Assignment:
Two identical water tanks labeled A and B are resting at the same elevation and are linked via a pipe with a valve. The cross sectional area of each of the tanks is 1m^2. The valve demonstrates linear behavior (volumetric flow is linear with pressure drop) and will allow a flow of 0.5 m^3/min under a pressure drop equivalent to 1 meter of H20. Both tanks are initially half full with water. At time t=0, 1 m^3 of water is instantaneously dumped into tank A. Develop an expression for the level of tank B as a function of time assuming that the valve is the only flow restriction in the system.
Provide complete and step by step solution for the question and show calculations and use formulas.