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Differential equations - 2 Water tanks

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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.

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The expert examines differential equations of two water tanks.

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