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Question: problem 1 figure 1 shows a twotank hydraulic system the...

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Problem 1. Figure 1 shows a two-tank hydraulic system. The pump takes water from the sump (reservoir) at atmospheric pressure Pm and increases the pressure by the constant amount APpRH where H is the pressure head. Assume that the constant pressure head H is ater than the vertical-wall height of tank 1. Flow through all valves is laminar (a) Derive the complete mathematical model with tank pressures P1 and P2 as the dynamic variables and head H as the input variable (b) Introduce the gage pressure PP Ptm and P.2- P2 Patm as dynamic variables, and rewrite the mathematical models obtained in (a) in terms of Pi and 2respectively (c) Write the linear system of equations that model the complete fluid systems. (d) Write the linear system of equation in matrix form. PR205) H(s) (e) Derive the mathematical equation of the transfer function Tank 1 Tank 2 Base pressure, P Base pressure, P Pump Area, A Area, A 0 Valve, R Valve, R2 Valve, R Sump (reservoir) Fig.1. Two-tank hydraulic system
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