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A problem on the two dimensional slow viscous fluid motion obeying the Stokes equations is solved in terms of the Earnshaw stream function, when a line source and equal line sink are arbitrarily situated in a viscous fluid bed between two fixed co-axial circular cylinders. Fluid mechanical properties of interest, such as drags and torques acting upon the cylinders are calculated. Also we have shown the variation of the forces per unit length on the inner cylinder with its radius keeping outer cylinder fixed, whose radius is assumed to be one. 1