POTENTIAL FLOW AROUND A THIN OBLATE BODY OF REVOLUTION

Steady potential flow around a thin oblate body of revolution is studied. The part of the potential due to the presence of the body is represented as a superposition of potentials due to sources and dipoles distributed over a disk lying entirely inside the body. The boundary condition leads to a linear integral equation for the singularity densities. This equation can be solved asymptotically as the thinness ratio of the body approaches zero. This leads to a uniform representation of the potential, which is valid close to and even on the surface of the body, as well as far from it. Formulas are presented for the virtual mass of the body, the surface speed of the fluid and the pressure coefficient on the body.