U-tube, of uniform cross section $S$ and opened at both ends, is filled with a liquid column of length $L$ and density $\rho$. In equilibrium the water levels in both arms are at same height. What goes on if liquid in one arm is somehow raised, with a temporary subpressure for example, and then released?
I understand the system will try to return to and tend to oscillate about equilibrium. But I am at a loss as to what exactly drives that. Presently, I can derive the angular frequency of the oscillation as $\omega^2 = 2 g/L$ from the energy balance. But I would like to understand the Newtonian equation.
Pressure at both liquid surfaces is the same so there is no external net force on the fluid as a whole, right? There should be hydrostatic difference in pressure between points A and B equal to $\Delta p = \rho g (2 x)$ which I guess drives the liquid. What's the pressure at C? How does pressure changes from A to B to C?
(Here's link to a similar post, but which doesn't resolve my confusion.)