The flow equations of the Rankine half body are solved using the principle of superposition, combining the solutions of the linear flow of the stream and the circular flow of the source.
Given the linear flow field  and the source , we have
The stagnation point for this flow can be determined by equating the velocity to zero in either directions. Because of symmetry of flow in y-direction, stagnation point must lie on x-axis.
Equating both  and  to zero, we obtain .
At  and  we have stagnation points.
Now, we note that , so following this constant streamline gives the outline of the body:
Then,  describes the half body outline.