Mathematical relations are obtained for velocities and pressure distribution for a fluid entering the peripheral clearance of a pair of rotating concentric disks that converges and discharges through an opening at the center. Both, the flows in the gap of corotating disks and in the gap of contrarotating disks can be predicted using the present analytical solutions. The prediction of instability of radial velocity for corotating disks at the speed ratio of unity is very important for practical applications. The radial velocity profile is similar to a parabolic profile exactly at speed ratio of unity. The profile drastically changes with the small difference of $\xb11%$ in the disks’ rotation. The radial convection was observed in the tangential velocity at a low radius. Centrifugal force caused by disk rotation highly influences the flow resulting in backflow on the disks. The pressure consists of friction losses and convective inertia. Therefore, the pressure decrease is high for increased speed ratio, throughflow Reynolds number, and rotational Reynolds number. The pressure decrease for the flow between contrarotating disks is lesser than that for the flow between corotating disks due to decreased viscous losses in the tangential direction. This study provides valuable guidance for the design of devices where disks are rotated independently by highlighting the instabilities in the radial velocity at the speed ratio of unity.