The added mass of a deformable cylinder moving in a liquid

Let an infinitely long cylinder move perpendicular to its length in an infinite mass of liquid which is at rest at infinity. If the cylinder is rigid, the whole effect of the presence of the liquid may be represented by adding to the inertia per unit length of the solid cylinder the mass per unit length of the displaced fluid. If, however, the cylinder is elastically deformable, the mass of the moving fluid depends on the change in shape of the, initially circular, cross-sections of the cylinder. Thus the added mass is no longer a constant, but a function of the pressure exerted by the fluid on the solid cylinder.