A theory is developed for an incompressible fluid in a steady three-dimensional rotational flow. Solutions are obtained subject to the restriction of small perturbations and are determinant provided that the vorticity distribution along the axis of rotation is known. Effects of viscosity are included. Closed-form expressions for the zeroth-order circulation and stream function and first-order circulation are given, with other higher-order expressions requiring high-speed computers. Experimental results of radial variation of axial velocity in the core show a distribution more elaborate than Gaussian.