Water Oscillation in Surge-Tanks in Exposure with Turbulent Resistance: An Analytical Investigation

We investigate the derivation of an analytical solution to the oscillation of water in the U-tubes representing the motion of fluid in the surge-tanks applications. We show that by proper mathematical transformations and tools of functional analysis, an analytical solution may be obtained in spite of the high nonlinearity of governing differential equations. This would make such ODE much more tractable, as a result of which new light may be shed on the physics involved.