Two two-dimensional deposits (infinite in the direction perpendicular to the paper, see Figure of width L and height HO, both open to the atmosphere, are still connected through a two-dimensional channel of length 2L formed by two parallel flat plates separated by a distance h L. Initially, the height of the liquid (density and viscosity) in the tank on the left is HO, while in the one on the right is HO/2, so, after opening the channel, the liquid go from left to right through the inside the horizontal channel. It is requested: a) Assuming that the movement of the liquid through the channel is practically unidirectional, with dominant viscous forces compared to inertial forces, obtain a differential equation for H1(t). b) Characteristic time it takes for the liquid to move from one tank to another and reach a stationary state. c) Adimensionalize the equation from the first section and integrate it. Pa L Pa L H(t) H2(t) 2L Ho