© 1953 by Oxford University Press
THE STEADY FLOW OF A VISCOUS FLUID PAST AN ELLIPTIC CYLINDER AND A FLAT PLATE AT SMALL REYNOLDS NUMBERS
( University of Kyoto Japan )
In PARTI the exact solution of Oseen's equations of motion for the steady flow of an incompressible viscous fluid past an elliptic cylinder is obtained, in terms of elliptic coordinates. The solution gives as a limiting case the flow past a flat plate.
The drag experienced by the elliptic cylinder is discussed in PARTII, with special reference to both the pressure drag and the frictional drag. It is thus found that, as long as the calculations are based upon Oseen's equations, the total drag can be analysed into pressure and frictional drags proportional to the axes of the cylinder respectively for any value of the Reynolds number. Further, expansion formulae correct to the fourth power of the Reynolds number are derived for the drag on the elliptic cylinder and on a flat plate, and numerical values of the drag coefficient are computed from these formulae.
PARTIII deals with the general expression for the stream function representing the flow past the elliptic cylinder. An approximate formula for the stream function for the flow in the neighbourhood of the flat plate is then obtained. The velocity profiles as well as the stream-lines for a flat plate edgewise to the stream are drawn, while for a flat plate at right angles to the stream, the stream-lines show that there exists a pair of standing eddies behind the plate.
Lastly, the pressure distribution on the surface of the elliptic cylinder is calculated in PARTIV.