This problem was addressed by George Keith Batchelor(1951). Let formula_35 be the angular velocity at infinity. Now the pressure at formula_36 is formula_37. Hence formula_38 and formula_39. Then the boundary conditions for the fluid formula_17 are  Self-similar solution is obtained by introducing following transformation,  The self-similar equations are  with boundary conditions for the fluid formula_22 is  The solution is easy to obtain only for formula_48 i.e., the fluid at infinity rotates in the same sense as the plate. For formula_49, the solution is more complex, in the sense that many-solution branches occur. Evans(1969) obtained solution for the range formula_50. Zandbergen and Dijkstra showed that the solution exhibits a square root singularity as formula_51 and found a second-solution branch merging with the solution found for formula_52. The solution of the second branch is continued till formula_53, at which point, a third-solution branch is found to emerge. They also discovered an infinity of solution branches around the point formula_54. Bodoyni(1975) calculated solutions for large negative formula_55, showed that the solution breaks down at formula_56. If the rotating plate is allowed to have uniform suction velocity at the plate, then meaningful solution can be obtained for formula_57. For formula_58 (formula_59 represents solid body rotation, the whole fluid rotates at the same speed) the solution reaches the solid body rotation at infinity in an oscillating manner from the plate. The axial velocity is negative formula_60 for formula_61 and positive formula_62 for formula_63. There is an explicit solution when formula_64. Since both boundary conditions for formula_66 are almost equal to one, one would expect the solution for formula_66 to slightly deviate from unity. The corresponding scales for formula_68 and formula_69 can be derived from the self-similar equations. Therefore,  To the first order approximation(neglecting formula_71), the self-similar equation  becomes  with exact solutions  These solution are similar to an Ekman layer solution. The flow accepts a non-axisymmetric solution with axisymmetric boundary conditions discovered by Hewitt, Duck and Foster. Defining  formula_74  and the governing equations are  with boundary conditions  The solution is found to exist from numerical integration for formula_77.