The axisymmetric inviscid equation is governed by the Hicks equation, that reduces when no swirl is present (i.e., zero circulation) to
where  is the stream function,  is the radial distance from the axis, and  is the axial distance measured from the closed end of the cylinder. The function  is found to predict the correct solution. The solution satisfying the required boundary conditions is given by
where  is the radius of the cylinder and  is the injection velocity at the wall. Despite the simple-looking formula, the solution has been experimentally verified to be accurate. The solution is wrong for distances of order  since boundary layer separation at  is inevitable; that is, the Taylor–Culick profile is correct for .  The Taylor–Culick profile with injection at the closed end of the cylinder can also be solved analytically.
Although the solution is derived for the inviscid equation, it satisfies the non-slip condition at the wall since, as Taylor argued, any boundary layer at the sidewall will be blown off by flow injection. Hence, the flow is referred to as quasi-viscous.