Formulation of the Problem of The unsteady problem of the flexible wedge two-dimensionally (2D)

The unsteady problem of the flexible wedge two-dimensionally (2D) that enters an incompressible liquid, as well as idea, is considered. The horizontal free surface of the liquid is touched at the single point initially (t` = 1) by wedges as well as stared for the penetration of the liquid afterward at the fixed velocity V. The initial point of joining is taken as the system of Cartesian coordinate x` O y.` The line y` = 0 shows at t` = 0 the liquid free surface. With respect to the vertical line x` = 0, the wedge impact is symmetric that causes flow. Either flexible supported or simple, Euler beams models the sidewalls of wedges. The right wall is only considered below because of the flow summary. So, it denotes the normal glance of the beam such as w` (s,` t`), where the coordinate along with starting unreformed side wall is s` = 0, that corresponds for the tip of the wedge as well as s` = L to the last point of the beam. In simple words, the wedge caused the deflection of the beam that interacts with the liquid.

            We will have to recognize the flow of the liquid, the deflection of the walls of the wedge, the wetted parts dimensions of entering wedge, the distribution of the stress within the planting of wedge as well as the distribution of the pressure in the region of the liquid.

            The non-dimensional variable for this case is used below. The length of the beam, such as scale of the length is taken as well as the impact of the velocity V such as the scale of the velocity of the problem. During the penetration, the free surface stays undeformed if the wedge will be rigid. In this case, the wedge will be wet fully at the instant time T = (L/V) sin ( Γ) along with the displacement vertically of the wedge that will be equal to L sign ( Γ). The quantity of time scale is taken by T as well as the product of L sign ( Γ) as dislocation scale of the problem. In this research we are dealing with the coupled elastic wedge problem that interacts with the liquid to tiny angle of dead rose of the wedge as well as using the water model impact by Wagner (1932). The elastic wedge generates the potential flow as well as the two dimensional that is demonstrated by the potential velocity satisfying the equation.