Practical and Precise Formula for Wave Forces on Single Cylindrical Tank by Run-Up Tsunami

The method proposed in this paper for the calculation of the run-up tsunami forces and overturning moments acting on a cylindrical storage tank estimates the pressure distribution acting on the tank surface from the tsunami velocity and inundation depth and integrates them to obtain the time variation of the forces and overturning moments. To reflect the effect of non-hydrostatic pressure, the proposed method focuses on the pressure head distribution around the tank bottom \(h_{p} \left( \theta \right)\) . The pressure distribution at the side of the tank could be expressed as a linear function of \(h_{p} \left( \theta \right)\) and the water level distribution \(h_{l} \left( \theta \right)\) , but for the pressure distribution at the tank bottom, Archimedes’ principle is not applicable due to non-hydrostatic pressure. In this paper, the Laplace equation was used to estimate the pressure distribution at the bottom of the tank, which is obtained by introducing a small velocity assumption into the Poisson equation of pressure. The advantage of using the Laplace equation is that it can represent changes in vertical forces corresponding to the boundary condition around the tank. As an example, it is shown that the vertical force and overturning moment are significantly reduced by installing the impermeable wall in front of the tank.