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 -% A. Derive a differential equation model for the system behavior in terms of the liquid heights hi and h₂. B. Put the differential equations into second-order matrix form.

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 -% A. Derive a differential equation model for the system behavior in terms of the liquid heights hi and h₂. B. Put the differential equations into second-order matrix form.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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pump is open to 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 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 Ap Your Tasks: R₁ Pa ÍRN A₁ R₂ Ple 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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