Influence of fluid's viscosity

The natural frequency is the same for the four viscosities so the viscosity does not have any influence on the natural frequency.

The theoretical expression gives a natural frequency equal to 0,27 Hz but with Fluent results (plot) we obtain a natural frequency equal to 0,35 Hz. The expression is not right.

The expression of the natural frequency is modified supposing that it depends on all the dimensions of the problem. The expression becomes : $ \displaystyle f_0 = \frac{k}{2 \pi} \sqrt{\frac{g}{L*}} $ with L*=L*(L,h) a characteristic length and k a constant. We will find this characteristic length studying the influence of the initial level (h) and of the tank's length (L) on the natural frequency (f0).