Consider a system as illustrated below:
There are two 55 gallon barrels used to store water coming down the gutter. These barrels are connected together on the bottom to maintain equal water level between them. They are fed by a 4" vertical pipe connected to a 2" horizontal pipe.
When the 4" vertical pipe on one end fills with water, the water will run into the horizontal pipe and begin to fill the barrels. Will the barrels maintain the same level as in the 4" dia. vertical pipe, assuming input flow rate isn't too much to overwhelm the 2" horizontal pipe? In other words: is $h_1 = h_2$ in the diagram? I think it should be so, so if it is true what physical principle is at work to keep the levels equal when the diameter of the barrel is different than the diameter of the pipe?