where ϝ1XL and ϝ1XT are the forces on the plate due to the jump at the leading and trailing edges of the plate, respectively, given by Eq. (32b), and nL and nT are the unit normal vectors on the plate leading and trailing edges, respectively, and are pointing out of the fluid. We note here that since the plate is thin, the two-dimensional horizontal force is the force per unit length (into the page) and per unit thickness, and thus has the same dimension as pressure.
In two-dimensions, the vertical wave induced force on the plate is calculated by integrating the pressure differential on the top and bottom surfaces of the plate