Since there is no rotation at large ,  becomes independent of  resulting in . Hence  and .
Here the boundary conditions for the fluid  are
Self-similar solution is obtained by introducing following transformation,  
where  is the fluid density.
The self-similar equations are
with boundary conditions for the fluid  are
The coupled ordinary differential equations need to be solved numerically and an accurate solution is given by Cochran(1934). The inflow axial velocity at infinity obtained from the numerical integration is , so the total outflowing volume flux across a cylindrical surface of radius  is . The tangential stress on the disk is . Neglecting edge effects, the torque exerted by the fluid on the disk with large () but finite radius  is
The factor  is added to account for both sides of the disk. From numerical solution, torque is given by . The torque predicted by the theory is in excellent agreement with the experiment on large disks  up to the Reynolds number of about , the flow becomes turbulent at high Reynolds number.