ON THE FORCE AND MOMENT ON A BODY IN AN INCOMPRESSIBLE FLUID, WITH APPLICATION TO RIGID BODIES AND BUBBLES AT HIGH AND LOW REYNOLDS-NUMBERS

An analysis is made of the force and moment exerted on a rigid body in unsteady motion in a uniform incompressible, viscous or inviscid fluid. Integral formulae are derived which express the force and moment in terms of the velocity and vorticity of the fluid and the velocity of the body. The results extend a previous investigation of this problem (1), and permit the identification of the separate influences of added mass, normal stresses induced by free vorticity, and viscous skin friction. Illustrative applications are made to airfoil theory, to the calculation of the induced drag of a vortex street and the force on a cylinder moving in a slowly varying rotational mean flow, and to the determination of the viscous drag experienced by solid spheres and bubbles. The theory gives a direct prediction of the drag on a bubble in high-Reynolds-number motion, in contrast to the usual approach in which the drag is determined by equating the viscous dissipation to the work done by the drag force.