The figure below shows a liquid-level system in which two tanks have cross-sectional areas, A₁ and A₂, respec- tively. A pump is connected to tank 1 through a valve of linear resistance R₁. The inlet to the pump is open to atmosphere, and the pressure of the fluid increases by Ap when crossing the pump. The liquid flows from tank 1 to tank 2 through a valve of linear resistance R₂ and leaves tank 2 through a valve of linear resistance R3, exiting at at- mospheric pressure. Assume the density p of the liquid is constant and note that both tanks are open to atmosphere as shown. Pa Your Tasks: Ap Pa A₁ R₂ Pa A₂ R3 → 9 A. Derive a differential equation model for the system behavior in terms of the liquid heights h₁ and h₂. B. Put the differential equations into second-order matrix form.

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Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. There are various mechanisms by which, transfer of heat takes place i.e. thermal conduction, convection, radiation or by change of phase. All these mechanisms have their own specific features which sometimes occur simultaneously within the same system.