4. Consider the two interacting tanks in the figure below. F h F2 A hp F3...

 

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4. Consider the two interacting tanks in the figure below. F h F2 A hp F3 A2 The F's denote volumetric flowrates (m/min). The variables h and h denote the liquid heights in tanks 1 and 2, respectively; the variable hp denotes the relative height of tank 1 to tank 2. If F = kh - - h+hp (a) Determine the differential equation relating F and F3 to h and h (b) Linearize the system around the steady state: F = = 2 m/min, h and h = 3 m. Parameters: A: = = 5 m, 10 m (cross-sectional area of tank 1), A = 5 m (cross-sectional area of tank 2), hp = 2 m, and k = 1 m.5/min. 4. Consider the two interacting tanks in the figure below. F h F2 A hp F3 A2 The F's denote volumetric flowrates (m/min). The variables h and h denote the liquid heights in tanks 1 and 2, respectively; the variable hp denotes the relative height of tank 1 to tank 2. If F = kh - - h+hp (a) Determine the differential equation relating F and F3 to h and h (b) Linearize the system around the steady state: F = = 2 m/min, h and h = 3 m. Parameters: A: = = 5 m, 10 m (cross-sectional area of tank 1), A = 5 m (cross-sectional area of tank 2), hp = 2 m, and k = 1 m.5/min.