic viscosity x and y components qf velocity velocity of cylinder stream function vorticity viscous drag force surface resistance resistance mesh element voltages corresponding to and $ ratio of cylinder diameter to wall separation.

An electrical analogue method for determining the viscous drag on cylinders falling symmetrically between parallel walls for Reynolds numbers in the range 0-30

“…These analogues consist of two plane meshes each composed of a rectangular array of equal resistors, linked at corresponding points by resistors of higher value. Curtis and Sherry (1970) and Curtis and Marr (1978) gave details of a similar method using two sheets of conducting paper linked at corresponding points by resistors of resistance higher than the resistance per square of the paper. Palmer and Redshaw (1955) gave details of an analogue for the solution of twodimensional stress problems which give equations similar to (2) and (3) above.…”