On the Force and Moment acting on an Infinite Cylinder moving in a Flow of an Incompressible Perfect Fluid with Uniform Vorticity

Abstract

In the present paper, theoretical study is made on the force and moment of the fluid pressure acting on an elliptic cylinder which moves in a flow of a perfect incompressible fluid having uniform vorticity. Making use of the pressure integral which is valid for flows having uniform vorticity, general expressions for the force and moment acting on the elliptic cylinder in a flow, of which the stream function when undisturbed is an integral expression of the second degree with respect to the coordinates X and Y, are obtained. Applying these formulae to a flow of uniform shear which has been investigated by Ray, it is found that his expression for the moment is erroneous. Furthermore, writing the equations of motion for the cylinder moving freely in a flow of uniform vorticity, some special solutions of these equations are obtained. Lastly, applications to the aerodymical problems are made and the lift and moment on a plane aerofoil placed in a uniform shearing flow or in a flow of uniform rotation are calculated by determining the value of the strength of the additional circulation so as to make the fluid velocity at the trailing edge finite applying Joukowski's assumption in the aerofoil theory