Use a static analysis to calculate the pressure distribution for low operating frequencies, where the compression of the fluid (and thus the stiffening effect) is negligible. The resulting pressure distribution can then be used to extract a damping coefficient that reflects the damping effect of the fluid.
F is the total pressure force at the fluid structure interface and vz is the normal velocity component of the moving structure. A typical pressure distribution on a rectangular plate is shown in Figure 3.3: Pressure Distribution on a Plate at a Low Driving Frequency.