Fluid force on a plate moving up-and-down with a finite amplitude in the still fluid

To investigate the fluid force acting on a body oscillating with a finite amplitude in a fluid extending to the infinite space, the authors present a brief theory based on the virtual mass of the fluid taking account of the phase difference between the motion of the body and that of the virtual mass. The experiments mainly made on oscillating discs have shown fair agreement with the theory, and given the following findings: (1) The variation of the fluid force occurs in sinusoidal form just as predicted by the theory. (2) The magnitude of the force is proportional to S to the 1.8 times D-cubed times omega-squared, where S is stroke, D diameter, and omega circular frequency. (3) The phase difference is almost stationary in the range between 30 and 40 degrees, being insensitive to S, D and omega. (4) The virtual mass increases with S/D, amounting to 3.7 times the value for the inviscid fluid when S/D is unity.