An Experimental Determination of Hydrodynamic Masses and Mechanical Impedances

Abstract

The study of the forces acting on a body due to the body’s motion through a fluid is facilitated by the introduction of a “hydrodynamic” mass i.e. The mass of fluid that appears to be carried by the body as the body accelerates in the fluid. If the body’s motion is periodic, the relation between the hydrodynamic forces acting on the body and the body velocities is described by a mechanical or acoustical impedance. Hydrodynamic masses have been computed from ideal fluid theory for mathematically “easy” shapes-spheres, circular discs, etc. There are three methods available for the computation of hydrodynamic mass; the impedance approach, the kinetic energy method, and Darwin’s “drift” method. Each of these methods is presented in appendices. Mechanical impedances have been computed for a very limited number of shapes. The mechanical impedance is computed directly by integration of pressures over the body (the impedance approach). An alternate method of impedance computation in the computation of hydrodynamic mass from one of the above methods. The computation of damping constants follow from viscous flow theory. Because of the difficulty encountered when the computation of hydrodynamic mass or mechanical impedance is attempted for an irregular body, it becomes necessary to determine hydrodynamic masses and mechanical impedances experimentally for bodies of irregular shape. This thesis presents the results of an extensive experimental investigation into hydrodynamic masses and mechanical impedances for many bodies of complex shape. Three techniques were employed for these measurements. The relative merits of each are discussed. A table is presented that compiles hydrodynamic mass factors from the literature show mechanical impedances for different bodies. Mechanical impedances are not available in the literature.